Frontiers in Heat and Mass Transfer (FHMT), 5, 15 (2014) DOI: 10.5098/hmt.5.15 Global Digital Central ISSN: 2151-8629 EFFECT OF MAGNETIC FIELD ON INDIRECT NATURAL CONVECTION FLOW ABOVE A HORIZONTAL HOT FLAT PLATE Tapas Ray Mahapatra a , Sumanta Sidui b , Samir Kumar Nandy c* a Department of Mathematics, Visva-Bharati, Santiniketan - 731 235, India b Department of Mathematics, Ajhapur High School, Burdwan - 713 401, India c Department of Mathematics, A.K.P.C Mahavidyalaya, Hooghly – 712 611, India Abstract The effect of variable transverse magnetic field on steady two-dimensional indirect natural convection flow of an incompressible viscous fluid over a horizontal hot flat plate is theoretically studied. The governing partial differential equations are transformed into ordinary ones by similarity transformation and solved numerically using fourth order Runge-Kutta method with shooting technique. The results are obtained for the skin friction coefficient and the local Nusselt number as well as the dimensionless velocities, temperature for some values of the magnetic parameter (M) subject to either prescribed (constant or variable) surface temperature or prescribed (variable) heat flux. It is seen that the skin friction coefficient decreases with increase in M for all the cases. Keywords: Steady flow; Magnetic field; Indirect natural convection; Variable Heat Flux. 1. INTRODUCTION Flow past a hot vertical plate adjacent to a viscous fluid at a lower temperature is a simple example of natural convection flow. In this case the convection takes place in boundary layer originating at the lower edge of the plate. Heat transferred from the plate to the fluid leads to an increase in temperature of the fluid near the wall causing decrease in density there and gaining buoyancy fluid moves upwards along the plate. The free convection of heat from a heated vertical plate in a fluid has been extensible studied for many years. Squire (1953) gave a review of the work. Subsequently Ostrach (1953) studied numerical solution for the free convection flow around a heated vertical plate for a wide range of values of Prandtl number. However if the plate is horizontal the buoyancy has no component along its length and if the boundary layer exist it must be of a different kind. Natural convection flow of this different character can occur over a horizontal semi-infinite plate facing upward with temperature (  ) higher than that ( ∞ ) of the surrounding fluid (see Fig.1). In front of the plate, the temperature of the fluid is  ∞ everywhere so that in this static field, there is a pressure distribution p, satisfying,  =  ∞  ⁄ where  ∞ is the density of the fluid in this region. As heat is transferred from the plate to the fluid, the fluid temperature is larger than  ∞ above the plate and so the density () is less than  ∞ .The reduced pressure gradient |  ⁄ |=  <  ∞  gives rise to reduced pressure close to the plate. Thus there is a pressure drop along the plate which is taken as the x- direction. Due to this induced pressure gradient in the x-direction fluid flows parallel to the plate. This flow has a boundary layer character at large Grashof number and is known as indirect natural convection and was first studied by Stewartson (1958). The same problem was revisited by Gill et al. (1965). He pointed out that Stewartson's conclusion that boundary layer solution exist only when the heated plate faces downward is erroneous. They showed that boundary layer solution exists only when the heated plate faces upward and gave the correct solution to the * Corresponding author. Email: nandysamir@yahoo.com problem. On the other hand, Wickern (see in Schlichting (2000)) investigated natural convection flow over a horizontal plate subject to uniform heat flux. There are many studies about natural convection flow caused by immersing a hot surface in a fluid saturated porous medium at constant ambient temperature. Chamkha (2003) analyzed the heat and mass transfer laminar boundary layer flow in the presence of heat generation/absorption. Later, Chen (2004) investigated the heat and mass transfer effects of an electrically conducting fluid in magneto hydrodynamic natural convection adjacent to vertical surface. Ahmed (2010) studied the effects of chemical reaction and viscous dissipation on unsteady heat and mass transfer along an infinite vertical porous plate in the presence of magnetic field. On the other hand, Kim (2000) studied MHD natural convection flow past a moving vertical plate embedded in a porous medium. Siddiqa et al. (2010) investigated laminar natural convection flow of a viscous fluid over a semi-infinite flat plate inclined at a small angle to the horizontal. The natural convection boundary layer flow on a vertical surface in a porous medium with prescribed constant surface heat flux was considered by Merkin (2012). Very recently, a boundary layer analysis was performed for the steady laminar natural convection of a electrically conducting viscous incompressible fluid above a horizontal plate in the presence of a transverse magnetic field by Samanta and Guha (2014). In this paper we analyze the effect of variable transverse magnetic field on the steady two-dimensional indirect natural convection flow of an incompressible viscous fluid over a hot horizontal plate which is subject to either prescribed (constant or variable) surface temperature or prescribed (variable) heat flux. 2 FLOW ANALYSIS A sketch of the physical problem already described in the above introduction is given in Fig. 1, where the x−axis is taken along the plate with the origin at the front end of the plate and y−axis is perpendicular Frontiers in Heat and Mass Transfer Available at www.ThermalFluidsCentral.org 1