thermomechanical fractional model of two immiscible temhd

We introduce a mathematical model of unsteady thermoelectric MHD flow and heat transfer of two immiscible fractional second-grade fluids, with thermal fractional parameters αi and mechanical fractional parameters βi, i=1,2. The Laplace transform with respect to time is used to obtain the solution in the transformed domain. The inversion of Laplace transform is obtained by using numerical method based on a Fourier-series expansion. The numerical results for temperature, velocity, and the stress distributions are represented graphically for different values of αi and βi. The graphs describe the fractional thermomechanical parameters effect on the case of two immiscible fluids and the case of a single fluid.