Thermo-magnetic interaction in a viscoelastic micropolar medium by considering a higher-order two-phase-delay thermoelastic model

This work aims to theoretically analyze the nonuniform heat transfer through a micropolar miniature half-space by investigating the magneto-thermo-viscoelastic interactions. To examine the micromechanical coupling and the influence of thermo-mechanical relaxation, a higher-order two-phase-lag thermoelastic concept and a viscoelastic model of Kelvin–Voigt type are considered. The theoretical framework has been extended to incorporate the Eringen’s nonlocal model to include the small-scale effects. The so-called Hall effect occurs in a conductive material when it is subjected to a high magnetic field orthogonal to the direction of the current traveling through it. Without nonlocality and viscoelastic effects, it is possible to achieve different types of generalized theories of thermoelasticity. The governing equations are developed and numerically solved using Laplace transforms. The Laplace transform is then inverted numerically using a method based on Fourier series expansion, and then the numerical values of physical fields are presented. The consequences of variations in nonlocality, viscoelasticity and the Hall effect are finally demonstrated and a comparison between the findings of this study and those for the generalized thermoelastic models are reported.