Dynamic Thermal Control of Nanofluid Systems: A Numerical Approach to Evaluate Performance of Proportional, Proportional-Integral, and Proportional-Integral- Differential Controllers in Hybrid Cooling Circuits

Dynamic Thermal Control of Nanofluid Systems: A Numerical Approach to Evaluate Performance of Proportional, Proportional-Integral, and Proportional-Integral- Differential Controllers in Hybrid Cooling Circuits | 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 Article Dynamic Thermal Control of Nanofluid Systems: A Numerical Approach to Evaluate Performance of Proportional, Proportional-Integral, and Proportional-Integral- Differential Controllers in Hybrid Cooling Circuits Farheen Zaman, Ashfaq Raveed, Aditto Arif Rahman, Rafi Bin Dastagir, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8816033/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 Purpose – This study numerically investigates the combined effects of a constant cooling circuit and a variable cooling circuit inside a square enclosure having vents with Al 2 O 3 -water nanofluid using P, PI, and PID controllers. Design/methodology/approach – The cavity contains two constant inlet ports, two controlled inlet ports, an outlet port, four isothermal cylindrical heat sources, and a temperature probe at the center of the cavity to evaluate the temperature and return feedback to the flow controllers continuously. The surrounding walls are at ambient temperature, and the nanofluid discharge is at ambient conditions at the outlet. The controllers control the inlet flow velocity and the oscillations, overshoot, settling tim e and steady state error in the values of the temperature (θ) taken nondimensionally at the center are analyzed. The governing Navier-Stokes and energy equations are solved through the Galerkin finite element method with appropriate initial and boundary conditions. Simulations were carried out for proportional gain ( K p = 0.001, 0.002, 0.003 ms −1 K −1 ), the integral gain ( K i = 0.011, 0.013, 0.015 ms −2 K −1 ), and the derivative gain ( K d = 0.0001, 0.0003, 0.0005 mK −1 ) for three different controllers. Calibration of different controllers (P, PI, and PID) is done in a systematic manner. Findings − The results illustrate that the PID controller yields the best thermal management. Using only the P controller, there always remains a steady state error, which is eliminated by the PI controller. The PI and PID controllers, on the basis of settling time and overshoot, have similar levels of performance. Originality/value – The evaluation of P, PI, and PID Controllers in Hybrid Cooling Circuits gives useful insights into optimal use of nanofluids and controllers for cooling and the techniques to optimize the controller parameters for enhanced thermal stability and performance commonly seen in microelectronics or bio-electronics. Physical sciences/Energy science and technology Physical sciences/Engineering Physical sciences/Mathematics and computing Physical sciences/Physics Nanofluid Heat Exchanger PID controller Variable Cooling Circuit Constant Cooling Circuit Electronic cooling Full Text 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-8816033","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":597729565,"identity":"6fc55ab4-58a2-48f3-8021-b6d523966a52","order_by":0,"name":"Farheen 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inlet ports, two controlled inlet ports, an outlet port, four isothermal cylindrical heat sources, and a temperature probe at the center of the cavity to evaluate the temperature and return feedback to the flow controllers continuously. The surrounding walls are at ambient temperature, and the nanofluid discharge is at ambient conditions at the outlet. The controllers control the inlet flow velocity and the oscillations, overshoot, settling tim\u0026nbsp;\u0026nbsp; e and steady state error in the values of the temperature (θ) taken nondimensionally at the center are analyzed. The governing Navier-Stokes and energy equations are solved through the\u0026nbsp; Galerkin finite element method with appropriate initial and boundary conditions. Simulations were carried out for proportional gain (\u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e = 0.001, 0.002, 0.003 ms\u003csup\u003e−1\u003c/sup\u003eK\u003csup\u003e−1\u003c/sup\u003e), the integral gain (\u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e = 0.011, 0.013, 0.015 ms\u003csup\u003e−2\u003c/sup\u003eK\u003csup\u003e−1\u003c/sup\u003e), and the derivative gain (\u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e = 0.0001, 0.0003, 0.0005 mK\u003csup\u003e−1\u003c/sup\u003e) for three different controllers. Calibration of different controllers (P, PI, and PID) is done in a systematic manner.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFindings \u003c/strong\u003e− The results illustrate that the PID controller yields the best thermal management. Using only the P controller, there always remains a steady state error, which is eliminated by the PI controller. The PI and PID controllers, on the basis of settling time and overshoot, have similar levels of performance.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eOriginality/value – \u003c/strong\u003eThe evaluation of P, PI, and PID Controllers in Hybrid Cooling Circuits gives useful insights into optimal use of nanofluids and controllers for cooling and the techniques to optimize the controller parameters for enhanced thermal stability and performance commonly seen in microelectronics or bio-electronics.\u003c/p\u003e","manuscriptTitle":"Dynamic Thermal Control of Nanofluid Systems: A Numerical Approach to Evaluate Performance of Proportional, Proportional-Integral, and Proportional-Integral- Differential Controllers in Hybrid Cooling Circuits","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-27 04:26:37","doi":"10.21203/rs.3.rs-8816033/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":"787ec61d-01fe-4ce8-ab61-eec6f25609c3","owner":[],"postedDate":"February 27th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":63610206,"name":"Physical sciences/Energy science and technology"},{"id":63610207,"name":"Physical sciences/Engineering"},{"id":63610208,"name":"Physical sciences/Mathematics and computing"},{"id":63610209,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2026-03-19T11:56:18+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-27 04:26:37","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8816033","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8816033","identity":"rs-8816033","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}