Heat Removal from a Human Eye for Different Environmental Conditions - A CFD Study Using a Full-Scale Manikin

Heat Removal from a Human Eye for Different Environmental Conditions - A CFD Study Using a Full-Scale Manikin | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Heat Removal from a Human Eye for Different Environmental Conditions - A CFD Study Using a Full-Scale Manikin Farnaz Feyli, Mahmood Yaghoubi, Goodarz Ahmadi, Omid Abouali This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3997744/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The eye is an important organ of the human body, and its physiology can change mainly due to the ambient air temperature and velocity. In this study, a three-dimensional computational model for airflow around a full-scale manikin and the flow inside the eye is developed and used to evaluate the heat removal from the manikin eyes due to natural and forced convection under different environmental conditions. For natural convection, it was assumed that the movement of surrounding air was only due to the buoyancy effect in the body's thermal plume. Uniform air velocity and temperature far from the manikin were assumed for combined natural and forced convection. For simulating the velocity and temperature distribution, equations of continuity, momentum, energy, and turbulence transport model were solved numerically. The results for specific conditions were compared with the available experimental data reported in the literature and acceptable agreement was found. The validated computation model was used for several simulations of wind velocities and air temperatures. It was found that the eye surface temperature distribution predicted by the present model is closer to the experimental data than the earlier numerical studies for detached eyeballs using a constant convective heat transfer coefficient. The present results showed that the convective heat transfer coefficient over an eye surface depends strongly on the airflow velocity and temperature near the head. eye heat transfer numerical modeling manikin natural convection force convection Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Introduction The eye is one of the most important organs of the human body. The changes in ambient temperature may affect the eye's physiology. Studying temperature distribution in the eye under different environmental conditions is important for understanding eye physiology and its interaction with the environment. Currently, an experimental facility for in vivo temperature measurement inside the eye is unavailable. However, some earlier experimental studies [ 1 ]–[ 4 ]measured the eye's surface temperature. Due to the limitations of in vivo measurement, researchers tried to evaluate the fluid flow and temperature distribution inside the eye by numerical simulation. Amara[ 5 ] investigated the effect of laser power and wavelength on the eye tissues by modeling a human eye exposed to laser irradiation. Heys and Barocas[ 6 ] studied the movement of pigment particles released near the iris tip to predict the formation of Krukenberg’s spindle. Ooi et al.[ 7 ] studied the effect of tumors on temperature distribution inside an eye. Karampatzakis and Samaras[ 8 ] studied the impact of an artificial intraocular lens on the eye temperature distribution. Li et al.[ 9 ] simulated the 2D and 3D models of an eye and investigated the effect of hyperthermia treatment on healthy eye tissues. Narasimhan and Jha[ 10 ] modeled Pan Retinal Photocoagulation (PRP), a retinal laser surgical process, and found eye temperature distribution under different conditions. Abouali et al.[ 11 ] used a computational modeling approach to study the unsteady flow in the vitreous cavity due to saccadic eye movement. They studied the flow dynamics of the vitreous after complete vitreous liquefaction and for post-vitrectomy eyes (Vitreous gel is substituted with silicon oil and balanced salt solution). Abouali et al.[ 12 ] also modeled the aqueous humor flow in the anterior chamber due to saccadic movements. They showed that mixing the aqueous humor due to the saccadic movements increased the heat transfer in the anterior chamber and through the cornea. Modareszadeh and Abouali[ 13 ] simulated the motion of vitreous humor for the real shape of a human vitreous chamber filled with the gel- with a viscoelastic model. Bhandari et al. [ 14 ] have developed a computational model to investigate topical drug delivery in the aging human eye. Their research explores the impact of aging on various eye parameters, including heat transfer, aqueous humor flow, intraocular pressure, and drug distribution across different eye regions and orientations. Bayat et al. [ 15 ]–[ 17 ] studied partial vitreous liquefaction (PVL) flow dynamics as a two-phase viscoelastic-Newtonian fluid in 2D and 3D human eye models. Rahman et al. [ 18 ] studied the anatomical and physiological changes in the human eye as it ages. They have developed a model to analyze the thermos-fluid dynamics of the aging human eye, incorporating four physiological changes into their simulations: metabolism, blood perfusion, tear evaporation, and aqueous humor flow. Tang et al. [ 19 ] conducted simulations of the aqueous humor (AH) flow within human eyes, featuring diverse morphological structures and physical characteristics. They acquired the velocity distribution and temperature distribution of the aqueous humor flow. All these earlier studies modeled the anterior chamber or the entire eyeball and the cornea as the boundary of the computational domain in contact with the ambient air. The heat transfer through the eyelid was not included in the earlier models. But when the eye is open, in addition to the cornea, a part of the sclera is also in contact with the ambient air. In some earlier studies, the temperature distribution obtained from the IR thermograph[ 6 ] is applied to the cornea as a boundary condition. In other research, the constant ambient convection heat transfer coefficient experimentally measured by Lagendijk[ 20 ] for a rabbit eye is used for the boundary condition at the cornea. Some researchers studied the effect of different parameters like ambient temperature and convection coefficient on the eye temperature distribution [ 21 ]–[ 25 ]) None of these earlier works investigated the corresponding environmental condition for the assumed convection coefficients. Natural and forced heat transfer coefficients for different body parts under various environmental conditions were studied before in the literature. Dear et al.[ 26 ] reported experimentally measured convection and radiation heat transfer coefficients under natural and forced convection conditions for different parts of a seated and a standing manikin. Their measurement for force convection is performed for air velocities in the range of 0.1-5 m/s. They also reported some correlations for radiation and convection heat transfer coefficients for different body parts for different airflow velocities. Serensen and Voigt[ 27 ] found a seated manikin's natural heat transfer coefficient experimentally and numerically. They also investigated radiation heat transfer in their numerical simulation. Craven and Settles[ 28 ] provide particle image velocimetry (PIV) measurement of the thermal plume velocity at the top of the human head created due to the temperature difference between the body and ambient air in a standard room with moderate thermal stratification. They compared their experimental data with their CFD model and reported that the room thermal stratification significantly affected the thermal plume. Ono et al.[ 29 ] used a combined experimental and numerical approach to study the heat transfer coefficient of a standing manikin for different air velocities. They validated their CFD code by their experimental data and presented a correlation for body heat transfer coefficient for different air velocities and turbulence intensities. Kurazumi et al.[ 30 ] experimentally investigated the effect of postures on the conduction, convection, and radiation heat transfer of a manikin in an environmental chamber. Zhang et al.[ 31 ] reviewed manikins' experimental and numerical heat transfer studies. They considered three geometrical models (the first model was constructed using several cubes, the second one was developed using a sphere and cylinders and the third geometry resembles a standing human body). Their numerical results for the third model are more compatible with experimental measurements. Jia et al.[ 32 ] studied the details of a thermal plume created around a seated and heated manikin due to temperature differences with the environment. They used an LBM computational model for a rectangular-shaped manikin in a small room. Salmanzadeh et al.[ 33 ] numerically and experimentally investigated the effect of a thermal plume around a seated manikin on the particle transport in a cubicle. Ruzic and Bikic[ 34 ] simulated thermal conditions in vehicle cabins and studied natural and forced convection heat transfer between the manikin and the environment. Lee et al.[ 35 ] experimentally measured a seated manikin's natural convection[ 33 ] heat transfer coefficient. They validated their numerical results with experimental data and used their simulation to find the force heat transfer coefficient for different air velocities. Hasama et al.[ 36 ] studied the attributes of air circulation produced by ceiling fans around a thermal manikin and the convective heat exchange resulting from the airflow distribution through both experimental methods and CFD while considering both standing and seated positions. In the present study, flow and heat transfer inside the eye of a three-dimensional manikin are simulated for both natural and mixed convection flows around the body. Particular attention was given to the variation of temperature inside the eye. In the present work, the manikin's surroundings were added to the computational model to study the heat transfer through the eye for different environmental conditions. Using this approach, the heat transfer coefficient over the cornea is obtained through the solution and it is not set with a rough approximation as a boundary condition. Model Description To create a geometrical model of a human body, a 3D CAD model of a standing male manikin is used, shown in Fig. 1 . The CAD model is converted to the STL file smoothed and scaled to 1.77 m height. To decrease numerical complexity, some simplifications are done on the model such as closing the lips and nostrils, removing eyelashes, ears, and nails, and smoothing the feet. The resulting simplified manikin model is shown in Fig. 2 , which resembles a normal man and is more realistic than models used in the previous simulations [ 27 ], [ 28 ], [ 32 ], [ 34 ], [ 37 ]). To model the eye with the dimensions presented by ([ 8 ], [ 38 ], [ 39 ]), a 3D computational model is created in GAMBIT 2.4.6 software by rotating a 2D model (shown in Fig. 3) around the optical axis. The axial diameter is 26 mm, and the vertical diameter is 23.65 mm, which leads to a total volume of 7.36 cm 3 for the eye. The developed eye model consists of a cornea, anterior chamber, posterior chamber, iris, lens, vitreous, and sclera. For simplification, the retina and choroid, which are very thin compared to the sclera, are not considered in the present model. Finally, the eye model is attached to the manikin using ANSYS 14.5 (ICEM,) as shown in Fig. 4 . The selected computational domain for the airflow is sufficiently large that the boundaries do not affect the thermal plume flow field around the manikin. Typically, the air far from the manikin is assumed to be stagnant for the natural convection case. Figure 5a shows the dimensions of the computational domain used for the airflow study. The domain independence study is performed by measuring heat transfer from the eye surface of the manikin. Table 1 shows the size of boxes used for various computational domains to study mixed convection. Table 1 also compares the heat flux and transfer coefficient for different domain sizes. It is seen that the simulation results for domains 2 and 3 are relatively close. Accordingly, the domain with a dimension of botwo 2 is selected for the rest of the analysis. Figure 