Analytical solution of thermal analysis of two-dimensional functionally graded plate

In this study, the closed form solution of the heat transfer problem of a two-dimensional heterogeneous plate under the influence of an external force in steady state is considered under general boundary conditions. It is assumed that the heat production and thermal conductivity of this plate, which is considered to be in steady state, change exponentially in two directions. The analytical solution of the inhomogeneous partial differential equation obtained under these conditions is obtained by using the separation of variables method. Arbitrary functions given in the boundary conditions are used to test the accuracy of the solution. The results are discussed on the graphs obtained according to different heat flux values.