Unsteady hydromagnetic motion of non-miscible fluids via an inclined co-axial porous cylinders

It is known from the literature that there are several studies that have examined the motion of hydromagnetic fluid through various conduits under the assumption that induced magnetic and electric fields are negligible. However, when an electrically conducting fluid flows under the influence of an external magnetic field, then an electromotive force (EMF) is induced. This EMF pushes the charges, creating an induced current which generate its own magnetic field. These EMFs and induced currents further increased or decreased the separation of charges within the fluid element to achieve the electrical equilibrium state and hence affect the induced electric field within the fluid element. These induced electric and magnetic fields are inherently linked to the fluid motion and become significant when the magnetic Reynolds number is sufficiently large. The motivation behind the present work lies in understanding the complex interactions of magnetic fields with the motion of fluids when both the induced electric and magnetic fields are strongly coupled with the fluid flow. This work have investigated the unsteady hydrodynamic flow of electrically conducting immiscible micropolar–Newtonian fluids through an annular domain formed by two concentric, inclined cylinders and filled with porous media, in the presence of induced magnetic and electric fields. This model presents convection flow of immiscible fluids under the influence of a significant magnetic Reynolds number with thermal relaxation time and employs the Navier’s slip conditions for velocity at the cylinder’s boundaries. The transport of non-miscible fluids within a porous medium under the existence of externally imposed uniform magnetic field is governed by the Brinkman model, and the governing differential equations associated with the model are solved by the Laplace Transform Finite Difference (LTFD) method, along with the Stehfest algorithm for numerical inversion. The numerical solution of hydrodynamic properties, along with induced magnetic and electric fields, is displayed for various emerging parameters, such as permeability parameter, Hartmann number, magnetic Reynolds number, Prandtl number, and slip parameter. The noteworthy findings of the present investigation are that the impact of the magnetic Reynolds number on the immiscible fluids’ velocity is negligible at the interface region, and the influence of the magnetic interactions parameter is inversely proportional to the induced magnetic field. This study also concluded that by enhancing the Grashof number, the pressure gradient and flow rate are increased. Further, this study concluded that by increasing 50% of the Prandtl number, the interfacial temperature of non-miscible fluids is decreased by 35.32%, while an increase in thermal relaxation time results in an approximate 33.01% enhancement in the rate of heat transfer. The results of the present study may be applicable in liquid-metal cooling, fuel cells, and nuclear reactor cooling loops where managing convective and electromagnetic interactions in immiscible fluids through porous media systems is crucial.