5 illustrates the computational domain used for both the natural and mixed convection cases. Table 1 Comparison of size of the domain, heat transfer coefficient and average convective heat transfer rate for the total surface of the manikin for different computational domains tested for mixed convection. Case number of computational domains Number of grids Size of the computational domain L×W×H (m 3 ) Average heat transfer coefficient (Wm − 2 K − 1 ) Average convective surface heat flux (W/ m 2 ) 1 1843365 0.95×0.76×1.79 20.2 308.2 2 5847579 4.95×7.76×3.80 17.8 270.6 3 7617363 7.5×12×6 17.6 267.8 Computational Modelling The eyeballs and the space between the manikin and the surrounding cube (shown in Fig. 5) are considered a computational domain. To study the flow field, the following assumptions are made: The airflow is incompressible and steady and around the manikin is in turbulent regime. The experiment of Clark and Toy [ 40 ] showed that the flow is laminar around a standing nude human for height shorter than 0.9m with (T skin =306 K, T air =293 K, and Grashof number = 2×10 9 ) but the regime becomes fully turbulent for a manikin taller than 1.5 m (Grashof number = 10 10 ). The eyes are located on the head; therefore, assuming a turbulent flow around the manikin head is especially justified. It is assumed that the liquid flow in the eye anterior chamber is laminar because of the low velocity in the small anterior chamber. The physical properties of air are constant and determined at the film temperature. Boussinesq approximation is adopted for the density variation since the temperature difference is sufficiently small with βΔT < < 1 [ 41 ]. The body force in these flows is only due to gravity. Governing Equations a) Temperature distribution inside the solid part of the eyeball is obtained by solving the following heat conduction equation [ 8 ]: $$-\nabla . \left(k\nabla T\right)=A-B\left(T-{T}_{bl}\right)$$ 1 where T is temperature, k is thermal conductivity, T bl is blood temperature, A is the metabolic heat generation rate and B is the term associated with the blood perfusion rate. Only aqueous humor (AH) in the anterior chamber is considered liquid). Governing equations of conservation of mass, momentum, and energy for laminar flow of aqueous humor (AH) are expressed as: \(\nabla .\overrightarrow{v}=0\) (2) \(\rho (\overrightarrow{v}\bullet \nabla\) ) (3) \(\nabla \bullet \left(k\nabla T\right)-\rho C\left(\overrightarrow{v } \bullet \nabla T\right)=0\) (4) where the Boussinesq approximation is used for density variation. Here, β is the fluid's volume expansion coefficient, C is heat capacity, and T ref =34 ˚C is a reference temperature. Several turbulence models are investigated to predict the thermal plume due to natural convection. The RNG k-ε model with three different types of boundary conditions (scalable wall function, enhanced wall treatment, low Reynolds) and the SST k-ω model were used in the present study. Among these models, the RNG k-ε model with enhanced wall treatment is better matched to the experimental data for the heat transfer coefficient over the body and no inconsistent jump over the contours. Therefore, this model was used for further simulations. All the testing steps are repeated for mixed convection, and the RNG k-ε model combined with the enhanced wall treatment option is selected for the rest of the simulations. The details of the continuity, momentum, energy, and the RNG k-ε turbulence model equations are not shown here for brevity, and they can be found in (ANSYS manual). Boundary Conditions To investigate mixed convection heat transfer from the manikin, uniform air velocity with 6% turbulent intensity and 0.7 m length scale (approximately similar to the experimental conditions of De dear et al. [ 26 ]) is applied on the inlet boundary. Zero gradients for flow parameters are considered at the outlet boundary condition. Enhanced wall treatment boundary condition is used on wall surfaces such as the computational domain's manikin surface, bottom, upper and side walls. In addition, the symmetry and uniform velocity boundary conditions are also tested on the upper face and sides of the computational domain. Due to the use of sufficiently large computational domains, the effects of these different boundary conditions on the heat transfer from the manikin were found to be negligible. Therefore, the results can also resemble the outdoor conditions. Air with different velocities and temperatures as summarized in Table 3 , are used on the inlet boundary of the computational domain. Manikin surface temperature is assumed to be 34 ˚C. When the ambient air speed is less than 0.2 m/s, the heat transfer from the human skin is mainly treated as natural convection. The force convection has also been simulated for a velocity higher than this. The selected range of air velocity (0.2-5 m/s) covers indoor and outdoor environmental conditions. Table 3 Environmental conditions for computations Air velocity (m/s) Environmental temperature (˚C) 0.0 0 20 0.3 0 20 1.0 0 20 5.0 0 20 To study natural convection conditions, a pressure inlet is applied on the side surfaces of the computational domain. Enhanced wall treatment is applied on the upper and lower surfaces of the domain. Also, a zero gradient type boundary condition is considered an outlet boundary condition on the upper surface of the computational domain. Numerical simulations are performed for two ambient air temperatures of 0, 20 ˚C. To consider heat flux between parts of the cornea and sclera that have contact with the inside of the body, the following equation is applied, respectively: In this equation, the temperature of blood vessels T bl , near the sclera is assumed to be constant, h s is the heat transfer coefficient between the inside of the body and the eye, B corresponds to the term associated with the blood perfusion rate, and A is the metabolic heat generation rate. Thermal properties and the quantities considered for Eq. ( 14 ) are summarized in Table 4 and Table 5 . Table 4 Thermal properties of the biological materials of eye layers Material Density ρ(hg m − 3 ) Specific heat c(J kg − 1 K − 1 ) Thermal conductivity k(W m − 1 K − 1 ) Basal metabolism (W m − 3 ) Blood perfusion power equivalent (W m-3 K-1) Cornea 1050 a 4178 a 0.58 a - - Sclera 1050 a 3800 b 0.58 b 22000 b 80000 b Anterior chamber 996 a 3997 a 0.58 a - - Iris 1050 a 3600 b 0.52 b 10000 b 35000 b Lens 1000 a 3000 a 0.4 a - - Vitreous chamber 1100 a 4178 a 0.603 a - - a [ 38 ] b [ 42 ] Table 5 Physical parameters at the boundaries of the eye Parameter Description Value h s Body heat transfer coefficient (W m − 2 K − 1 ) 65 a T bl Blood temperature (˚C) 37 E Evaporation rate (W m − 2 ) 40 a σ Stefan-Boltzmann constant (W m − 2 K − 4 ) 5.67×10 − 8 ε Emissivity of corneal surface 0.975 a a [ 38 ] No slip boundary condition on the anterior chamber surface, which is assumed to be rigid and impermeable, is imposed. Mechanical properties of eye layers are considered homogenous and isotropic. To consider radiation heat transfer from the eye surface, the heat flux given as is added to each element of the eye surface that is in contact with the environment. A UDF (User-defined function) was developed and incorporated into the ANSYS-FLUENT. According to the previous studies of [ 21 ], the evaporation rate from a normal eye ranges from 40–100 W/m 2 . Here, the lowest value of E = 40 W/m 2 is used to obtain the highest temperatures in the eye. The evaporation heat loss is included using the same procedure used for the radiation heat transfer. The commercial fluid dynamic software package ANSYS-FLUENT is used for numerical simulation. An unstructured grid is developed for the environmental chamber around the manikin using the ANSYS (ICEM) software. To resolve the boundary layer around the eye, five layers of extruded triangular prisms are used with an initial size of 0.01 cm and a growth rate of 1.1 between the layers. Since the focus of the present study is the heat transfer from the eyes, most grid elements are placed around the head, particularly near the eyes, as shown in Fig. 6 . The grids are fine near the manikin and become course far from the manikin. Since the enhanced wall treatment is used as the turbulent wall boundary condition, the value of y + should be less than 5 for the grid points adjacent to the manikin surface as a requirement for the used turbulence model. In these simulations, it is made sure that this condition is satisfied. For the case of natural convection with a body temperature of 34˚C and environmental temperature of 22 ˚C, the average value of y + for the first grid points near the manikin body is equal to 0.62. To generate a computational grid for the anterior eye chamber, a structured grid is used for the 2D geometry shown in Fig. 7 . Then, by rotating this grid around the optical axis, the 3D structured grid is created. The eye grid is integrated with the manikin grid using an unstructured grid in the cornea and sclera. To have a smooth transition between the structured grid inside the eye and the unstructured grid outside, rectangular elements on the outer surface of the structured grid are separated into two triangles by ANSYS (ICEM) software to be a base for the unstructured grid of cornea and sclera as illustrated in Fig. 8 . The grid independence study is performed for various grid sizes, and finally, the cases with about 5 and 6 million cells are selected for natural and mixed convection cases, respectively. Validation of the Numerical Method There is no available experimental data for airflow around the manikin shown in Fig. 2 . Therefore, to validate the computational model, the simulation results are compared with experimental and numerical data for airflow around another manikin and the liquid motion in a separate eye model. a) Validation of the eye flow model To validate the simulation model for the aqueous humor flow in the eye, the velocity field in the anterior chamber for the thermal boundary conditions of Karampatzakis and Samaras[ 8 ] is simulated and the predicted velocity profile along the pupillary axis is compared with the numerical results of [ 8 ]in Fig. 9 . This figure shows good agreement of the predicted velocity distribution with earlier simulation. The deviation seen is due to a slight difference between the two geometries. The maximum velocity reported for the numerical study of Karampatzakis and Samaras[ 8 ] is 3.36×10 − 4 (m/s). In the current work, the maximum velocity is 3.39×10 − 4 (m/s), which is quite close. But the second peak differs by a factor of 2. The details of the geometry of Karampatzakis and Samaras ([ 8 ], [ 28 ] ) are not available and it was impossible to compare more information on the flow field. b) Validation for natural convection around manikin: Two cases were studied for validating the natural convection flow simulations around the manikin. 1- The flow field and heat transfer of a manikin standing in the center of a box is investigated. A comparison of the present simulation results with the experimental data and numerical results of [ 28 ]for velocity magnitude along almost the plume centerline as a function of height from the floor is shown in Fig. 10 . It is seen that there is an acceptable agreement of the present simulation results with the experimental measurements of [ 28 ]. The Maximum plume velocities reported by Craven and Settle[ 28 ] for the experimental data and their numerical model, respectively, were 0.24 m/s and 0.20 m/s. The present simulation predicts a maximum velocity of 0.25 m/s, which agrees with the experiment measurement. 2- de Dear et al.[ 26 ] reported the natural heat transfer coefficient of the head and the entire body for 12 K temperature differences, respectively, as 3.6 and 3.4 W/(m 2 .K). These values are close to the results of the present study of 3.36 and 3.12 W/(m 2 .K) to the heat transfer coefficients. c) Validation for mixed convection flows around the manikin: To validate the results for mixed convection around the manikin, the experimental condition of de Dear et al.