Magnetohydrodynamic forced convection and heat transfer of a Casson fluid flow in an anisotropic porous channel with Isoflux boundaries

Theoretical analysis of magnetohydrodynamic fully developed forced convective flow and heat transfer characteristics of a non-Newtonian electrically conducting Casson fluid through a porous channel filled with anisotropic porous material bounded by two impermeable horizontal walls subject to constant heat flux applied to the outer walls is investigated. The extended Darcy-Brinkmann model govern the flow inside the porous channel and accounts for the presence of the inertia term, which allows for the no-slip boundary conditions at the walls. The principal axis of anisotropic permeability is oriented from 0 to π/2 radians. The equations governing the system are solved using the inbuilt “DSolve” in Mathematica 11.1 for the velocity and temperature profiles as well as the Nusselt number (Nμ), which characterizes the rate of heat transfer in the system. The effects of various parameters on the velocity, temperature and heat transfer profiles are displayed through graphs and discussed quantitatively. From the results we observed that the velocity profile reduced as the Casson parameter (ß), anisotropic ratio (Kr), orientation angle (φ), and Hartmann number (Hα) increased, whereas the velocity profile increased when the Darcy number (Dα) and apparent viscosity (λ) increased. Similarly, these variables also had similar effect on the temperature profile of the fluid. On the other hand, the heat transfer profile, as measured by Nusselt number, increased when the Casson parameter (ß), anisotropic ratio (Kr) and Hartmann number (Hα) increased, while increasing the orientation angle (φ) and apparent viscosity (λ) decreased the Heat Transfer Profile. Upon further investigation, the heat transfer profile was shown to be maximum along the path of least permeability in the anisotropic porous media under investigation.