Two-Dimensional Heat Conduction Problem in a Functionally Graded Plate with a Slanting Boundary to the Functional Gradation

This article presents analytical results for temperature in a functionally graded material plate (FGMP) with a slanting boundary to the functional gradation subjected to a partial heating. The heat conductivity is expressed in terms of a exponential function of the position. The general solution of the heat conduction equation for FGMP with a slanting boundary to the functional gradation is derived by use of the variable separation method and the analytical solution, which satisfies the boundary condition is obtained. Numerical calculations are carried out for ZrO2/Ti-6Al-4V and ZrO2/stainless (SUS304) functionally graded plates, when the ceramic surface is partially heated. Temperature and heat flux are graphically displayed for these two cases.