[ 26 ] is applied to the present modeling and the results are shown in Fig. 11 . In their experiment, the manikin surface temperature was equal to 34 ˚C and the ambient temperature was 20 ˚C. A general agreement between the present computational work and experimental measurements can be observed. The deviation is possibly due to different geometries for the manikins and experimental and numerical errors. The manikin in their work had hair and clothes. In addition, a large cylindrical drum (1.5 m tall and 0.5 m diameter) was installed upstream on the floor in the wind tunnel to generate large-scale eddies in the experiment. Also, Ono et al.[ 29 ] reported that the convective heat transfer coefficient of a seated manikin for 1 (m/s) air velocity and 10% turbulent intensity is h c =12.9 (W/m 2 .K). This value is close to that in the current study, which is h c =11.95 (W/m 2 .K). Results and Discussions The validated computational model is used and the airflow and temperature fields and heat transfer from a standing manikin with attached eyes for different environmental air velocities and temperatures are computed. Typical velocity distribution around the manikin for different air velocities and ambient temperatures are shown in Fig. 12 . Although the thermal plume above the manikin head becomes different with an open-like boundary (like [ 27 ]), heat transfer and velocity around the eye does not change noticeably. Therefore, present results also can be used for outdoor conditions. In the case of natural convection, the velocity in the thermal plume reaches 0.8 m/s. The velocity behind the head is higher than that in the front of the head. The velocity close to the eye, which is the focus of this study, is less than 0.1 m/s. The velocity field changes considerably when the wind blows toward the manikin. A plume formed over the head for free convection, while for wind-blowing conditions, a large separation zone is observed on the back of the manikin. The velocity increases compared to the free stream and reaches almost 1.5 m/s between the legs and 1.3 m/s over the head. The air velocity close to the eye is around 0.3 m/s, which is three times that in the case of free convection. Figure 13 illustrates the velocity vectors in the vertical middle plane of manikin's left eye for different ambient air velocities and environmental temperatures. This figure shows that a circulation flow forms in the aqueous humor due to temperature differences across the anterior chamber. As expected, by increasing the air velocity and temperature difference between the body and the environment, the circulating flow in the anterior chamber becomes stronger due to increasing heat flux between the eye and the environment. The effect of environmental air velocity and temperature on the average convective heat transfer coefficient and average heat flux over the eye is summarized in Tables 8 and 9 . The data in these tables show that the heat transfer coefficient and heat flux over the eye change significantly when the airflow velocity increases. According to Baldwin and Maynard [ 43 ], air velocity in indoor conditions is approximately 0.3 m/s, and based on the current results, the convection heat transfer coefficient is h ̅ = 11 W/m 2 .K which is consistent with the values reported in [ 9 ], [ 21 ]–[ 25 ], [44]. This value, however, is valid only for indoor conditions and the heat transfer coefficient changes for different environmental conditions, as presented in Table 8 . According to the results, some investigators used very large convection coefficients ([ 22 ], [ 24 ], [25]) such as 100 W m −2 K −1 which does not occur even in high air velocity and ambient temperature. Table 8 . Variation of average convective heat transfer coefficient (W/(m 2 .K)) of manikin eye. Table 9 . Variation of average convective heat flux (W/m 2 ) of manikin eye. Contours of convective heat transfer coefficient and heat flux over the manikin head for 1 m/s ambient airflow velocity at the temperature of 20˚C are shown in Fig. 14 . As expected, in the bulge (gibbosity) parts of the manikin, heat transfer is higher. Temperature contours on the surface of the eye for different air velocities are shown in Fig. 15. It is seen that the temperature distribution on the eye surface is not uniform. As expected, due to the convexity of the cornea, the maximum heat transfer occurs in this region, and hence, minimum eye temperature appears on the cornea. The isotherm contours of the eye are elliptical, similar to the observation of [ 3 ]. It is also seen that the far-field air temperature does not have a noticeable effect. This is because the thermal plume around the body controls the airflow and temperature fields near the head, and the temperature contours on the eye's surface do not change. For the mixed convection case, the far-field air temperature slightly affects the eye surface temperature, but the difference between far-field temperatures of 0˚C and 20˚small. For a more comprehensive examination of the fluctuations in human eye temperature, a calibrated thermographic camera was employed to capture thermal images of the subjects. The room temperature was rigorously maintained within a narrow range of ± 0.1˚C by a control system comprising a computer, three thermocouples, and an air cooling and heating unit. Further details regarding the control room and the experimental procedures can be found in the work of Mahdavi and Yaghoubi [ 24 ]. The room temperatures selected for this study were 20, 23, and 25˚C, with the corresponding thermal image of the eye displayed in Fig. 16 . Notably, the observed temperature variations on the surface of the eye were minimal, supporting the assumption that the eye's temperature could be considered relatively constant at T = 34˚C. Figure 17 shows the temperature distribution at the eye vertical mid-plane for different environmental air velocities and temperatures. The surface temperature of the eye and anterior regions of the eye increases slightly for higher ambient temperatures and lower air velocities. For a 20˚C difference in the environmental temperature, the surface temperature of the eye differs by 1˚C for the natural convection case and about 3˚C for the mixed convection case with an airflow velocity of 1 m/s. The convective heat transfer coefficient of the eye for manikin alone and manikin with attached eyes for different environmental air velocities and temperatures are presented in Table 10 . When only the manikin without the eye globe is modeled, the temperature boundary condition is set on the uncovered surface of the cornea and sclera (34˚C). Table 10 depicts the differences which shows the importance of solving the eye coupled with the surrounding parts of the manikin. Table 10 . Average heat transfer coefficient (W/m 2 .K) of an eye for different models (T = 20 ˚C). Table 11 compares the effect of convection and radiation on the eye for different ambient air velocities and temperatures. It is seen that the convection and radiation heat fluxes are in the same order for low air velocities which correspond to the indoor conditions. With the free stream air velocity increase, the convection dominates the heat transfer from the eye compared with the radiation. Table 11 . Convective and radiative heat transfer rate (W/m 2 ) from an eye at different ambient air velocities and temperatures. Conclusions In the present study, the airflow velocity and temperature distribution of flow around a manikin and inside the eye were simulated using a model for eyes connected to a standing manikin. The convective heat transfer coefficient and heat flux over the eye were evaluated for different ambient air velocities and temperatures. The simulation results showed: Modeling the airflow surrounding the manikin, including the face and the eyes and solving coupled system with the motion of aqueous humor inside the anterior chamber of the eye leads to more accurate results. The coupled simulations make the predicted eye temperature distribution more similar to the experimental data. The simulation results for air velocities in the range of 0 to 5 m/s and ambient temperatures of 0 and 20˚C showed that the convective heat transfer coefficient of the eye varied in the range of 4.7–43.1 W/m 2 .K and the heat flux varied in the range of 115.4 W/m 2 to 1185.2 W/m 2 . Therefore, assuming a constant convective heat transfer coefficient irrespective of the environmental conditions is not appropriate for the thermal modeling of the eye. These results could be of interest to the reasons for the dryness of the eye due to an increase in heat transfer at high airflow velocities and low air temperatures. Natural convection due to temperature difference across the eye anterior chamber became markedly stronger by the increased air velocity and decreased air temperature. For the range of parameters studied, the maximum velocity of aqueous humor inside the anterior chamber of the human eye changed from 0.2 mm/s to 0.6 mm/s. That is, the variation in environmental conditions had a noticeable influence on the aqueous humor motion in the eyes. For high air velocities and low ambient temperature, the convective heat transfer became dominant compared to evaporation and radiation from the eye. Declarations Author Contribution F.F. wrote the main manuscript text, Conducted research, performed literature review andM.Y. , G.A, O.A mentored the research process, edited the manuscript, and provided guidance on research direction. All authors reviewed the manuscript. 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J Biomech Eng 134(2):021002 Modarreszadeh A, Abouali O (2014) Numerical simulation for unsteady motions of the human vitreous humor as a viscoelastic substance in linear and non-linear regimes. J Nonnewton Fluid Mech 204:22–31 Bhandari A, Bansal A, Sinha N (2020) Effect of aging on heat transfer, fluid flow and drug transport in anterior human eye: a computational study. J Controlled Release 328:286–303 Bayat J, Emdad H, Abouali O (2020) Numerical investigation of partially liquefied vitreous dynamics as two-phase viscoelastic-Newtonian fluid flow in a planar cavity due to oscillatory motion. Int J Multiph Flow 127:103259 Bayat J, Emdad H, Abouali O (2020) 3D numerical investigation of the fluid mechanics in a partially liquefied vitreous humor due to saccadic eye movement. Comput Biol Med 125:103955 Bayat J, Emdad H, Abouali O (2022) A mechanical model of partially liquefied vitreous dynamics induced by saccadic eye movement within a realistic shape of vitreous cavity. Phys Fluids, 34, 2 Rahman MA, Rabbani M, Maruf MH, Islam A, Shihavuddin ASM (2022) Characterizing the Aging Process of the Human Eye: Tear Evaporation, Fluid Dynamics, Blood Flow, and Metabolism-Based Comparative Study, Biomed Res Int , vol. 2022 Tang H, Qin Z, Wen B (2022) Geometric model and numerical study of aqueous humor hydrodynamics in the human eye, Comput Math Methods Med , vol. 2022 Lagendijk JJW (1982) A mathematical model to calculate temperature distributions in human and rabbit eyes during hyperthermic treatment. Phys Med Biol 27(11):1301 Scott JA (1988) A finite element model of heat transport in the human eye. Phys Med Biol 33(2):227 Ng EYK, Ooi E-H (2006) FEM simulation of the eye structure with bioheat analysis. Comput Methods Programs Biomed 82(3):268–276 Cvetkovic M, Cavka D, Poljak D (2006) A simple finite element model of heat transfer in the human eye, in International Conference on Software in Telecommunications and Computer Networks , IEEE, 2006, pp. 27–31 Wang H, Qin QH (2010) FE approach with Green’s function as internal trial function for simulating bioheat transfer in the human eye. Archives Mech 62(6):493–510 Shafahi M, Vafai K (2011) Human eye response to thermal disturbances De Dear RJ, Arens E, Hui Z, Oguro M (1997) Convective and radiative heat transfer coefficients for individual human body segments. Int J Biometeorol 40:141–156 Sørensen DN, Voigt LK (2003) Modelling flow and heat transfer around a seated human body by computational fluid dynamics. Build Environ 38(6):753–762 Craven BA, Settles GS (2006) A computational and experimental investigation of the human thermal plume Ono T, Murakami S, Ooka R, Omori T (2008) Numerical and experimental study on convective heat transfer of the human body in the outdoor environment. J Wind Eng Ind Aerodyn 96:10–11 Kurazumi Y, Tsuchikawa T, Matsubara N, Horikoshi T (2008) Effect of posture on the heat