MHD micropolar fluid flow in porous media

Abstract

The analysis of mass and heat transfer in magnetohydrodynamic (MHD) flows has significant applications in heat exchangers, cooling nuclear reactors, designing energy systems and casting and injection processes of different types of fluids. On the other hand, extraction of crude oil, the flow of human or animal blood, as well as other polymer fluids or liquid crystals are just some examples of micropolar fluid flows. Due to the broad application spectrum of the theory of micropolar fluid flows, and the significance the impact the external magnetic field has on the flow of these fluids, this paper considers the stationary flow of a micropolar fluid between two plates under the influence of an external magnetic field which is perpendicular to the direction of the flow. Stationary plates are maintained at constant and different temperatures, while the whole problem is considered in the non-inductive approximation. The equation system used to define the physical problem under consideration is reduced to the system of differential equations that have been solved analytically and the solutions of which are of general nature. In addition to the solutions for velocity, microrotation and temperature, the paper gives solutions for shear stress at plates, the Nusselt number and flow rate. The provided solutions have been applied in order to reach some general conclusions about the influence of the magnetic field and physical characteristics of a micropolar fluid and the characteristics of porous media on the nature of micropolar fluid flows in porous media by means of chart analysis. General conclusions, obtained in the result analysis in this paper, give us the opportunity to understand the flows of micropolar fluids and highlight their significance.