Analytical and Numerical Study of Temperature Distribution in Functionally Graded Fins

Abstract

This work investigates heat conduction in a functionally graded Fin subjected to gradual cooling/heating at its boundaries analytically and numerically. It is assumed that the thermal properties of the functionally graded material are coordinated changes in the fin length direction. The linear model is applied to determine the physical properties of the functionally graded materials. To analyze the thermal behavior of the heat sink, two approximate analytical methods are used: first, the method relies on the mean value theorem. The second method relies on the principle of equivalent properties. The Numerical solution carried by ANSYS APD depends on stepped variation of properties. The results showed that the factor of property ratio controls temperature levels where the temperature levels at the end of the functionally graded fin change exponentially with the factor of property ratio. The effect of functionally graded material starts within the length where the maximum effect appears at the fin's end. The maximum absolute error percentage between the analytical and numerical results is (6.756%), which means a good match between both solutions.