Brinkman–Forchheimer model of creeping flow of electromagnetohydrodynamic micropolar fluid through a swarm of cylindrical particles: Cell model technique
Pramod Kumar Yadav, Priya Srivastava
Abstract
This paper deals with a heat transfer methodology to explore the electromagnetohydrodynamic (EMHD) flow of a micropolar fluid through a membrane composed of impermeable cylindrical particles covered by heterogeneous porous layer. Here, the authors assumed that the micropolar fluid's viscosity and the permeability of the porous medium are inversely proportional to temperature and position, respectively. In this work, the cell model technique is adopted to examine the motion of micropolar fluid. Here, the flow through cylindrical particles is due to a uniform pressure gradient, and an electric and magnetic field is applied in the radial and tangential directions of the cylinder, respectively. The Brinkman–Forchheimer equation is used to model the flow of micropolar fluid through the porous cylindrical particle. The exact solution of the present model is intractable due to the presence of a non-linear term with temperature-dependent viscosity, and hence the governing equations of the problem are solved by employing the implicit finite difference method (FDM). The numerical solution for the linear and angular velocities, temperature, Kozeny constant, and hydrodynamic permeability of membrane are displayed in graphical and tabular form for the various emerging parameters such as Hartmann number, slip parameter, apparent viscosity, Forchheimer parameter, and Brinkman number. The noteworthy findings of the present investigation are the suppressed Kozeny constant when the Brinkman number increased, while the hydrodynamic permeability is enhanced with increasing the Brinkman number. Additionally, it is observed that the hydrodynamic permeability of micropolar fluid is increased with increasing the strength of electric field. Conversely, an increase in the Forchheimer parameter leads to a decrease in the fluid velocity and an increase in the temperature of the micropolar fluid. The current study's findings have the potential to improve our comprehension of crucial industrial and medical applications.