transfer areas of the human body. Build Environ 43(10):1555–1565 Zhang Y, Novieto D, Ji Y (2009) Human environmental heat transfer simulation with CFD–the advances and challenges Jia X, McLaughlin JB, Derksen J, Ahmadi G (2013) Simulation of a mannequin’s thermal plume in a small room. Comput Math Appl 65(2):287–295 Salmanzadeh M, Zahedi G, Ahmadi G, Marr D, Glauser M (2012) Effect of thermal plume adjacent to the body on the movement of indoor air aerosol particles. J Aerosol Sci 53:29–39 Ružić DA, Bikić SM (2014) An approach to the modeling of a virtual thermal manikin. Therm Sci 18(4):1413–1423 Lee S, Nogami M, Yamaguchi S, Kurabuchi T, Ohira N (2013) Evaluation of heat transfer coefficients in various airconditioning modes by using thermal manikin Hasama T, Mihara K, Sekhar C, Cheong KWD, Tham KW (2022) Assessment of airflow and heat transfer around a thermal manikin in a premise served by DOAS and ceiling fans. Build Environ 214:108902 Anselm B et al (2007) Efficacy of forced-air warming systems with full body blankets. Can J Anesth 54(1):34 Ooi E-H, Ng EY-K (2008) Simulation of aqueous humor hydrodynamics in human eye heat transfer. Comput Biol Med 38(2):252–262 Charles MW, Brown N (1975) Dimensions of the human eye relevant to radiation protection (dosimetry). Phys Med Biol 20(2):202 Clark RP, Toy N (1975) Natural convection around the human head. J Physiol 244(2):283–293 Bykalyuk A, Kuznik F, Johannes K (2013) Transient free laminar convection in the vicinity of a thermal conductive vertical plate. Int J Mech Mechatronics Eng 7(12):2506–2515 Hirata A (2007) Improved heat transfer modeling of the eye for electromagnetic wave exposures. IEEE Trans Biomed Eng 54(5):959–961 Baldwin PEJ, Maynard AD (1998) A survey of wind speeds in indoor workplaces. Ann Occup Hyg 42(5):303–313 Ooi E-H, Archarya UR (2008) A comparative study between the two-dimensional and three-dimensional human eye models. Math Comput Model 48:5–6 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3997744","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":276158545,"identity":"cb72976a-8950-4d45-b270-ede60e982a15","order_by":0,"name":"Farnaz Feyli","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9klEQVRIie3PsUrEMBzH8V8IpEs0jv9wgq/Qm0Q46atcOaiLvoJEDnpLdT4n3+Lmlq66C1l06eTQ24pksKGutucmmO+Q/AP/zxAgFPqDRWa4FcBN2faTiCaILIdbGzBTbT3hvyFc+nGSRC/NW+dAitK7evG5OzvmYO3+eoTIq/N5IUF6m5r65sHOcw6uH3c/kwSZIEm4jV89KSzrieBHI0SqRmgXgxJPLgqbTBPKxEwuQTH1BJ1NDyCNmJ2WRPT8bqp7Y1c5Z+vRv0iVCf3hFqQ2q7rtnL182qyrdj9CviPgZAmw3D+YmdwfUmV/uAOXQ6FQ6F/1BR2dTAXj2btCAAAAAElFTkSuQmCC","orcid":"","institution":"Shiraz University","correspondingAuthor":true,"prefix":"","firstName":"Farnaz","middleName":"","lastName":"Feyli","suffix":""},{"id":276158546,"identity":"b6c6c31c-3375-44ea-9893-b5632f423332","order_by":1,"name":"Mahmood Yaghoubi","email":"","orcid":"","institution":"Shiraz University","correspondingAuthor":false,"prefix":"","firstName":"Mahmood","middleName":"","lastName":"Yaghoubi","suffix":""},{"id":276158547,"identity":"b87adcec-f8e5-4d80-ae30-286b1ed01f9b","order_by":2,"name":"Goodarz Ahmadi","email":"","orcid":"","institution":"Clarkson University","correspondingAuthor":false,"prefix":"","firstName":"Goodarz","middleName":"","lastName":"Ahmadi","suffix":""},{"id":276158548,"identity":"6da6c34c-14db-4670-bcde-1fbbb72718f6","order_by":3,"name":"Omid Abouali","email":"","orcid":"","institution":"Shiraz University","correspondingAuthor":false,"prefix":"","firstName":"Omid","middleName":"","lastName":"Abouali","suffix":""}],"badges":[],"createdAt":"2024-02-28 20:47:24","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3997744/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3997744/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":52031800,"identity":"24494e0f-3a4c-4668-ada1-db2049b2e74b","added_by":"auto","created_at":"2024-03-05 16:33:17","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":360039,"visible":true,"origin":"","legend":"\u003cp\u003eOriginal manikin that is considered for the present study.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-3997744/v1/7ae1cbf1845643a272180b58.png"},{"id":52033320,"identity":"5a303071-bd30-496d-a940-38734a574f57","added_by":"auto","created_at":"2024-03-05 16:41:17","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":230052,"visible":true,"origin":"","legend":"\u003cp\u003eSimplified manikin geometry that is used in the present study.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-3997744/v1/44d6409286b761a56deaee12.png"},{"id":52031799,"identity":"5eaf0f87-fc0a-451b-9906-9a3e5d284291","added_by":"auto","created_at":"2024-03-05 16:33:17","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":54484,"visible":true,"origin":"","legend":"\u003cp\u003ea) 2D and b) 3D eye model used in the present study.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-3997744/v1/4fb4afd1bf1e2e371cf44778.png"},{"id":52033321,"identity":"14733000-5b8e-4a79-a13a-fb3e3819d96f","added_by":"auto","created_at":"2024-03-05 16:41:17","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":249423,"visible":true,"origin":"","legend":"\u003cp\u003ea) Head of the manikin with the attached eyes. b) An enlarged view of the attached eyes.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-3997744/v1/9438e17727346cdcc242f25e.png"},{"id":52031803,"identity":"96227bf3-feef-4b07-837a-b4950db3f810","added_by":"auto","created_at":"2024-03-05 16:33:17","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":157898,"visible":true,"origin":"","legend":"\u003cp\u003eComputational domain used for: \u0026nbsp;a) Natural convection and b) Mixed convection.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-3997744/v1/430ed4b642213a78f9438759.png"},{"id":52034283,"identity":"a743e678-deb0-49e9-84fd-d57540a85dd6","added_by":"auto","created_at":"2024-03-05 16:49:17","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":258774,"visible":true,"origin":"","legend":"\u003cp\u003eComputational mesh on the manikin surface: a) Total body. b) Around the eyes. c) Side view of the symmetry- plane. d) Enlarged view of the computational manikin head at the symmetry plane\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-3997744/v1/b09094417c7bcae3001b4c3e.png"},{"id":52031809,"identity":"9778c6fc-cf00-4a80-afab-1a0c6273a3f2","added_by":"auto","created_at":"2024-03-05 16:33:17","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":113163,"visible":true,"origin":"","legend":"\u003cp\u003eComputational mesh in the 2D section of eye used in this study.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-3997744/v1/7e045896caffd4588ea523d0.png"},{"id":52031815,"identity":"e43fedda-283d-41a0-8aae-c3e71343fdbb","added_by":"auto","created_at":"2024-03-05 16:33:17","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":369383,"visible":true,"origin":"","legend":"\u003cp\u003eSmooth transition of rectangular elements of structured grid to triangular elements for unstructured grid\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-3997744/v1/901f4c714bb38382e71457a9.png"},{"id":52031807,"identity":"94caa7a1-99d2-4575-ac56-feb33afe9bb0","added_by":"auto","created_at":"2024-03-05 16:33:17","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":63725,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of the predicted aqueous humor velocity along pupillary axis with the simulations of [8].\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-3997744/v1/8f1f05c2456e139419762041.png"},{"id":52033318,"identity":"6ae42773-b40f-47da-a55c-2a01eb20cc57","added_by":"auto","created_at":"2024-03-05 16:41:17","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":123783,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of the predicted plume centerline velocity distribution over the manikin head with the results of [28].\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-3997744/v1/89a626d1f5d420e95b201f0f.png"},{"id":52031805,"identity":"57e997aa-161d-4cc7-bccd-5c75c9435e67","added_by":"auto","created_at":"2024-03-05 16:33:17","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":14556,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of average convective heat transfer coefficient (W/ (m\u003csup\u003e2\u003c/sup\u003e.k)) for various air velocities.\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-3997744/v1/677db9a4d1e398b08253c438.png"},{"id":52031806,"identity":"94894442-df61-4132-baf8-0bbd91044975","added_by":"auto","created_at":"2024-03-05 16:33:17","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":402575,"visible":true,"origin":"","legend":"\u003cp\u003eAirflow velocity distribution around the manikin at the mid-vertical plane.\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-3997744/v1/bb82ec0dace7984d1997a7ed.png"},{"id":52031813,"identity":"3442c996-87d7-4ee9-aa45-05ab31d055c5","added_by":"auto","created_at":"2024-03-05 16:33:17","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":115093,"visible":true,"origin":"","legend":"\u003cp\u003eStreamlines and velocity magnitude contours along the vertical mid-plane of the left eye of the manikin.\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-3997744/v1/f012e31a36f438f26d3ea3d5.png"},{"id":52031812,"identity":"fbdabaf9-e713-4ed3-a0c9-9314f2af023d","added_by":"auto","created_at":"2024-03-05 16:33:17","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":124633,"visible":true,"origin":"","legend":"\u003cp\u003eContours of a) convective heat transfer coefficient (W/(m\u003csup\u003e2\u003c/sup\u003e.K)) and b) heat flux (W/m\u003csup\u003e2\u003c/sup\u003e) of manikin (V∞= 1m/s, T∞= 20 ˚C).\u0026nbsp;\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-3997744/v1/e71af6640393468698605461.png"},{"id":52031814,"identity":"6336f869-0953-434b-9d8c-53f576f3be7a","added_by":"auto","created_at":"2024-03-05 16:33:17","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":167480,"visible":true,"origin":"","legend":"\u003cp\u003eTemperature contours (K) on the surface of the left manikin eye.\u003c/p\u003e","description":"","filename":"15.png","url":"https://assets-eu.researchsquare.com/files/rs-3997744/v1/061713670a4c345cafd6c692.png"},{"id":52033323,"identity":"838253f0-c460-4d9c-a056-9c2b205d629e","added_by":"auto","created_at":"2024-03-05 16:41:17","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":304118,"visible":true,"origin":"","legend":"\u003cp\u003eTemperature contours (˚C) of human eye taken by thermograph (Air in the far field is stagnant, T∞= 25 ˚C).\u003c/p\u003e","description":"","filename":"16.png","url":"https://assets-eu.researchsquare.com/files/rs-3997744/v1/9e9ba12ddfd6405f3883d48b.png"},{"id":52033319,"identity":"9ded8546-3c21-41cb-820c-6cd8d47477a1","added_by":"auto","created_at":"2024-03-05 16:41:17","extension":"png","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":127934,"visible":true,"origin":"","legend":"\u003cp\u003eTemperature distribution at the eye mid-plane.\u003c/p\u003e","description":"","filename":"17.png","url":"https://assets-eu.researchsquare.com/files/rs-3997744/v1/149c01bdfd6b285b0460cd04.png"},{"id":54710549,"identity":"37412204-7e46-4742-8e9f-0d092a996eb9","added_by":"auto","created_at":"2024-04-15 14:35:45","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3319647,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3997744/v1/aa480b63-0f11-4608-b2ca-fdc3d5c95f10.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eHeat Removal from a Human Eye for Different Environmental Conditions - A CFD Study Using a Full-Scale Manikin\u003c/p\u003e","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe eye is one of the most important organs of the human body. The changes in ambient temperature may affect the eye's physiology. Studying temperature distribution in the eye under different environmental conditions is important for understanding eye physiology and its interaction with the environment. Currently, an experimental facility for in vivo temperature measurement inside the eye is unavailable. However, some earlier experimental studies [\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]–[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]measured the eye's surface temperature. Due to the limitations of in vivo measurement, researchers tried to evaluate the fluid flow and temperature distribution inside the eye by numerical simulation. Amara[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] investigated the effect of laser power and wavelength on the eye tissues by modeling a human eye exposed to laser irradiation. Heys and Barocas[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] studied the movement of pigment particles released near the iris tip to predict the formation of Krukenberg’s spindle. Ooi et al.