Exact solutions of unsteady MHD free convection in a heat absorbing fluid flow past a flat plate with ramped wall temper
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RESEARCH
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Exact solutions of unsteady MHD free convection in a heat absorbing fluid flow past a flat plate with ramped wall temperature Raj Nandkeolyar1 , Mrutyunjay Das2 and Precious Sibanda1* * Correspondence: [email protected] 1 School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Scottsville, Pietermaritzburg, 3209, South Africa Full list of author information is available at the end of the article
Abstract Unsteady MHD free convection and mass transfer from a viscous, incompressible, electrically conducting and heat absorbing fluid flow past a vertical infinite flat plate is investigated. The flow is induced by a general time-dependent movement of the vertical plate, and the cases of ramped temperature and isothermal plates are studied. Exact solutions of the governing equations are obtained. The Sherwood number, Nusselt number and skin friction coefficients are obtained for both ramped temperature and isothermal plates. Some applications of practical interest are discussed for different types of plate motions. The numerical values of species concentration, fluid temperature and fluid velocity are displayed graphically whereas the numerical values of Sherwood number, the Nusselt number and skin friction are presented in tabular form, for different parameter values for both ramped and isothermal plates.
1 Introduction The investigation of the effects of a magnetic field on the flow of a viscous, incompressible and electrically conducting fluid is important in many practical applications, such as in MHD power generators and boundary layer flow control. Due to this fact, a large number of researchers have contributed to the literature on the flow of fluids in the presence of a magnetic field. Hayat et al. [] investigated the flow of a third-grade fluid on an oscillating porous plate in the presence of a transverse magnetic field. They obtained an analytic solution of the governing nonlinear boundary layer equations. Hayat et al. [] also obtained the exact solution of an oscillatory boundary layer flow bounded by two horizontal flat plates, one of which was oscillating in its own plate and the other was at rest. Seth et al. [] obtained the exact solution for the effects of Hall current on the rotating Hartmann flow in the presence of an inclined magnetic field. Magnetohydrodynamic free convection finds applications in fluid engineering problems such as MHD pumps, accelerators and flow meters, plasma studies, nuclear reactors, geothermal energy extraction, etc. Free convective flow past a vertical plate in the presence of a transverse magnetic field has been studied by several researchers. Kim [] studied the magnetohydrodynamic convective heat transfer past a semi-infinite vertical porous moving plate with variable suction. The combined effects of thermal and mass diffusion on the unsteady free convection flow of a viscous incompressible fluid over an ©2013 Nandkeolyar et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http
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