Thermoelastic diffusion phase-lag model for a layer with internal heat and mass sources

•Bulk thermoelastic diffusion perturbations with phase-lag effects are investigated in a multi-component continuum layer.•Algorithm is proposed for the analytical building of Green's functions.•Coupled fields and relaxation effects are demonstrated in three different calculation examples.•Heat and mass transfer laws in Cattaneoform in solids can describe relaxation processes nature with an acceptable accuracy level. This paper analyses a problem of unsteady bulk thermoelastic diffusion perturbations propagation in a multi-component layer. The local equilibrium model describes one-dimensional physical processes in the continuum. It includes the coupled equations of elastic medium motion, heat transfer and mass transfer with cross-diffusion effects. The model also considers phase-lag effects in a continuum with internal heat and mass sources. The unknown functions of displacement, temperature and concentration increments are investigated in the Green's functions and the boundary conditions integral convolution form. We use the integral Laplace transform to time and the Fourier expansion into series by a spatial coordinate to find Green's functions. It allows us to reduce the problem to a system of linear algebraic equations. The Fourier series coefficients originals are found using known theorems and operational calculus tables. The numerical algorithms used is minimised, and Green's functions are analytically found. Calculation examples are represented and analysed.