Multi thermal relaxations for thermodiffusion problem in a thermoelastic half-space

•A novel model is presented to study thermoelastic diffusion behavior of a 1D half-space.•The RPL, G–L, L–S and classical models of thermoelasticity are mutual into a unified formulation.•The exact solution of motion, heat conduction and mass diffusion equations has been obtained.•Solutions are considered to define the thermoelastic diffusion behavior of the medium.•The validity of results is acceptable by comparing the present model with those due to other theories. This paper presents a novel multi-phase-lag model to study the thermoelastic diffusion behaviour of a one-dimensional half-space. The multi-phase-lag, the Green–Lindsay, the Lord–Shulman models as well as the classical theory of thermoelasticity are mutual into a unified formulation. The exact solution of three coupled equations, namely; motion, heat conduction and mass diffusion equations; has been obtained. Solutions determining for initial and boundary conditions are considered to define the thermoelastic diffusion behavior of the medium. The validity of results is acceptable by comparing the temperature, dilatation, displacement, stresses, concentration, and chemical potential according to the present multi-phase-lag theory with those due to other thermoelasticity theories.