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This article has been devoted to investigating the thermoelastic diffusion problem of an infinite medium. The simple and refined single/dual-phase-lag Green–Naghdi models with and without energy dissipation are proposed. The exact solution of thermodiffusion coupling equations has been obtained considering the regularity conditions. The distributions of the non-dimensional temperature, dilatation, displacement, stresses, concentration and chemical potential are obtained and illustrated graphically. The validity of results is acceptable by comparing all outcomes. Benchmark results are reported to help other investigators in their future comparisons.

Refined dual-phase-lag Green–Naghdi models for thermoelastic diffusion in an infinite medium