A numerical study on heat transfer and MHD flow of a Newtonian through a porous channel—Local thermal nonequilibrium model

 Vast numbers of studies concentrate on the thermal equilibrium state whereas in many real-world applications the model exists in the nonequilibrium state. Also, local thermal non-equilibrium precisely represents the thermohydroflow characteristics. Therefore, the current study examines the heat transfer and fluid flow characteristics of the magnetohydrodynamic flow of a Newtonian fluid through a local thermal non-equilibrium (LTNE) porous channel in the presence of the induced magnetic field. The mathematical model of the prescribed flow encloses the coupled nonlinear equations which are difficult to approach analytically. Hence, they are solved numerically using the shooting method with the Newton–Raphson method. The implications of various physical parameters of the problem on fluid flow, induced magnetic field, current density, temperature profiles, and heat transfer are elucidated with the aid of plots and tables. From the examination, it is clear that the porous medium significantly influences the characteristics of the fluid flow. That is, the least value of the Darcy number is related to a higher momentum field. Another interesting phenomenon is that the induced magnetic field remarkably enhances when the Darcy number is high, whereas the process is contrary to the current density. The effect of LTNE on the flow characteristics and heat transfer ceases for higher values of inter-phase heat transfer coefficient and the ratio of thermal conductivities, which gives rise to the local thermal equilibrium (LTE) situation. Furthermore, the amount of heat transport is maximum in the LTE case compared to that of the LTNE case.