Thermal impedance and transient temperature due to a spot of heat on a half-space

Analytical solutions are proposed in this paper to calculate the thermal impedance and transient temperature in a semi-infinite body subjected to a heat spot. Two cases of uniform and non-uniform heat flux are considered. These solutions are developed using integral transforms and are given in exact expression forms, without any restrictive hypothesis. They include special functions such as Bessel, Struve and hypergeometric functions. Many softwares to treat these functions are available (eg. Maple, Mathematica and others). The solutions are validated through comparisons with available models treating particular cases. The transient temperatures and impedances are presented for different spatial distributions of the heat flux dissipated by the spot.