A homotopy analysis solution to unidirectional heat transfer through a functionally graded plate with temperature-dependent thermal conductivity under constant heat flux

This paper investigates a functionally graded plate with temperature-dependent thermal conductivity. The plate is exponentially graded through its thickness and is subject to a constant and uniform heat flux. The Homotopy Analysis Method (HAM) is employed to obtain the temperature profile. Besides, convergence of the solution is studied by providing the h-curves. Furthermore, the accuracy of this technique is verified via comparing the results with those obtained using the software Mathematica and acceptable agreements have been achieved. Finally, the nonlinear thermal response of the plate to the heat flux is considered.

کلیدواژه ها:

functionally graded plate ، temperature-dependent thermal conductivity ، Homotopy analysis method ، Constant heat flux