Construction and Investigation of the Third-Order Approximation to the Solution of the Heat-Conduction Equation for Thin Shallow Shells by Using Legendre Polynomials in the Case of Stationary Heat Exchange

By using the N th order approximation of temperature function and its first derivative by Legendre polynomials, we construct the solution of problem of heat conduction for a thin-walled shallow isotropic shell and deduce the system of resolving equations for the N th approximation. For the first and third approximations, we solve this problem for the case of concentrated heat sources. In the third approximation, we also construct the plots of the dependences of temperature on the distance to the heat source and on the curvature of the shell under the conditions of symmetric or asymmetric stationary heat exchange.