Modified equations of heat transfer and diffusion in solids

Abstract: We discuss heat and mass transfer equations based on modified relationships for heat flux (Fourier's law) and diffusing impurity flux (Fick's law). It is shown that the proposed modification leads to second-order elliptic equations that describe the change in profiles of temperature and impurity concentration with a finite velocity. One-dimensional heat transfer processes in plates are considered as an example.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysisexactly solvable and integrable systemsfluid dynamics

Audience: researchers in the topic

Mathematical models and integration methods