Fractional order heat conduction law in micropolar thermo-viscoelasticity with two temperatures

Abstract

Present work is concerned with the transient solution of a half-space problem in the context of fractional order micropolar thermo-viscoelasticity involving two temperatures whose surface is acted upon by a uniformly distributed thermal source. Medium is assumed initially quiescent. The formulation is applied to the fractional generalization of the Lord–Shulman theory with microstructure effects and the non-dimensional equations are handled by employing an analytical–numerical technique based on Laplace and Fourier transforms. The numerical estimates of the displacement, stresses and temperatures are computed for magnesium crystal like material and corresponding graphs are plotted to illustrate and compare theoretical results. All the fields are found to be significantly affected by the fractional parameter, viscosity and two temperature parameter. The phenomenon of finite speed of propagation is observed graphically for each field. Some particular cases have also been inferred from the present study.