Thermal analysis of convective-radiative porous fin heat sinks made from functionally graded materials using the Galerkin method

In this study, we enhance the cooling efficiency of electronic systems, addressing the increased heat dissipation due to high-performance microprocessors. The trend of miniaturization in electronics necessitates innovative thermal management solutions. Our research focuses on a convective-radiative porous heat sink embedded with functionally graded material (FGM), designed to improve cooling for consumer electronics. Using numerical simulations and the Galerkin Method to solve thermal models, we examine the thermal properties of FGMs following linear and power-law functions. We examine the effects of the FGM's inhomogeneity index, and convective and radiative parameters, on the thermal execution of the porous heat sink. Results indicate that increasing the inhomogeneity index and enhancing convective and radiative parameters significantly improve thermal efficiency. Additionally, the temperature gradient along the FGM fin remains minimal compared to conventional fins, regardless of the parameters. To validate our findings, we compare our thermal predictions from the Galerkin Method with results from the Runge-Kutta method combined with shooting and homotopy analytical methods, showing strong agreement. This study highlights the potential of convective-radiative porous heat sinks with FGM to significantly improve thermal management in electronic systems.