Application of the successive over relaxation method for analyzing the dusty flow over a surface subject to convective boundary condition

Abstract

Heat transport features of a dusty fluid flow within a resistive porous medium are numerically interpreted under the magnetohydrodynamic environment. Fluid and dust phase characteristics are overlooked against the preeminent parameters. The main concern, in this work, is to analyze how much the resistive porous media affects the dusty flow in the presence of Lorentz force. The use of convection boundary conditions will aid attain the desired heat transfer rate in engineering applications. The nonlinear partial differential equations governing the fluid and dust phase are transmuted into a system of coupled and highly nonlinear ordinary differential equations which are first discretized using central differences, and then tackled numerically using the successive over-relaxation (SOR) method. This technique creates an effective way to solve complex dynamical problems comprising highly nonlinear-coupled differential equations. The flow features of the concerned problem are explored for different parameters such as the magnetic field, the porosity of the medium, the relative density of the two phases, ratio of free stream velocity, specific heat capacity ratio of the fluid to the dust phase as well as Prandtl number. Our results may be helpful to understand the dusty airflow during storms, mud particles in canals, ponds, and rivers.