55 Pragna Mistry, D.C. Joshi International Journal of Computer & Mathematical Sciences IJCMS ISSN 2347 – 8527 Volume 6, Issue 7 July 2017 Comparison of Numerical Results A Boundary Layer Problem Of A Free Convection Over A Vertical Plate with a Variable Wall Temperature And Internal Heat Generation In A Pours Medium Saturated with a Non – Newtonian Fluid Pragna Mistry 1 Research Scholar, Department of Mathematics, VNSGU, Surat. Gujarat. India. Assistant Professor, Department of Mathematics, VNSGU, Surat. Gujarat. India. D.C. Joshi 2 Associate Professor, Department of Mathematics, VNSGU, Surat. Gujarat. India. ABSTRACT This work is focused on the study of the boundary layer analysis for the free convection flow over a vertical flat late embedded in a porous medium saturated by a power – law non-Newtonian fluid. We assume that the temperature is a function of the distance from the origin and there is an internal heat source within the porous medium. The conservation equations of mass, momentum and energy for a porous medium saturated with a non-Newtonian power-law fluid are transformed from partial differential equations into ordinary differential equations by using similarity transformation. These equations are solved numerically using the shooting technique and B-Spline Collocation methods and the results are compared. Comparison of numerical results with previously published work, are performed and good agreement is obtained. And then used to study the effect of the power-law temperature parameter and power-low fluid index on the heat transfer characteristics. KEYWORDS Convection heat transfer, B-Spline Collocation method, Non-Newtonian Fluid, Similarity Solution. INTRODUCTION Convection heat transfer from vertical surfaces and wedges embedded in porous media has been the subject of many investigations. This is due to the fact that these flows have many engineering and geophysical applications such as geothermal reservoirs, drying of porous solids, thermal insulation, enhanced oil recovery, groundwater pollution, and underground energy transport. The subject of thermal convection in porous media has gained increasing research interest during the past several decades. This is due to the presence of porous media in a wide range of geophysical and engineering applications of current interest. These applications include geothermal energy extraction drying processes, groundwater contamination, thermal energy storage, heat pipes, building insulation, separation processes in chemical industry, filtration processes heat transfer enhancement especially in high heat flux applications such as cooling of electronic equipment, to name just a few applications. A number of industrially important fluids such as molten plastics, polymers, pulps, foods and slurries and fossil fuels which may saturate underground beds display non-Newtonian fluid behavior. Non-Newtonian fluids exhibit a non-linear relationship between shear stress and shear rate. Chen and Chen have presented similarity solutions for free convection of non-Newtonian fluids over vertical surfaces in porous media. Mehta and Rao have investigated buoyancy induced flow of non-Newtonian fluids over a non-isothermal horizontal plate embedded in a porous medium. Also, Mehta and Rao have analyzed buoyancy-induced flow of non- Newtonian fluids in a porous medium past a vertical plate with non-uniform surface heat flux. Jumah and Mujumdar have considered free convection heat and mass transfer of non-Newtonian power-law fluids with