The wave equations for simultaneous heat and mass transfer in moving media—Structure testing, time-space transformations and variational approach

Abstract

The functionals leading to the linear wave equations that govern heat conduction as well as simultaneous heat and mass transfer in moving media (in Eulerian representation) are obtained. These functionals are found simply by substituting equations of the time-space transformations into the functional of a quiescent medium which, in the general case, contains some matrix function as an important term. This function is associated with the matrix of the relaxation coefficients that appear in a general flux-force relationship, equation (41), which generalizes the Cattaneo equation [1] for a multipotential case and which evolves into the classical Onsager [2]expression when the relaxation effects are neglected. A synthesis of the linear wave equations and corresponding variational principles is obtained together with many new results. The logically self-consistent mathematical theory of simultaneous heat and mass transfer involving relaxation effects is developed and its direct application to thermal diffusion in a two-component fluid is given. This theory shows, in matrix notation, an important and remarkable analogy to the theory of pure heat conduction with non-Fourier heat flux.