[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] studied the effect of tumors on temperature distribution inside an eye. Karampatzakis and Samaras[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] studied the impact of an artificial intraocular lens on the eye temperature distribution. Li et al.[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] simulated the 2D and 3D models of an eye and investigated the effect of hyperthermia treatment on healthy eye tissues. Narasimhan and Jha[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] modeled Pan Retinal Photocoagulation (PRP), a retinal laser surgical process, and found eye temperature distribution under different conditions. Abouali et al.[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] used a computational modeling approach to study the unsteady flow in the vitreous cavity due to saccadic eye movement. They studied the flow dynamics of the vitreous after complete vitreous liquefaction and for post-vitrectomy eyes (Vitreous gel is substituted with silicon oil and balanced salt solution). Abouali et al.[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] also modeled the aqueous humor flow in the anterior chamber due to saccadic movements. They showed that mixing the aqueous humor due to the saccadic movements increased the heat transfer in the anterior chamber and through the cornea. Modareszadeh and Abouali[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] simulated the motion of vitreous humor for the real shape of a human vitreous chamber filled with the gel- with a viscoelastic model.\u003c/p\u003e \u003cp\u003eBhandari et al. [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] have developed a computational model to investigate topical drug delivery in the aging human eye. Their research explores the impact of aging on various eye parameters, including heat transfer, aqueous humor flow, intraocular pressure, and drug distribution across different eye regions and orientations. Bayat et al. [\u003cspan additionalcitationids=\"CR16\" citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]–[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] studied partial vitreous liquefaction (PVL) flow dynamics as a two-phase viscoelastic-Newtonian fluid in 2D and 3D human eye models. Rahman et al. [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] studied the anatomical and physiological changes in the human eye as it ages. They have developed a model to analyze the thermos-fluid dynamics of the aging human eye, incorporating four physiological changes into their simulations: metabolism, blood perfusion, tear evaporation, and aqueous humor flow. Tang et al. [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] conducted simulations of the aqueous humor (AH) flow within human eyes, featuring diverse morphological structures and physical characteristics. They acquired the velocity distribution and temperature distribution of the aqueous humor flow.\u003c/p\u003e \u003cp\u003eAll these earlier studies modeled the anterior chamber or the entire eyeball and the cornea as the boundary of the computational domain in contact with the ambient air. The heat transfer through the eyelid was not included in the earlier models. But when the eye is open, in addition to the cornea, a part of the sclera is also in contact with the ambient air. In some earlier studies, the temperature distribution obtained from the IR thermograph[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] is applied to the cornea as a boundary condition. In other research, the constant ambient convection heat transfer coefficient experimentally measured by Lagendijk[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] for a rabbit eye is used for the boundary condition at the cornea. Some researchers studied the effect of different parameters like ambient temperature and convection coefficient on the eye temperature distribution [\u003cspan additionalcitationids=\"CR22 CR23 CR24\" citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]–[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]) None of these earlier works investigated the corresponding environmental condition for the assumed convection coefficients.\u003c/p\u003e \u003cp\u003eNatural and forced heat transfer coefficients for different body parts under various environmental conditions were studied before in the literature. Dear et al.[\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] reported experimentally measured convection and radiation heat transfer coefficients under natural and forced convection conditions for different parts of a seated and a standing manikin. Their measurement for force convection is performed for air velocities in the range of 0.1-5 m/s. They also reported some correlations for radiation and convection heat transfer coefficients for different body parts for different airflow velocities. Serensen and Voigt[\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] found a seated manikin's natural heat transfer coefficient experimentally and numerically. They also investigated radiation heat transfer in their numerical simulation. Craven and Settles[\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e] provide particle image velocimetry (PIV) measurement of the thermal plume velocity at the top of the human head created due to the temperature difference between the body and ambient air in a standard room with moderate thermal stratification. They compared their experimental data with their CFD model and reported that the room thermal stratification significantly affected the thermal plume. Ono et al.[\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] used a combined experimental and numerical approach to study the heat transfer coefficient of a standing manikin for different air velocities. They validated their CFD code by their experimental data and presented a correlation for body heat transfer coefficient for different air velocities and turbulence intensities. Kurazumi et al.[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e] experimentally investigated the effect of postures on the conduction, convection, and radiation heat transfer of a manikin in an environmental chamber. Zhang et al.[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] reviewed manikins' experimental and numerical heat transfer studies. They considered three geometrical models (the first model was constructed using several cubes, the second one was developed using a sphere and cylinders and the third geometry resembles a standing human body). Their numerical results for the third model are more compatible with experimental measurements. Jia et al.[\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e] studied the details of a thermal plume created around a seated and heated manikin due to temperature differences with the environment. They used an LBM computational model for a rectangular-shaped manikin in a small room. Salmanzadeh et al.[\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e] numerically and experimentally investigated the effect of a thermal plume around a seated manikin on the particle transport in a cubicle. Ruzic and Bikic[\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e] simulated thermal conditions in vehicle cabins and studied natural and forced convection heat transfer between the manikin and the environment. Lee et al.[\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e] experimentally measured a seated manikin's natural convection[\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e] heat transfer coefficient. They validated their numerical results with experimental data and used their simulation to find the force heat transfer coefficient for different air velocities. Hasama et al.[\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e] studied the attributes of air circulation produced by ceiling fans around a thermal manikin and the convective heat exchange resulting from the airflow distribution through both experimental methods and CFD while considering both standing and seated positions.\u003c/p\u003e \u003cp\u003eIn the present study, flow and heat transfer inside the eye of a three-dimensional manikin are simulated for both natural and mixed convection flows around the body. Particular attention was given to the variation of temperature inside the eye. In the present work, the manikin's surroundings were added to the computational model to study the heat transfer through the eye for different environmental conditions. Using this approach, the heat transfer coefficient over the cornea is obtained through the solution and it is not set with a rough approximation as a boundary condition.\u003c/p\u003e"},{"header":"Model Description","content":"\u003cp\u003eTo create a geometrical model of a human body, a 3D CAD model of a standing male manikin is used, shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The CAD model is converted to the STL file smoothed and scaled to 1.77 m height. To decrease numerical complexity, some simplifications are done on the model such as closing the lips and nostrils, removing eyelashes, ears, and nails, and smoothing the feet. The resulting simplified manikin model is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, which resembles a normal man and is more realistic than models used in the previous simulations [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e], [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e], [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e], [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]).\u003c/p\u003e\u003cp\u003eTo model the eye with the dimensions presented by ([\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e], [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]), a 3D computational model is created in GAMBIT 2.4.6 software by rotating a 2D model (shown in Fig.\u0026nbsp;3) around the optical axis. The axial diameter is 26 mm, and the vertical diameter is 23.65 mm, which leads to a total volume of 7.36 cm\u003csup\u003e3\u003c/sup\u003e for the eye.\u003c/p\u003e\u003cp\u003eThe developed eye model consists of a cornea, anterior chamber, posterior chamber, iris, lens, vitreous, and sclera. For simplification, the retina and choroid, which are very thin compared to the sclera, are not considered in the present model. Finally, the eye model is attached to the manikin using ANSYS 14.5 (ICEM,) as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eThe selected computational domain for the airflow is sufficiently large that the boundaries do not affect the thermal plume flow field around the manikin. Typically, the air far from the manikin is assumed to be stagnant for the natural convection case. Figure\u0026nbsp;5a shows the dimensions of the computational domain used for the airflow study. The domain independence study is performed by measuring heat transfer from the eye surface of the manikin. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the size of boxes used for various computational domains to study mixed convection. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e also compares the heat flux and transfer coefficient for different domain sizes. It is seen that the simulation results for domains 2 and 3 are relatively close. Accordingly, the domain with a dimension of botwo 2 is selected for the rest of the analysis. Figure\u0026nbsp;5 illustrates the computational domain used for both the natural and mixed convection cases.\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\"×\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of size of the domain, heat transfer coefficient and average convective heat transfer rate for the total surface of the manikin for different computational domains tested for mixed convection.