New analytical solutions of the heat conduction equation obtained by utilizing a self-similar Ansatz are presented in cylindrical and spherical coordinates. Then, these solutions are reproduced with high accuracy using recent explicit and unconditionally stable finite difference methods. After this, real experimental data from the literature regarding a heated cylinder are reproduced using the explicit numerical methods as well as using Finite Element Methods (FEM) ANSYS workbench. Convection and nonlinear radiation are also considered on the boundary of the cylinder. The verification results showed that the numerical methods have a high accuracy to deal with cylindrical and spherical bodies; also, the comparison of the temperatures for all approaches showed that the explicit methods are more accurate than the commercial software.

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