Three-dimensional quasi-steady-state problem of moving heat and diffusion sources in an infinite solid

The three-dimensional quasi-steady-state temperature and moisture concentration induced by a constantly moving point heat source and a constantly moving point diffusion source in an infinite isotropic solid are derived. Here the thermodiffusion (Soret) and the diffusionthermo (Dufour) effects are taken into account in our modelling. It is observed that the obtained coupled set of partial differential equations can be decoupled into two independent differential equations for two newly introduced functions, whose solutions can be expediently derived in a moving coordinate system which moves together with the point source. The results show that two positive effective diffusivities are needed to describe the hygrothermal field. Numerical results are presented to illustrate the distributions of the hygrothermal Green’s functions. This research can be considered as an extension of the well-known Jaeger–Rosenthal solution for a moving heat source to the more complex situation in which there exists coupling between heat and moisture. In the Appendix we also present the temperature and the moisture concentration induced by instantaneous heat source and diffusion source by using the known result of an instantaneous heat source and the decoupling methodology presented in this research. Some interesting physical interpretations are presented for the instantaneous heat source and instantaneous diffusion source.