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCase number of computational domains\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNumber of grids\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSize of the computational\u003c/p\u003e \u003cp\u003edomain L×W×H (m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAverage heat transfer coefficient\u003c/p\u003e \u003cp\u003e(Wm\u003csup\u003e− 2\u003c/sup\u003eK\u003csup\u003e− 1\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eAverage convective surface heat flux\u003c/p\u003e \u003cp\u003e(W/ m\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1843365\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\"×\" colname=\"c3\"\u003e \u003cp\u003e0.95×0.76×1.79\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20.2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e308.2\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5847579\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\"×\" colname=\"c3\"\u003e \u003cp\u003e4.95×7.76×3.80\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e17.8\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e270.6\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e7617363\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\"×\" colname=\"c3\"\u003e \u003cp\u003e7.5×12×6\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e17.6\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e267.8\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e"},{"header":"Computational Modelling","content":"\u003cp\u003eThe eyeballs and the space between the manikin and the surrounding cube (shown in Fig.\u0026nbsp;5) are considered a computational domain. To study the flow field, the following assumptions are made: The airflow is incompressible and steady and around the manikin is in turbulent regime. The experiment of Clark and Toy [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e] showed that the flow is laminar around a standing nude human for height shorter than 0.9m with (T\u003csub\u003eskin\u003c/sub\u003e =306 K, T\u003csub\u003eair\u003c/sub\u003e=293 K, and Grashof number = 2×10\u003csup\u003e9\u003c/sup\u003e) but the regime becomes fully turbulent for a manikin taller than 1.5 m (Grashof number = 10\u003csup\u003e10\u003c/sup\u003e). The eyes are located on the head; therefore, assuming a turbulent flow around the manikin head is especially justified. It is assumed that the liquid flow in the eye anterior chamber is laminar because of the low velocity in the small anterior chamber.\u003c/p\u003e\u003cp\u003eThe physical properties of air are constant and determined at the film temperature. Boussinesq approximation is adopted for the density variation since the temperature difference is sufficiently small with βΔT \u0026lt; \u0026lt; 1 [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. The body force in these flows is only due to gravity.\u003c/p\u003e\u003cp\u003e \u003cb\u003eGoverning Equations\u003c/b\u003e \u003c/p\u003e\u003cp\u003ea) Temperature distribution inside the solid part of the eyeball is obtained by solving the following heat conduction equation [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]:\u003c/p\u003e\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$-\\nabla . \\left(k\\nabla T\\right)=A-B\\left(T-{T}_{bl}\\right)$$\u003c/div\u003e \u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003cp\u003ewhere T is temperature, k is thermal conductivity, T\u003csub\u003ebl\u003c/sub\u003e is blood temperature, A is the metabolic heat generation rate and B is the term associated with the blood perfusion rate. Only aqueous humor (AH) in the anterior chamber is considered liquid).\u003c/p\u003e\u003cp\u003eGoverning equations of conservation of mass, momentum, and energy for laminar flow of aqueous humor (AH) are expressed as:\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e\u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\nabla .\\overrightarrow{v}=0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(2)\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\rho (\\overrightarrow{v}\\bullet \\nabla\\)\u003c/span\u003e\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(3)\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\nabla \\bullet \\left(k\\nabla T\\right)-\\rho C\\left(\\overrightarrow{v } \\bullet \\nabla T\\right)=0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(4)\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003ewhere the Boussinesq approximation is used for density variation. Here, β is the fluid's volume expansion coefficient, C is heat capacity, and T\u003csub\u003eref\u003c/sub\u003e =34 ˚C is a reference temperature.\u003c/p\u003e\u003cp\u003eSeveral turbulence models are investigated to predict the thermal plume due to natural convection. The RNG k-ε model with three different types of boundary conditions (scalable wall function, enhanced wall treatment, low Reynolds) and the SST k-ω model were used in the present study. Among these models, the RNG k-ε model with enhanced wall treatment is better matched to the experimental data for the heat transfer coefficient over the body and no inconsistent jump over the contours. Therefore, this model was used for further simulations.\u003c/p\u003e\u003cp\u003eAll the testing steps are repeated for mixed convection, and the RNG k-ε model combined with the enhanced wall treatment option is selected for the rest of the simulations.\u003c/p\u003e\u003cp\u003eThe details of the continuity, momentum, energy, and the RNG k-ε turbulence model equations are not shown here for brevity, and they can be found in (ANSYS manual).\u003c/p\u003e\u003ch2\u003eBoundary Conditions\u003c/h2\u003e\u003cp\u003eTo investigate mixed convection heat transfer from the manikin, uniform air velocity with 6% turbulent intensity and 0.7 m length scale (approximately similar to the experimental conditions of De dear et al. [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]) is applied on the inlet boundary. Zero gradients for flow parameters are considered at the outlet boundary condition. Enhanced wall treatment boundary condition is used on wall surfaces such as the computational domain's manikin surface, bottom, upper and side walls. In addition, the symmetry and uniform velocity boundary conditions are also tested on the upper face and sides of the computational domain. Due to the use of sufficiently large computational domains, the effects of these different boundary conditions on the heat transfer from the manikin were found to be negligible. Therefore, the results can also resemble the outdoor conditions. Air with different velocities and temperatures as summarized in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e3\u003c/span\u003e, are used on the inlet boundary of the computational domain. Manikin surface temperature is assumed to be 34 ˚C.\u003c/p\u003e\u003cp\u003eWhen the ambient air speed is less than 0.2 m/s, the heat transfer from the human skin is mainly treated as natural convection. The force convection has also been simulated for a velocity higher than this. The selected range of air velocity (0.2-5 m/s) covers indoor and outdoor environmental conditions.\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eEnvironmental conditions for computations\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAir velocity (m/s)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eEnvironmental temperature (˚C)\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1.0\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5.0\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003eTo study natural convection conditions, a pressure inlet is applied on the side surfaces of the computational domain. Enhanced wall treatment is applied on the upper and lower surfaces of the domain.\u003c/p\u003e\u003cp\u003eAlso, a zero gradient type boundary condition is considered an outlet boundary condition on the upper surface of the computational domain.\u003c/p\u003e\u003cp\u003eNumerical simulations are performed for two ambient air temperatures of 0, 20 ˚C. To consider heat flux between parts of the cornea and sclera that have contact with the inside of the body, the following equation is applied, respectively:\u003c/p\u003e\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\"\u003e\u003cbr\u003e\u003c/p\u003e\u003cp\u003eIn this equation, the temperature of blood vessels T\u003csub\u003ebl\u003c/sub\u003e, near the sclera is assumed to be constant, h\u003csub\u003es\u003c/sub\u003e is the heat transfer coefficient between the inside of the body and the eye, B corresponds to the term associated with the blood perfusion rate, and A is the metabolic heat generation rate. Thermal properties and the quantities considered for Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e14\u003c/span\u003e) are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e4\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThermal properties of the biological materials of eye layers\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"9\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\" colspan=\"2\"\u003e \u003cp\u003eMaterial\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eDensity\u003c/p\u003e \u003cp\u003eρ(hg m\u003csup\u003e− 3\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eSpecific heat\u003c/p\u003e \u003cp\u003ec(J kg\u003csup\u003e− 1\u003c/sup\u003eK\u003csup\u003e− 1\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eThermal conductivity\u003c/p\u003e \u003cp\u003ek(W m\u003csup\u003e− 1\u003c/sup\u003eK\u003csup\u003e− 1\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003eBasal metabolism\u003c/p\u003e \u003cp\u003e(W m\u003csup\u003e− 3\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eBlood perfusion power equivalent\u003c/p\u003e \u003cp\u003e(W m-3 K-1)\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eCornea\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003e1050\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4178\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e0.58\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eSclera\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003e1050\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3800\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e0.58\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e22000\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e80000\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eAnterior chamber\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003e996\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3997\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e0.58\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eIris\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003e1050\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3600\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e0.52\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e10000\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e35000\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eLens\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003e1000\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3000\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e0.4\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eVitreous chamber\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003e1100\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4178\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e0.603\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"9\"\u003e\u003csup\u003ea\u003c/sup\u003e[\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd colspan=\"9\"\u003e\u003csup\u003eb\u003c/sup\u003e[\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePhysical parameters at the boundaries of the eye\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDescription\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eh\u003csub\u003es\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eBody heat transfer coefficient (W m\u003csup\u003e− 2\u003c/sup\u003e K\u003csup\u003e− 1\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e65\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT\u003csub\u003ebl\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eBlood temperature (˚C)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e37\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eE\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eEvaporation rate (W m\u003csup\u003e− 2\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e40\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eσ\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eStefan-Boltzmann constant (W m\u003csup\u003e− 2\u003c/sup\u003e K\u003csup\u003e− 4\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.67×10\u003csup\u003e− 8\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eε\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eEmissivity of corneal surface\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.975\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"4\"\u003e\u003csup\u003ea\u003c/sup\u003e [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003eNo slip boundary condition on the anterior chamber surface, which is assumed to be rigid and impermeable, is imposed. Mechanical properties of eye layers are considered homogenous and isotropic.