Abstract
Unsteady as well as steady natural convection flow in a vertical channel in the presence of uniform magnetic field applied normal to the flow region and temperature dependent variable thermal conductivity is studied. The nonlinear partial differential equations governing the flow have been solved numerically using unconditionally stable and convergent semi-implicit finite difference scheme. For steady case, approximate solutions have been derived for velocity, temperature, skin friction, and the rate of heat transfer using perturbation series method. Results of the computations for velocity, temperature, skin friction, and the rate of heat transfer are presented graphically and discussed quantitatively for various parameters embedded in the problem. An excellent agreement was found during the numerical computations between the steady-state approximate solutions and unsteady numerical solutions at steady-state time. In addition, comparison with previously published work is performed and the results agree well.
Highlights
In recent years, the interest in the study of hydromagnetic flow in a channel region has been growing rapidly because of its extensive engineering applications
This study provided the basic knowledge for the development of many MHD devices, such as MHD pumps, MHD generators, brakes, flow meters, plasma studies, and geothermal energy extraction
The present paper is committed to study unsteady as well as steady natural convection flow of a viscous, incompressible fluid between two parallel vertical walls in the presence of transverse magnetic field and temperature dependent variable thermal conductivity when convection between the vertical parallel walls is set up by a change in the temperature of the walls compared to the fluid temperature
Summary
The interest in the study of hydromagnetic flow in a channel region has been growing rapidly because of its extensive engineering applications. Unsteady free convection heat transfer with MHD effects in a channel region can be found in [2]. An exact solution for unsteady hydromagnetic free convection flow with constant heat flux is to be found in [10]. (see [19]) studied steady MHD flow with variable thermal conductivity over an inclined radiative isothermal permeable surface. To the best of our knowledge, the problem of unsteady/ steady hydromagnetic convective flow between two vertical walls heated symmetrically/asymmetrically in the presence of variable thermal conductivity has not been studied. The present paper is committed to study unsteady as well as steady natural convection flow of a viscous, incompressible fluid between two parallel vertical walls in the presence of transverse magnetic field and temperature dependent variable thermal conductivity when convection between the vertical parallel walls is set up by a change in the temperature of the walls compared to the fluid temperature
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