International Journal of Engineering Science Invention ISSN (Online): 2319 – 6734, ISSN (Print): 2319 – 6726 www.ijesi.org ||Volume 5 Issue 10|| October 2016 || PP. 49-66 www.ijesi.org 49 | Page MHD Mixed Convection Flow of casson Nanofluid over a Non- Linear Permeable Stretching Sheet in The Presence of Heat Generation or Absorption G Kamala*, Gangadhar K**, M. V Ramanamurthy*, P Suresh*** * Department of Mathematics & Computer Science, Osm,naia University, Hyderabad -7, Telangana, India, **Department of Mathematics, Acharya Nagarjuna University, Ongole, Andhra Pradesh -523001, India *** Department of Mathematics & Hmanities,Chaitanya Bharathi Institute Of Technology,Hyderabad-75, Telangana,India. Abstract: In this paper, numerical analysis has been carried out on the problem of magnetic hydro dynamic mixed convection flow of a Casson nanofluid past a nonlinear permeable stretching sheet with viscous dissipation in the presence of double stratification and heat generation or absorption. The governing partial differential equations were transformed into a system of ordinary differential equations using suitable similarity transformations. The resultant ordinary differential equations were then solved using Bvp4c mat lab solver. Effects of the physical parameters on the velocity, temperature and concentration profiles as well as the local skin friction coefficient, the heat and mass transfer rates are depicted in tabular form and discussed. The results indicate that the local Nusselt number decreases with an increase in both Brownian motion parameter (Nb) and the thermophoresis parameter (Nt). However the local Sherwood number (??) increases with an increase in the parameter Nb. But it decreases as the values of Nt increases. Besides it was found that the surface temperature of a sheet increases with an increase in the heat generation (Q>0) or absorption parameter (Q<0). Comparison of present results with previous reported results has been found in excellent agreement. Keywords: Nonlinear permeable stretching sheet, MHD, mixed convection, Casson nanofluid, double stratification. I. Introduction The flow over a stretching sheet is relevant to several important engineering applications in the field of metallurgy and chemical engineering process. These applications involve the cooling of continuous strips or filaments by drawing them through a quiescent fluid. The steady two dimensional boundary layer flow of Newtonian fluid over a stretching surface has been studied by Crane. After this pioneering work the flow field over a stretching surface has drawn considerable attention and a good amount of literature has been generated on this problem. Javad and Sina (2012) investigated the effect of viscous dissipation on non liner stretching sheet and they concluded that the dimensionless temperature increases with increases in the nonlinear stretching parameter n. Mukhopadhaya (2013) studied the boundary layer flow over a porous non-linearly stretching sheet with partial slip at the boundary and he concluded that the rate of transport is considerably reduced with increasing values of non-linearly stretching parameter. Khan et al. (2014) investigated the three dimensional flow and heat transfer over a non-linearly stretching sheet. Khan and Hashim (2015) investigated the boundary layer flow and heat transfer to carreau fluid over a non linear stretching sheet and they concluded that on increasing the values of stretching parameter was to thin the momentum boundary layer thickness; however the opposite trend was noted for thermal boundary layer thickness. Vijayalakshmi and Shankar (2016) studied the effect of thermal radiation on boundary layer flow of viscous fluid over nonlinear stretching sheet with injection or suction. Nanofluid is a new type of heat transfer fluid which contains a base fluid and nanoparticles. The term nanofluid is proposed by Choi (1995). The boundary layer flow and heat transfer over a permeable stretching sheet due to a nanofluid with the effect of magnetic field, slip boundary condition and thermal radiation have been investigated by Ibrahim and Shankar (2013) and they concluded that the local Nusselt number decreases with an increase in both Brownian motion parameter Nb and thermophoresis parameter Nt. However, the local Sherwood number increases with an increase in both thermophoresis parameter Nt and Lewis number Le, but it decreases as the values of Nb increase. Khan et al. (2014) studied the combined effects of Navier slip and magnetic field on boundary layer flow with heat and mass transfer of water-based nanofluid containing gyrotactic microorganisms over a vertical plate and they concluded that the magnetic field suppresses the dimensionless velocity and increases the dimensionless temperature inside the boundary layers. Lakshminarayana and Gangadhar (2014) concluded that the temperature and mass volume friction increases in the presence of thermophoresis parameter and the temperature increases and the mass volume friction decreases