Temperature fields generated by a circular heat source (CHS) in an infinite medium: Analytical derivation and comparison to finite element modeling

Abstract

This paper is the first in a series of papers describing the temperature fields created by a circular area heat source (CHS) in various situations. In this paper, the derivation of the solution of the 3D transient heat flow from an embedded finite CHS supplying heat to an infinite medium is shown by employing different methods. The different adopted techniques include Laplace, Hankel and Fourier Cosine transforms, and solutions are based on first principles with minimum assumptions. Both isotropic and orthotropic infinite media are considered. Finite element simulations performed in COMSOL Multiphysics are provided and compared with the analytical solutions, with deviations between analytical solution and simulation of <1 mK for a typical temperature rise of 1 K. Fitting of the numerical results with the analytical solutions is performed to extract the thermal transport properties of the media, which are found to deviate by a maximum of 1.7% for all considered cases.