In this paper, the steady two-dimensional hydromagnetic free convective flow of an incompressible viscous and electrically conducting fluid between two parallel vertical porous plates has been considered. The effect of induced magnetic field arising due to the motion of an electrically conducting fluid is taken into account. The governing equations of the motion are a set of simultaneous ordinary differential equations and their analytical solutions in dimensionless form have been obtained for the velocity field, the induced magnetic field and the temperature field. The expression for the induced current density has been also obtained. The effects of various non-dimensional parameters on the velocity profile, the induced magnetic field profile, the temperature profile and the induced current density profile have been shown in the graphs. It is found that the effect of suction parameter is to decrease the velocity field and induced current density while it has increasing effect on the induced magnetic field.
This article aims to explore the impressive impact of emerging parameters on transient fully evolved free convective flow inside a vertical cylinder containing a porous material. The mathematical formulation of the model related to the considered physical circumstance is presented under compatible boundary conditions. Closed-form solutions are received for the velocity field, the temperature distribution, mass flux, skin friction, and the Nusselt number in terms of Bessel functions and modified Bessel functions of the first kind. Impressive effects of parameters such as the Darcy number Da, Prandtl number Pr, viscosity ratio M, and also time t on both the velocity and temperature distribution have been explored employing graphs and tables. It is irradiated by analysis that flow erection, heat transfer rate, skin friction, and mass flux are admirably impacted by the Prandtl number, the Darcy number, viscosity ratio parameter, and time. It is found that both the velocity and temperature field profiles rise with the rising value of time and ultimately attain their steady state. Moreover, the Prandtl number and the viscosity ratio parameter reduce the velocity profiles, while the reverse phenomenon occurs with the Darcy number. K E Y W O R D S Darcy number, laminar flow, natural convection, porous medium
An analysis is performed for the steady MHD free convective flow between two vertical walls assuming that the fluid is viscous, incompressible, and electrically conducting. The impacts of the Newtonian cooling/heating and induced magnetic field have been considered in the mathematical formulation of the problem. The nondimensionalized simultaneous differential equations, governing the problem, have been solved analytically for the temperature, the velocity, and the induced magnetic field. The manifestations have been made for the induced current density, the skin-friction, and the mass flux. The impact of the Hartmann number, the Biot number, and the magnetic Prandtl number on the velocity, the induced magnetic field, and the induced current density diagrams have been presented by considering a temperature-dependent source/sink. It is inspected that the velocity, the induced magnetic field, and the induced current density diagrams have decreasing tendency with rise in the value of the Hartmann number. Further, it is also noticed that with enhancement in the magnetic Prandtl number the velocity diagram decreases, but the induced magnetic field and the induced current density diagrams have increasing nature. It is beheld that the impression of Newtonian cooling/heating is to reduce/raise the velocity as well as the induced magnetic field and the induced current density. The impacts of the governing parameters on the skin-friction and mass flux have also been concluded dealing with their numerical values given in the tables.
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