Fiber-reinforced magneto-thermoelastic composite material with hyperbolic two-temperature, fractional-order three-phase lag and new modified couple stress theory

The paper aims to study the new modified couple stress theory in fiber-reinforced magneto-thermoelastic medium (FrMTM) with Hall current, rotation and with hyperbolic two-temperature (H2T) due to ramp-type heat. The Fourier's law of heat conduction with fractional-order (Fo) three-phase lag (TPL) derivative is used to form the model of the problem. Laplace and Fourier's transforms are used to solve this mathematical model. The displacement components, temperature change, couple stress and axial stress components are calculated in the transformed domain and have been converted in the physical domain with the numerical inversion technique. These physical quantities are drawn graphically using the MATLAB software to show the effects of the FoTPL theory for different values of fractional-order parameter alpha and different theories of thermoelasticity, namely, the FoTPL theory, the FoGN-III theory, the FoGN-II theory and the FoTPLGN-II theory.