Effects of Maxwell velocity slip and Smoluchowski temperature conditions on thermal radiative MHD Fe_3O_4-Al_2O_3-Cu/H_2O tri-hybrid nanofluid flow past an exponential shrinking surface with entropy production: A stability analysis performance

Abstract This investigation aims to determine the existence of a dual solution in magnetohydrodynamic (MHD) thermal radiative tri-hybrid nanofluid flow over an exponential shrinking surface by considering mass suction effects at the surface. Furthermore, the impacts of Smoluchowski temperature and Maxwell velocity effects are taken into account. The products on various flow fields are examined for three different types of fluid: mono nanofluid ($Fe_3O_4$/$H_2O$), hybrid nanofluid ( $Fe_3O_4$-$Al_2O_3$/$H_2O$), and tri-hybrid nanofluid ($Fe_3O_4$-$Al_2O_3$-$Cu$/$H_2O$). Estimating entropy production is also included in the current work. The similarity transformation is used to translate the nonlinear partial differential equations (PDEs) into a set of ordinary differential equations (ODEs). The numerical MATLAB function bvp4c is utilized in the construction and solution of governing higher-order nonlinear ODEs. The stability of these numerical solutions is achieved by finding the lowest eigenvalue because of the duality present in the solutions. A minimum eigenvalue that is positive denotes the upper stable solution branch, whereas a minimal eigenvalue that is negative indicates the bottom unstable solution branch. A tabular and graphic analysis is conducted on the impact of emergent factors on temperature, skin friction coefficient, Nusselt number, entropy generation, etc. The results also demonstrate that when mono nanofluid changes to hybrid nanofluid and hybrid nanofluid to tri-hybrid nanofluid, the velocity and profile improve. It has been demonstrated that the fluid's temperature and the pace at which heat is transferred are greatly influenced by the thermal radiation parameter. The magnetic field aggravates flow in the case of a stable solution. The production of entropy is also accelerated considerably by thermal radiation. The current optimization technique offers a new and beneficial insight into the production of plastic films, heat exchangers, polymer sheets, crude oil, and electronic devices. Therefore, it is advised to use the results to create an industrial device setup.