Thermodiffusion interactions in a homogeneous spherical shell based on the modified Moore-Gibson-Thompson theory with two time delays

The main objective of the present paper is to investigate the relationship between the thermal processes and diffusion in thermoelastic solids. For this reason, a new model of thermo-diffusion interactions has been derived, which, unlike the traditional models, allows the thermo-diffusion waves to propagate at finite speeds. The Moore-Gibson-Thompson (MGT) equation is an essential part of the proposed model, as it is included in the mass diffusion and thermal conductivity equations by adding two relaxation times. The introduced model is then used to investigate a one-dimensional thermodiffusion problem for a homogeneous spherical shell. In the field of the Laplace transform, the analytical expressions for different transformed thermophysical fields are found. Moreover, a numerical inversion algorithm is used to obtain the physical domain solutions. The differences between the presented model and previous theories are graphically presented and discussed in detail. It is exhibited that depending on the relaxation time taken into account, the magnitude of the mass flow rate and heat waves can meaningfully change.

Automated summary

The main objective of this paper is to investigate the relationship between thermal processes and diffusion in thermoelastic solids. A new model that allows thermo-diffusion waves to propagate at finite speeds has been derived. The model is used to investigate a one-dimensional thermodiffusion problem for a homogeneous spherical shell, and analytical expressions for different transformed thermophysical fields are found. The differences between the presented model and previous theories are graphically presented and discussed.