Jeffreys heat conduction in coupled semispaces subjected to interfacial heating

Abstract

A Jeffreys heat conduction problem for coupled semispaces subjected to the action of an interfacial heat source was defined. An analytical solution of the problem was derived for a polynomial specific power of the heat source using the Laplace transform approach. The asymptotic and parametric analysis was performed for different ratios of thermal conductivities K1,2, thermal diffusivities k1,2, thermal relaxation times τ1,2 and coefficients α1,2 indicating the relative contribution of Fourier heat conduction. It was found that Jeffreys heat conduction results in continuous variation of the contact temperature, whilst its particular case — Cattaneo heat conduction — is accompanied by a step change of the contact temperature at the initial time. Another finding is that the initial heat partition occurs due to the ratio of K1α1/k1 and K2α2/k2 under Jeffreys heat conduction and due to the different ratio of K1/k1τ1 and K2/k2τ2 under Cattaneo heat conduction. The solution applicability was demonstrated on the simulation example of ultrashort laser pulse welding. The type of heat conduction was revealed to have qualitative and quantitative impacts on the contact temperature and heat fluxes.