\u003c/p\u003e\u003cp\u003eTo consider radiation heat transfer from the eye surface, the heat flux given as\u003c/p\u003e\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\"\u003e\u003cbr\u003e\u003c/p\u003e\u003cp\u003eis added to each element of the eye surface that is in contact with the environment. A UDF (User-defined function) was developed and incorporated into the ANSYS-FLUENT.\u003c/p\u003e\u003cp\u003eAccording to the previous studies of [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], the evaporation rate from a normal eye ranges from 40–100 W/m\u003csup\u003e2\u003c/sup\u003e. Here, the lowest value of E = 40 W/m\u003csup\u003e2\u003c/sup\u003e is used to obtain the highest temperatures in the eye. The evaporation heat loss is included using the same procedure used for the radiation heat transfer.\u003c/p\u003e\u003cp\u003eThe commercial fluid dynamic software package ANSYS-FLUENT is used for numerical simulation. An unstructured grid is developed for the environmental chamber around the manikin using the ANSYS (ICEM) software. To resolve the boundary layer around the eye, five layers of extruded triangular prisms are used with an initial size of 0.01 cm and a growth rate of 1.1 between the layers. Since the focus of the present study is the heat transfer from the eyes, most grid elements are placed around the head, particularly near the eyes, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e6\u003c/span\u003e. The grids are fine near the manikin and become course far from the manikin.\u003c/p\u003e\u003cp\u003eSince the enhanced wall treatment is used as the turbulent wall boundary condition, the value of y\u003csup\u003e+\u003c/sup\u003e should be less than 5 for the grid points adjacent to the manikin surface as a requirement for the used turbulence model. In these simulations, it is made sure that this condition is satisfied. For the case of natural convection with a body temperature of 34˚C and environmental temperature of 22 ˚C, the average value of y\u003csup\u003e+\u003c/sup\u003e for the first grid points near the manikin body is equal to 0.62.\u003c/p\u003e\u003cp\u003eTo generate a computational grid for the anterior eye chamber, a structured grid is used for the 2D geometry shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e7\u003c/span\u003e. Then, by rotating this grid around the optical axis, the 3D structured grid is created.\u003c/p\u003e\u003cp\u003eThe eye grid is integrated with the manikin grid using an unstructured grid in the cornea and sclera. To have a smooth transition between the structured grid inside the eye and the unstructured grid outside, rectangular elements on the outer surface of the structured grid are separated into two triangles by ANSYS (ICEM) software to be a base for the unstructured grid of cornea and sclera as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e8\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eThe grid independence study is performed for various grid sizes, and finally, the cases with about 5 and 6\u0026nbsp;million cells are selected for natural and mixed convection cases, respectively.\u003c/p\u003e"},{"header":"Validation of the Numerical Method","content":"\u003cp\u003eThere is no available experimental data for airflow around the manikin shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Therefore, to validate the computational model, the simulation results are compared with experimental and numerical data for airflow around another manikin and the liquid motion in a separate eye model.\u003c/p\u003e\u003cp\u003ea) Validation of the eye flow model\u003c/p\u003e\u003cp\u003eTo validate the simulation model for the aqueous humor flow in the eye, the velocity field in the anterior chamber for the thermal boundary conditions of Karampatzakis and Samaras[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] is simulated and the predicted velocity profile along the pupillary axis is compared with the numerical results of [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e9\u003c/span\u003e. This figure shows good agreement of the predicted velocity distribution with earlier simulation. The deviation seen is due to a slight difference between the two geometries.\u003c/p\u003e\u003cp\u003eThe maximum velocity reported for the numerical study of Karampatzakis and Samaras[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] is 3.36×10\u003csup\u003e− 4\u003c/sup\u003e (m/s). In the current work, the maximum velocity is 3.39×10\u003csup\u003e− 4\u003c/sup\u003e (m/s), which is quite close. But the second peak differs by a factor of 2. The details of the geometry of Karampatzakis and Samaras ([\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e] ) are not available and it was impossible to compare more information on the flow field.\u003c/p\u003e\u003cp\u003eb) Validation for natural convection around manikin:\u003c/p\u003e\u003cp\u003eTwo cases were studied for validating the natural convection flow simulations around the manikin.\u003c/p\u003e\u003cp\u003e1- The flow field and heat transfer of a manikin standing in the center of a box is investigated. A comparison of the present simulation results with the experimental data and numerical results of [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]for velocity magnitude along almost the plume centerline as a function of height from the floor is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e10\u003c/span\u003e. It is seen that there is an acceptable agreement of the present simulation results with the experimental measurements of [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThe Maximum plume velocities reported by Craven and Settle[\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e] for the experimental data and their numerical model, respectively, were 0.24 m/s and 0.20 m/s. The present simulation predicts a maximum velocity of 0.25 m/s, which agrees with the experiment measurement.\u003c/p\u003e\u003cp\u003e2- de Dear et al.[\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] reported the natural heat transfer coefficient of the head and the entire body for 12 K temperature differences, respectively, as 3.6 and 3.4 W/(m\u003csup\u003e2\u003c/sup\u003e.K). These values are close to the results of the present study of 3.36 and 3.12 W/(m\u003csup\u003e2\u003c/sup\u003e.K) to the heat transfer coefficients.\u003c/p\u003e\u003cp\u003ec) Validation for mixed convection flows around the manikin:\u003c/p\u003e\u003cp\u003eTo validate the results for mixed convection around the manikin, the experimental condition of de Dear et al.[\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] is applied to the present modeling and the results are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e11\u003c/span\u003e. In their experiment, the manikin surface temperature was equal to 34 ˚C and the ambient temperature was 20 ˚C. A general agreement between the present computational work and experimental measurements can be observed. The deviation is possibly due to different geometries for the manikins and experimental and numerical errors. The manikin in their work had hair and clothes. In addition, a large cylindrical drum (1.5 m tall and 0.5 m diameter) was installed upstream on the floor in the wind tunnel to generate large-scale eddies in the experiment. Also, Ono et al.[\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] reported that the convective heat transfer coefficient of a seated manikin for 1 (m/s) air velocity and 10% turbulent intensity is h\u003csub\u003ec\u003c/sub\u003e =12.9 (W/m\u003csup\u003e2\u003c/sup\u003e.K). This value is close to that in the current study, which is h\u003csub\u003ec\u003c/sub\u003e=11.95 (W/m\u003csup\u003e2\u003c/sup\u003e.K).\u003c/p\u003e"},{"header":"Results and Discussions","content":"\u003cp\u003eThe validated computational model is used and the airflow and temperature fields and heat transfer from a standing manikin with attached eyes for different environmental air velocities and temperatures are computed. Typical velocity distribution around the manikin for different air velocities and ambient temperatures are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e12\u003c/span\u003e. Although the thermal plume above the manikin head becomes different with an open-like boundary (like [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]), heat transfer and velocity around the eye does not change noticeably. Therefore, present results also can be used for outdoor conditions.\u003c/p\u003e \u003cp\u003eIn the case of natural convection, the velocity in the thermal plume reaches 0.8 m/s. The velocity behind the head is higher than that in the front of the head. The velocity close to the eye, which is the focus of this study, is less than 0.1 m/s. The velocity field changes considerably when the wind blows toward the manikin. A plume formed over the head for free convection, while for wind-blowing conditions, a large separation zone is observed on the back of the manikin. The velocity increases compared to the free stream and reaches almost 1.5 m/s between the legs and 1.3 m/s over the head. The air velocity close to the eye is around 0.3 m/s, which is three times that in the case of free convection.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;13 illustrates the velocity vectors in the vertical middle plane of manikin's left eye for different ambient air velocities and environmental temperatures. This figure shows that a circulation flow forms in the aqueous humor due to temperature differences across the anterior chamber. As expected, by increasing the air velocity and temperature difference between the body and the environment, the circulating flow in the anterior chamber becomes stronger due to increasing heat flux between the eye and the environment.\u003c/p\u003e\u003cp\u003eThe effect of environmental air velocity and temperature on the average convective heat transfer coefficient and average heat flux over the eye is summarized in Tables\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e8\u003c/span\u003e and \u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e9\u003c/span\u003e. The data in these tables show that the heat transfer coefficient and heat flux over the eye change significantly when the airflow velocity increases. According to Baldwin and Maynard [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e], air velocity in indoor conditions is approximately 0.3 m/s, and based on the current results, the convection heat transfer coefficient is h ̅ = 11 W/m\u003csup\u003e2\u003c/sup\u003e.K which is consistent with the values reported in [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], [\u003cspan additionalcitationids=\"CR22 CR23 CR24\" citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]\u0026ndash;[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e], [44]. This value, however, is valid only for indoor conditions and the heat transfer coefficient changes for different environmental conditions, as presented in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e8\u003c/span\u003e. According to the results, some investigators used very large convection coefficients ([\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e], [25]) such as 100 W m\u003csup\u003e\u0026minus;2\u003c/sup\u003e K\u003csup\u003e\u0026minus;1\u003c/sup\u003e which does not occur even in high air velocity and ambient temperature.