Heat conduction in a semi-infinite solid subject to time-dependent surface heat fluxes: an analytical study

A closed-form model for the computation of the transient temperature and heat flux distribution in the case of a semi-infinite solid of constant properties is investigated. The temperature and heat flux solutions are presented for time-dependent, surface-heat flux of the forms: (i) {Mathematical expression}, (ii) {Mathematical expression}, and (iii) {Mathematical expression}, where λ is a real number and ν is a positive real number. The dimensionless (or reduced) temperature and heat flux solutions are presented in terms of the Whittaker function, the generalized representation of an incomplete Gamma function I_α (b, x) which can also be expressed by the complementary error functions. It is also demonstrated that the present analysis covers some well known (classical) solutions as well as a family of new solutions for the heat transfer through a semi-infinite solid.