Heat Transfer in a Porous Medium over a Stretching Surface 22 Jo urnal o f Me c hanic al Eng ine e ring , Vo l. ME 40, No . 1, June 2009 Tra nsa c tio n o f the Me c h. Eng . Div., The Institutio n o f Eng ine e rs, Ba ng la de sh HEA T TRA NSFER IN A PO RO US M EDIUM O V ER A STRETC HING SURFA C E W ITH INTERNA L HEA T G ENERA TIO N A ND SUC TIO N O R INJEC TIO N IN THE PRESENC E O F RA DIA TIO N Tamanna Sultana* 1 Institute of Natural Science, United International University (UIU), Dhaka-1209, Bangladesh Sumon Saha Department of Mechanical Engineering, The University of Melbourne, Victoria 3010, Australia Mohammad Mansur Rahman and Goutam Saha Department of Mathematics, University of Dhaka, Dhaka-1000, Bangladesh *Corresponding email: labsachin@gmail.com Abstract: Heat transfer in a porous medium over a stretching surface with internal heat generation and suction or injection has been analyzed numerically in the presence of radiation. In this analysis, the governing equations are transformed into a system of ordinary differential equations and solved them numerically using Nachtsheim-Swigert shooting iteration technique. The local similarity solutions for the flow and the heat transfer characteristics are presented graphically for various material parameters entering into the problem. The effects of the pertinent parameters on the local skin friction coefficient (viscous drag) and the Nusselt number (rate of heat transfer) are also displayed graphically. Keywords: Internal heat generation, suction, injection, radiation, Nusselt number. INTRODUCTION Boundary layer flow on continuous moving surface is a significant type of flow occurring in several engineering applications. Aerodynamic extrusion of plastic sheets, cooling of an infinite metallic plate in a cooling bath, the boundary layer along a liquid film in condensation processes and a polymer sheet or filament extruded continuously from a dye, or a long thread traveling between a feed roll and a wind-up roll, are examples for practical applications of continuous flat surface. As examples on stretched sheets, many metallurgical processes involve the cooling of continuous strips or filament by drawing them through a quiescent fluid and that in the process of drawing, when these strips are stretched. The flow field of a stretching wall with a power-law velocity variation was discussed by Banks 1 . Ali 2 and Elbashbeshy 3 extended the work of Banks 1 for a porous stretched surface with different values of the injection parameter. Gupta and Gupta 4 analyzed the stretching problem with constant surface temperature. Sriramula et al. 5 studied steady flow and heat transfer of a viscous incompressible fluid flow through porous medium over a stretching sheet. Pop and Na 6 studied free convection heat transfer of non-Newtonian fluids along a vertical wavy surface in a porous medium. Ali et al. 7 studied radiation effect on natural convection flow over a vertical surface in a gray gas. Following Mansour 8 studied the interaction of mixed convection with thermal radiation in laminar boundary layer flow over a horizontal, continuous moving sheet with constant suction/injection. Bakier and Gorla 9 considered the effect of thermal radiation on the mixed convection from horizontal surfaces in saturated porous media. Elbashbeshy and Bazid 10-14 re-analyzed the stretching problem discussed earlier by Elbashbeshy 3 including variable viscosity, internal heat generation, suction/injection and porous medium. Subhas and Veena 15 analyzed visco-elastic fluid and heat transfer in a porous medium over a stretching surface. In the present study, the thermal radiation interaction of the boundary layer flow over a stretching surface embedded in a porous medium with internal heat generation and suction or injection has been investigated. The similarity solutions have been Nomenclature C f Skin friction coefficient c p Specific heat at constant pressure h(x) Local heat transfer coefficient K Permeability parameter K ’ Permeability of the porous medium N Radiation parameter Nu x Nusselt number Pn Radiative Prandtl number Pr Prandtl number Q Volumetric rate of heat generation q r Rediative heat flux q w Heat flux Re x Local Reynolds number T Temperature within the boundary layer T w Temperature at the plate T ∞ Temperature outside the boundary layer u o Velocity of the plate v w Suction/Injection parameter u, v x and y velocity components x, y Cartesian co-ordinates Greek Symbols ș Dimensionless temperature ț Thermal conductivity ρ Density of the fluid ț 1 Mean absorption coefficient Ψ Stream function ȝ Coefficient of the dynamic viscosity ı 1 Stefan-Boltzmann constant Ș Similarity parameter Ȝ Heat generation or absorption parameter ȝ e Effective viscosity α c Thermal diffusivity of the porous medium IJ w Shear stress υ a Apparent kinematic viscosity