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eTable\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e8\u003c/strong\u003e\u003cstrong\u003e.\u003c/strong\u003e Variation of average convective heat transfer coefficient (W/(m\u003csup\u003e2\u003c/sup\u003e.K)) of manikin eye.\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" width=\"439\" height=\"159\"\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e9\u003c/strong\u003e\u003cstrong\u003e.\u003c/strong\u003e Variation of average convective heat flux (W/m\u003csup\u003e2\u003c/sup\u003e) of manikin eye.\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" height=\"148\" width=\"442\"\u003e\u003c/p\u003e\u003cp\u003eContours of convective heat transfer coefficient and heat flux over the manikin head for 1 m/s ambient airflow velocity at the temperature of 20˚C are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e14\u003c/span\u003e. As expected, in the bulge (gibbosity) parts of the manikin, heat transfer is higher.\u003c/p\u003e \u003cp\u003eTemperature contours on the surface of the eye for different air velocities are shown in Fig.\u0026nbsp;15. It is seen that the temperature distribution on the eye surface is not uniform. As expected, due to the convexity of the cornea, the maximum heat transfer occurs in this region, and hence, minimum eye temperature appears on the cornea. The isotherm contours of the eye are elliptical, similar to the observation of [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. It is also seen that the far-field air temperature does not have a noticeable effect. This is because the thermal plume around the body controls the airflow and temperature fields near the head, and the temperature contours on the eye's surface do not change. For the mixed convection case, the far-field air temperature slightly affects the eye surface temperature, but the difference between far-field temperatures of 0˚C and 20˚small.\u003c/p\u003e \u003cp\u003eFor a more comprehensive examination of the fluctuations in human eye temperature, a calibrated thermographic camera was employed to capture thermal images of the subjects. The room temperature was rigorously maintained within a narrow range of \u0026plusmn;\u0026thinsp;0.1˚C by a control system comprising a computer, three thermocouples, and an air cooling and heating unit. Further details regarding the control room and the experimental procedures can be found in the work of Mahdavi and Yaghoubi [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. The room temperatures selected for this study were 20, 23, and 25˚C, with the corresponding thermal image of the eye displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e16\u003c/span\u003e. Notably, the observed temperature variations on the surface of the eye were minimal, supporting the assumption that the eye's temperature could be considered relatively constant at T\u0026thinsp;=\u0026thinsp;34˚C.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;17 shows the temperature distribution at the eye vertical mid-plane for different environmental air velocities and temperatures. The surface temperature of the eye and anterior regions of the eye increases slightly for higher ambient temperatures and lower air velocities. For a 20˚C difference in the environmental temperature, the surface temperature of the eye differs by 1˚C for the natural convection case and about 3˚C for the mixed convection case with an airflow velocity of 1 m/s.\u003c/p\u003e \u003cp\u003eThe convective heat transfer coefficient of the eye for manikin alone and manikin with attached eyes for different environmental air velocities and temperatures are presented in Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e10\u003c/span\u003e. When only the manikin without the eye globe is modeled, the temperature boundary condition is set on the uncovered surface of the cornea and sclera (34˚C). Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e10\u003c/span\u003e depicts the differences which shows the importance of solving the eye coupled with the surrounding parts of the manikin.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e10\u003c/strong\u003e\u003cstrong\u003e.\u003c/strong\u003e Average heat transfer coefficient (W/m\u003csup\u003e2\u003c/sup\u003e.K) of an eye for different models (T = 20 ˚C).\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" height=\"148\" width=\"440\"\u003e\u003c/p\u003e\n\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e11\u003c/span\u003e compares the effect of convection and radiation on the eye for different ambient air velocities and temperatures. It is seen that the convection and radiation heat fluxes are in the same order for low air velocities which correspond to the indoor conditions. With the free stream air velocity increase, the convection dominates the heat transfer from the eye compared with the radiation.\u003c/p\u003e \n\u003cp\u003e\u003cstrong\u003eTable\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e11\u003c/strong\u003e\u003cstrong\u003e.\u003c/strong\u003e Convective and radiative heat transfer rate (W/m\u003csup\u003e2\u003c/sup\u003e) from an eye at different ambient air velocities and temperatures.\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" height=\"176\" width=\"555\"\u003e\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eIn the present study, the airflow velocity and temperature distribution of flow around a manikin and inside the eye were simulated using a model for eyes connected to a standing manikin. The convective heat transfer coefficient and heat flux over the eye were evaluated for different ambient air velocities and temperatures. The simulation results showed:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eModeling the airflow surrounding the manikin, including the face and the eyes and solving coupled system with the motion of aqueous humor inside the anterior chamber of the eye leads to more accurate results. The coupled simulations make the predicted eye temperature distribution more similar to the experimental data.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe simulation results for air velocities in the range of 0 to 5 m/s and ambient temperatures of 0 and 20˚C showed that the convective heat transfer coefficient of the eye varied in the range of 4.7\u0026ndash;43.1 W/m\u003csup\u003e2\u003c/sup\u003e.K and the heat flux varied in the range of 115.4 W/m\u003csup\u003e2\u003c/sup\u003e to 1185.2 W/m\u003csup\u003e2\u003c/sup\u003e. Therefore, assuming a constant convective heat transfer coefficient irrespective of the environmental conditions is not appropriate for the thermal modeling of the eye. These results could be of interest to the reasons for the dryness of the eye due to an increase in heat transfer at high airflow velocities and low air temperatures.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eNatural convection due to temperature difference across the eye anterior chamber became markedly stronger by the increased air velocity and decreased air temperature. For the range of parameters studied, the maximum velocity of aqueous humor inside the anterior chamber of the human eye changed from 0.2 mm/s to 0.6 mm/s. That is, the variation in environmental conditions had a noticeable influence on the aqueous humor motion in the eyes.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eFor high air velocities and low ambient temperature, the convective heat transfer became dominant compared to evaporation and radiation from the eye.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eF.F. wrote the main manuscript text, Conducted research, performed literature review andM.Y. , G.A, O.A mentored the research process, edited the manuscript, and provided guidance on research direction. All authors reviewed the manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eMapstone R (1968) DhETERMINANTS OF CORNEAL TEMPERATURE*t\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMapstone R Ocular thermography\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eEfron N, Young G, Brennan NA (1989) Ocular surface temperature, \u003cem\u003eCurr Eye Res\u003c/em\u003e, vol. 8, no. 9, pp. 901\u0026ndash;906, [Online]. Available: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://europepmc.org/abstract/MED/2791634\u003c/span\u003e\u003cspan address=\"http://europepmc.org/abstract/MED/2791634\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTan JH, Ng EYK, Acharya UR (2011) Evaluation of topographical variation in ocular surface temperature by functional infrared thermography. 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Phys Fluids, 34, 2\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRahman MA, Rabbani M, Maruf MH, Islam A, Shihavuddin ASM (2022) Characterizing the Aging Process of the Human Eye: Tear Evaporation, Fluid Dynamics, Blood Flow, and Metabolism-Based Comparative Study, \u003cem\u003eBiomed Res Int\u003c/em\u003e, vol. 2022\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTang H, Qin Z, Wen B (2022) Geometric model and numerical study of aqueous humor hydrodynamics in the human eye, \u003cem\u003eComput Math Methods Med\u003c/em\u003e, vol. 2022\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLagendijk JJW (1982) A mathematical model to calculate temperature distributions in human and rabbit eyes during hyperthermic treatment. Phys Med Biol 27(11):1301\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eScott JA (1988) A finite element model of heat transport in the human eye. 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Math Comput Model 48:5\u0026ndash;6\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"eye, heat transfer, numerical modeling, manikin, natural convection, force convection","lastPublishedDoi":"10.21203/rs.3.rs-3997744/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3997744/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe eye is an important organ of the human body, and its physiology can change mainly due to the ambient air temperature and velocity. In this study, a three-dimensional computational model for airflow around a full-scale manikin and the flow inside the eye is developed and used to evaluate the heat removal from the manikin eyes due to natural and forced convection under different environmental conditions. For natural convection, it was assumed that the movement of surrounding air was only due to the buoyancy effect in the body's thermal plume. Uniform air velocity and temperature far from the manikin were assumed for combined natural and forced convection. For simulating the velocity and temperature distribution, equations of continuity, momentum, energy, and turbulence transport model were solved numerically. The results for specific conditions were compared with the available experimental data reported in the literature and acceptable agreement was found. The validated computation model was used for several simulations of wind velocities and air temperatures. It was found that the eye surface temperature distribution predicted by the present model is closer to the experimental data than the earlier numerical studies for detached eyeballs using a constant convective heat transfer coefficient. The present results showed that the convective heat transfer coefficient over an eye surface depends strongly on the airflow velocity and temperature near the head.\u003c/p\u003e","manuscriptTitle":"Heat Removal from a Human Eye for Different Environmental Conditions - A CFD Study Using a Full-Scale Manikin","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-03-05 16:33:12","doi":"10.21203/rs.3.rs-3997744/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"c8833f41-d447-4544-9865-d42ee9ea9730","owner":[],"postedDate":"March 5th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-04-15T14:27:35+00:00","versionOfRecord":[],"versionCreatedAt":"2024-03-05 16:33:12","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3997744","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3997744","identity":"rs-3997744","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}