Modeling the magneto-thermoelastic diffusion in four-phase-lags memory dependent heat transfer

Abstract

Our present work aims to deal with a conceptual structure to investigate the generalized magneto-thermodiffusion relations in an isotropic medium in the context of four-phase lag thermoelastic model using a memory-dependent derivative (MDD). In this new model, the traditional Fourier’s heat conduction law and Fick’s mass diffusion law have been modified by introducing an improvised Taylor’s series expansion, which assimilates the MDD and incorporates four phase lags (FPL) generalized thermoelastic model. Utilizing the Laplace transformation technique as a mechanism, the control equations are presented in the Laplace domain, where they are decoded by incorporating a finite element (Galerkin) approach. The impact of the FPL parameters in several studied fields like stresses, temperature, and chemical potential has been demonstrated in the presence of MDD and magnetic field. A comparison of the results for different models like classical thermo-elasticity model, Lord-Shulman model, and FPL model is presented.