Mathematical Analysis of Magnetically Controlled Ferrofluid Transport for Electronic Thermal Systems

Abstract

The increasing thermal demands of modern electronic devices have intensified the need for efficient and controllable heat transfer mechanisms capable of sustaining system reliability and performance. In this study, a mathematical model is developed to investigate magnetically controlled ferrofluid transport in an electronic thermal system using an electrically conducting Fe₃O₄-water nanofluid flowing through a chemically reactive porous channel. The model incorporates the combined effects of magnetohydrodynamics (MHD), thermal radiation, variable electrical conductivity, porous resistance, and species diffusion on the transport behavior of the ferrofluid. Hybrid constitutive relations are employed to evaluate the effective viscosity and thermal conductivity of the nanofluid in order to capture nanoparticle interaction effects more accurately. The governing equations for momentum, energy, and concentration transport are transformed into dimensionless form using the Brinkman model. Analytical solutions are then obtained using the Laplace transform technique to derive closed-form expressions for velocity, temperature, and concentration distributions. The influence of important dimensionless parameters, including Reynolds number, Hartmann number, Prandtl number, Schmidt number, radiation parameter, chemical reaction parameter, and nanoparticle volume fraction, is investigated in detail. The results indicate that increasing nanoparticle concentration significantly enhances thermal conductivity and temperature distribution within the electronic cooling domain, while strong magnetic fields suppress fluid velocity due to Lorentz force effects. The radiation parameter is found to influence thermal boundary layer development, whereas higher Schmidt and Prandtl numbers reduce concentration and temperature diffusion respectively. Furthermore, chemical reaction effects contribute to species depletion and flow suppression within the porous medium. The present analytical model provides valuable physical insight into coupled magneto-thermal transport mechanisms and offers a predictive framework for the design and optimization of advanced electronic cooling systems employing ferrofluid technology.