A generalized magnetohydrodynamic two-phase free convection flow of dusty Casson fluid between parallel plates

This article aims to investigate the combined effects of the heat transfer and magnetic field on the electrically conducting magnetohydrodynamic two-phase free convective flow of dusty Casson fluid between parallel plates. The flow is caused by buoyancy force with heat transfer due to free convection. Moreover, the left plate moves at uniform velocity while the right plate is stationary, and all dust particles with spherical forms are scattered evenly throughout the fluid. Mathematically, the flow is described as partial differential equations. A newly introduced fractional derivative, namely Caputo-Fabrizio fractional derivative, is used to generalize the given derived system of PDEs. The problem is solved using joint applications of finite sine Fourier and Laplace transforms. Exact solutions of velocity and temperature profile are obtained. Moreover, the impact of different parameters like a magnetic parameter, Grashof number, Dusty fluid parameter, Casson parameter, Peclet number, Reynold number, and particle's mass parameter on temperature, and dust particle and Casson fluid velocity have been discussed. The graphical results for Casson fluid, dusty fluid, and temperature profiles are plotted through Mathcad-15. The behavior of Casson fluid and dusty fluid is matching for different embedded parameters. Moreover, the Nusselt number and skin friction are also determined. It is shown in Table 1 that by increasing the value of the peclet number, the rate of heat transfer decreases. Furthermore, Table 2 shows that by increasing the magnetic parameter, the skin friction decreases. Graphical results conclude that fractional Casson fluid model described a more realistic aspect of the both (Fliud and dust particle) velocities profile, temperature profile, rate of heat transfer and skin friction than the classical Casson fluid model.