New exact analytical solutions for the transient surface temperature of solids subjected to a non-uniform axisymmetric circular heat source

Abstract

This paper presents a set of new explicit analytical solutions for determining the transient surface temperature of semi-infinite solids subjected to a non-uniform axisymmetric circular heat source. The uniform heat flux, semi-elliptic one and flux with singularity (equivalent to a uniform temperature in steady-stae) are considered. These solutions are simple to use and can therefore be applied in many industrial areas such as electronic components, laser treatments and any problem of diffusion other than heat transfer. They can also be used to study the constriction phenomenon. Validations of these analytical solutions by comparison with numerical modeling are performed and show an excellent agreement. We show that for the same case of heat flux distribution, surface temperatures at two different radii can be connected by an explicit analytical transfer function which does not require the knowledge of the flux imposed by the heat source.