Jeffreys heat conduction in coupled semispaces subjected to interfacial heating

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 K-1,K-2, thermal diffusivities k(1,2), thermal relaxation times tau(1,2) and coefficients alpha(1,2) 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 K-1 root alpha(1) /k(1) and K-2 root alpha(2) /k(2) under Jeffreys heat conduction and due to the different ratio of K1/root k(1) tau(1) and K-2 /root k(2) tau(2) 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. (c) 2023 Elsevier Ltd. All rights reserved.

Automated summary

This paper defines a Jeffreys heat conduction problem for coupled semispaces with an interfacial heat source and derives an analytical solution using the Laplace transform approach. The asymptotic and parametric analysis reveals that Jeffreys heat conduction results in continuous variation of the contact temperature, while its particular case - Cattaneo heat conduction - causes a step change of the contact temperature at the initial time. The findings also show that the initial heat partition is determined by the ratios of thermal conductivities and diffusivities, as well as thermal relaxation times under different heat conduction types. The applicability of the solution is demonstrated through a simulation example of ultrashort laser pulse welding, highlighting the qualitative and quantitative impacts of heat conduction on contact temperature and heat fluxes.