www.tjprc.org editor@tjprc.org International Journal of Mathematics and Computer Applications Research (IJMCAR) ISSN(P): 2249-6955; ISSN(E): 2249-8060 Vol. 4, Issue 2, Apr 2014, 75-88 © TJPRC Pvt. Ltd. UNSTEADY FREE CONVECTION FLOW THROUGH A POROUS MEDIUM PAST A VERTICAL PLATE WITH CONSTANT SUCTION AND HEAT SINK UNDER THE EFFECT OF A MAGNETIC FIELD L. HARI KRISHNA 1 & R. RAMAKOTESWARA RAO 2 1 Assistant Professor, Department of Mathematics, Annamacharya Institute of Technology & Science, Rajampeta, Kadapa, Andhra Pradesh, India 2 Principal, Annamacharya Institute of Institute of Technology & Science, Rajampeta, Kadapa, Andhra Pradesh, India ABSTRACT In this paper, the unsteady MHD free convective flow through a porous medium bounded by an infinite vertical porous plate with heat sink is investigated. Approximate solution for the velocity field, temperature field, mean skin friction and mean rate of heat transfer are obtained. The effects of various emerging parameters on the velocity field, temperature field, mean skin friction and mean rate of heat transfer are discussed through graphs and tables in detail. KEYWORDS: MHD, Darcy Number, Source, Heat Sink 1. INTRODUCTION The problems in heat transfer have so many applications in Engineering Sciences such as the design of cooling systems for motors, generators and transformers. Chemical engineers are concerned with the evaporation, condensation, heating and cooling of fluids. An understanding of the laws of heat flow is important to structures and to the architect in the design of buildings. To estimate the cost, the feasibility and the size of the equipment necessary to transfer a specific amount of heat in a given time, detailed heat transfer analysis must be made. The dimensions of boilers, heaters, refrigerators and heat exchangers depend not only on the amount of heat to be transmitted but rather on the rate at which heat is to be transmitted under given conditions. It follows that in almost every branch of engineering, heat transfer problems are encountered which cannot be solved by thermodynamic reasoning alone but require an analysis based on the science of heat transfer. In the recent years, the problem of free convective unsteady flow through a porous medium bounded by an infinite vertical porous plate has attracted the attention of number of researcher because of its possible application in design of steam displacement process in an oil recovery and various geothermal systems. The free convective unsteady flow past an infinite porous plate with heat source was studied by Pop and Soundalgekhar [1]. Free convective flow of a electrically conducting fluids past a semi-infinite flat plate under influence of a magnetic field has been studied by Gupta [2] and Singh and owling [3]. MHD free convective flow with Hall current in a porous medium for electro solution was analyzed by Sattar and Alam [4]. Sahoo et al. [5] have studied MHD unsteady free convective past an infinite vertical plate with constant suction and heat sink. The study of unsteady hydro magnetic free convection flow of viscous incompressible and electrically conducting fluid past an infinite vertical porous plate in presence of constant suction and heat absorbing sinks has been discussed by