Modeling And Analysis Of Magnetohydrodynamic Free Convection Turbulent Fluid Flow Past A Vertical Infinite Porous Plate

Abstract

Magnetohydrodynamic (MHD) as an important field of study has developed over several years since its first experiment by Michael Faraday in 1832. The study is very significant in a number of ways including Biomedical sciences, engineering, Geophysics, astrophysics, Power generation among many others. There has been challenges of communications, security, power electric outages, medical issues among many others that need to be addressed. In this study, two dimensional hydro magnetic free convective flow of an incompressible viscous and electrically conducting fluid flow that is turbulent and past a vertical infinite porous plate is considered. The effect of induced magnetic field arising as a result of fluid motion that is electrically conducting is also taken into account. A mathematical model of MHD free convection fluid flow that is turbulent and past a vertical infinite porous plate is developed. The flow is impulsively started after which the analysis of the flow problem is carried out and modeled using conservation of mass, conservation of energy and conservation of momentum equations. The arising nonlinear partial differential equations are then solved using the explicit finite difference scheme. Obtained results are presented graphically and the effects of flow parameters on velocities and temperature profiles discussed. Many researchers have done investigations on magnetohydrodynamics but in spite of all these, fluid flow that is turbulent past a vertical infinite porous plate has not received much attention. Little has been done on the porous media and other non- dimensional parameters for a turbulent flow past a vertical infinite porous plate. Simulation of the discretized equations were done using MATLAB. The impacts of flow parameters on velocities and temperature profiles such as Grashof number (Gr), Magnetic parameter (M), Hall parameter (m), Prandtl number (Pr) and Turbulent prandtl number(𝑃𝑟𝑡) analyzed. It is evident from the results that during both the cooling and heating of the plate (𝐺𝑟 > 0 𝑎𝑛𝑑 𝐺𝑟 < 0), the primary velocity decreases with decrease in Hall parameter, 𝑚, and increased magnetic parameter, 𝑀. It also decreases during cooling of the plate as the Prandtl number, 𝑃𝑟, is increased and even during the heating of the plate as the Prandtl number, 𝑃𝑟, is decreased. For 𝐺𝑟 > 0 𝑎𝑛𝑑 𝐺𝑟 < 0, the secondary velocity decreases with decrease in Hall parameter, 𝑚, and increase in magnetic parameter, 𝑀. It also decreases during cooling of the plate as the Prandtl number, 𝑃𝑟 is increased and also during heating of the plate as the Prandtl number, 𝑃𝑟 is decreased. The results also shows that there is no significant effect on temperature profile during both cooling and heating of the plate as the Hall parameter is decreased. There is also no significant change during the cooling of the plate as the magnetic parameter is increased and even during the heating of the plate as the magnetic parameter is decreased. It is also evident that there is a decrease in temperature profile,𝜃, when the Prandtl number is increased in both the cooling and Heating of the plate.