An analytical solution for the temperature field around a cylindrical surface subjected to a time dependent heat flux

The analytical solution for the temperature field in an infinite solid medium which surrounds a cylindrical surface, determined by Carlslaw and Jaeger for the case of constant heat flux, is extended to the case of any time dependent heat flux. Then, with reference to a sinusoidally varying heat flux, the analytical solution is employed to determine benchmark results for the time evolution of the dimensionless temperature of the surface. These results are used to check the accuracy of the numerical solutions obtained by two different commercial codes: the finite-element code COMSOL Multiphysics and the finite-volume code FLUENT.