Exact Solution of Steady-state Heat Conduction for Axisymmetric Functionally Graded Circular Plate

Abstract:

An exact analysis of steady-state heat conduction was presented for the axisymmetric functionally graded circular plate. Based on the basic equation of heat conduction of an orthotropic functionally graded circular plate, assuming that the heat conductivity has the exponential dependence on the plate-thickness direction, an exact solution was obtained for the axisymmetric functionally graded circular plate subjected to arbitrary thermal loads on its upper and lower surfaces by means of variable separation method. With the variation of material graded distributions and plate-thickness, the influence of the temperature field distributions of the circular plate was studied through a numerical example. The obtained exact solution could serve as a benchmark result to assess other approximate methodologies.