Stationary temperature fields in the anisotropic ring plates of variable thickness considering the heat exchange with external environment

The solution of the axisymmetric stationary problem of the heat conductivity for profiled polar-orthotropic annular plates considering the heat exchange with external environment through the bases is presented. Thermophysical characteristics of the material of the plate are assumed to be temperature-independent. The temperature values on the contours of the annular plate are given. There are no internal heat sources in the plate. The temperature distribution in such plates will be axisymmetric. Analytical solutions of the stationary heat conductivity problem for the following anisotropic annular plates are presented: the plate of constant thickness, the back conical and the conical plate. The Volterra integral equation of the second kind corresponding to the given differential equation of the stationary heat conductivity for profiled anisotropic annular plates is written to obtain the solution in the general case. The kernels of the integral equation for anisotropic annular plates of power and exponential profiles are given explicitly. The solution of the integral equation is written by using the resolvent. It is indicated that due to the presence of irrational functions in the kernels of the integral equation it is necessary to apply numerical methods in the calculation of iterated kernels or numerically solve the Volterra integral equation of the second kind. A formula for the calculation of temperatures in anisotropic annular plates of an arbitrary profile is given.