http://www.iaeme.com/IJMET/index.asp 1216 editor@iaeme.com International Journal of Mechanical Engineering and Technology (IJMET) Volume 10, Issue 02, February 2019, pp. 1216-1225. Article ID: IJMET_10_02_126 Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=2 ISSN Print: 0976-6340 and ISSN Online: 0976-6359 © IAEME Publication Scopus Indexed MHD FLOW OVER A NONLINEARLY EXTENDING SURFACE ENTRENCHED IN A POROUS MEDIUM UNDER NONLINEAR RADIATION A. David Maxim Gururaj * , A.Manivannan, S.Dhanasekar and V.Parthiban Mathematics Division, School of Advanced Sciences, VIT University, Chennai, Tamilnadu, India *Corresponding Author ABSTRACT The prime objective of this paper is to investigate the steady, laminar, two dimensional hydromagnetic flows with heat transfer of an incompressible, viscous and electrically conducting fluid over a surface extending with a power-law velocity, entrenched in a porous medium under nonlinear radiation in the presence of a variable magnetic field. The radiative heat flux term is taken to be nonlinear using Rosseland diffusion approximation in general which is valid for small and large temperature difference the plate and the ambient fluid. Governing nonlinear partial differential equations are transformed to nonlinear ordinary differential equations by utilizing suitable similarity transformation. The resulting nonlinear ordinary differential equations for momentum and energy under linear and nonlinear radiation effects are solved numerically employing appropriate numerical schemes. The flow and thermal field sketches are found out and tabulated for various values of controlling factors involved in the problem. The non-dimensional rate of heat transfer and skin friction are also attained for diverse underlying factors and presented graphically. Keywords: Nonlinear Radaitive heat flux, Rosseland diffusion approximation, porous medium, Numerical schemes, Taylor series and nonlinearly extending surface Cite this Article: A. David Maxim Gururaj, A.Manivannan, S.Dhanasekar and V.Parthiban, Mhd Flow over a Nonlinearly Extending Surface Entrenched in a Porous Medium Under Nonlinear Radiation, International Journal of Mechanical Engineering and Technology, 10(2), 2019, pp. 1216-1225. http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&IType=2 1. INTRODUCTION A study of flow problem with heat and mass transfer over stretching porous surfaces has generated considerable interest because of its numerous industrial applications. Flow through