Abstract—The flow and heat transfer characteristics for natural convection along an inclined plate in a saturated porous medium with an applied magnetic field have been studied. The fluid viscosity has been assumed to be an inverse function of temperature. Assuming temperature vary as a power function of distance. The transformed ordinary differential equations have solved by numerical integration using Runge-Kutta method. The velocity and temperature profile components on the plate are computed and discussed in detail for various values of the variable viscosity parameter, inclination angle, magnetic field parameter, and real constant (λ). The results have also been interpreted with the aid of tables and graphs. The numerical values of Nusselt number have been calculated for the mentioned parameters. Keywords—Heat Transfer, Magnetic Field, Porosity, Viscosity I. INTRODUCTION ATURAL convection flow over vertical surfaces immersed in porous media has paramount importance because of its potential applications in soil physics, geohydrology, and filtration of solids from liquids, chemical engineering and biological systems. Study of fluid flow in porous medium is based upon the empirically determined Darcy’s law. Such flows are considered to be useful in diminishing the free convection, which would otherwise occur intensely on a vertical heated surface. In addition, recent developments in modern technology have intensified more interest of many researchers in studies of heat and mass transfer in fluids due to its wide applications in geothermal and oil reservoir engineering as well as other geophysical and astrophysical studies. Bejan and Khair [1] have studied the phenomenon of natural convection heat and mass transfer near a vertical surface embedded in fluid saturated porous medium. The effect of buoyancy force and thermal radiation in MHD boundary layer visco-elastic fluid flow over continuously moving stretching surface embedded in porous medium have been analyzed by Abel et al. [2]. An integral approach to the heat and mass transfer by natural convection from vertical plates with variable wall temperature and concentration in N.S. Tomer is with the Department of Applied Sciences and Humanities, itm University, Sector-23A, Gurgaon, Haryana 122 017, India (e-mail: tomar_ns@rediffmail.com ; phone: +919212080920; fax: + 91 124 2367488). Phool Singh is with the Department of Applied Sciences and Humanities, itm University, Sector-23A, Gurgaon, Haryana 122 017, India (e-mail: phool.singh24@gmail.com). Manoj Kumar is with the College of Basic Sciences and Humanities, G.B.Pant University of Agriculture and Technology, Uttarakhand-263145, India (e-mail: mnj_kumar2004@yahoo.com). porous media saturated with an electrically conducting fluid in the presence of transverse magnetic field has been studied by Cheng [3]. Sarangi et. al. [4] analyzed the unsteady free convective MHD flow and mass transfer of a viscous, incompressible, electrically conducting fluid past an infinite vertical, non-conducting porous plate with variable temperature. EL-Kabeir et. al. [5] analyzed natural convection from a permeable sphere embedded in a variable porosity porous medium due to thermal dispersion. Dual solutions in mixed convection flow near a stagnation point on a vertical porous plate are investigated by Ishak et. al. [6]. The steady two-dimensional laminar forced flow and heat transfer of a viscous incompressible electrically conducting and heat- generating fluid past a permeable wedge embedded in non- Darcy high-porosity ambient medium with uniform surface heat flux has been studied by Rashad and Bakier [7]. Abel et. al. [8] analyzed MHD flow and heat transfer to a laminar liquid film from a horizontal stretching surface. The effect of radiation on the heat and fluid flow over an unsteady stretching surface has been analyzed by El-Aziz [9]. Singh et. al. [10] studied the heat transfer over stretching surface in porous media with transverse magnetic field. Singh et. al. [11] and [12] also investigated MHD oblique stagnation-point flow towards a stretching sheet with heat transfer for steady and unsteady cases. Elbashbeshy et. al. [13] investigated the effects of thermal radiation and magnetic field on unsteady boundary layer mixed convection flow and heat transfer problem from a vertical porous stretching surface. The unsteady laminar magnetohydrodynamic (MHD) flow over a continuously stretching surface has been investigated by Ishak [14]. El-Aziz [15] investigated the flow and heat transfer over an unsteady stretching surface with Hall effect. Postelnicu [16] studied heat and mass transfer by natural convection at a stagnation point in a porous medium considering Soret and Dufour effects. The objective of the present study is to investigate the effect of various parameters like variable viscosity parameter, inclination angle, magnetic field parameter, and real constant (λ) on convective heat transfer along an inclined plate embedded in porous medium. The governing non-linear partial differential equations are first transformed into a dimensionless form and thus resulting non-similar set of equations has been solved using Shooting method technique. Results are presented graphically and discussed quantitatively for parameter values of practical interest from physical point of view. N.S. Tomer, Phool Singh and Manoj Kumar Effect of Variable viscosity on Convective Heat Transfer along an Inclined Plate Embedded in Porous Medium with an Applied Magnetic Field N World Academy of Science, Engineering and Technology International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering Vol:5, No:3, 2011 319 International Scholarly and Scientific Research & Innovation 5(3) 2011 scholar.waset.org/1999.7/1198 International Science Index, Physical and Mathematical Sciences Vol:5, No:3, 2011 waset.org/Publication/1198