Abstract
This work investigates the unsteady natural convection flow of a viscous, incompressible and electrically conducting fluid near an infinite vertical plate with ramped temperature and ramped motion. A unified closed form solution is obtained for the velocity field and skin friction coefficient corresponding to the case when the magnetic field fixed relative to the fluid or the moving boundary. It is assumed that the boundary plate has a ramped temperature profile and ramped motion subject to a uniform transverse magnetic field under the supposition of negligible induced magnetic field. Exact solutions of energy and momentum equations are obtained using the Laplace transform techniques. Graphical representations are attained for different values of the Prandtl number, magnetic field and heat sink parameter. Results show that wall ramped temperature and ramped motion tend to decrease fluid temperature, velocity, Nusselt number and skin friction.
Highlights
Rossow [1] was the first to study the hydrodynamic behaviour of the boundary layer on semi-infinite plate in the presence of a uniform transverse magnetic field
It is assumed that the boundary plate has a ramped temperature profile and ramped motion subject to a uniform transverse magnetic field under the supposition of negligible induced magnetic field
The aim of the present study is to investigate the unsteady magneto hydrodynamic free convection flow of heat generating/absorbing electrically conducting fluid near a vertical plate with a ramped temperature and ramped motion
Summary
Rossow [1] was the first to study the hydrodynamic behaviour of the boundary layer on semi-infinite plate in the presence of a uniform transverse magnetic field. The study continues to receive attention in the literature due to their important industrial and technological applications such as early stage of melting and in transient heating of insulating air gap by input at the start-up of furnaces. It provides the flow mechanism in some types of solar heating and ventilating passive systems. The vertical circuit boards include heat generating elements, and this situation can be modelled by parallel heated plates with the upward flow in the intervening space [2] Industrial applications such as underground disposal of radioactive waste materials, storage of foodstuffs, exothermic and/or endothermic chemical reactions, heat removal from nuclear fuel debris and dissociating fluids in packed bed reactors, etc. Industrial applications such as underground disposal of radioactive waste materials, storage of foodstuffs, exothermic and/or endothermic chemical reactions, heat removal from nuclear fuel debris and dissociating fluids in packed bed reactors, etc. the heat generating/absorbing effects are of much significance
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