Closed-form approximate solution for heat transfer analysis within functionally graded plate with temperature-dependent thermal conductivity

Abstract

This paper studies the steady-state heat transfer through a functionally graded plate in ultrahigh temperature environment. The thermal conductivity is assumed to be temperature-dependent and graded according to an exponential law through the thickness direction. The approximate analytical differential transformation method (DTM) is applied to evaluate the temperature distribution. The presence of the logarithmic nonlinearity in the differential equation is a problem that has not been encountered in the previous works involving heat transfer analysis. To handle this problem, the application of an appropriate algorithm is proposed. Subsequently, Newton Raphson method is applied to solve the nonlinearity of the radiative boundary condition. Fast convergence and good agreement of the results with those obtained by Ferrari’s method (FM) in a previous work are shown. The effect of different physical parameters on temperature distribution has been deeply analyzed. It is found that minor discrepancy occurs if the temperature-dependency of thermal conductivity is not taken into account.