Analysis of MHD Carreau fluid flow over a stretching permeable sheet with variable viscosity and thermal conductivity

An Analysis has been carried out to study the magnetohydrodynamic boundary layer flow of Carreau fluid with variable thermal conductivity and viscosity over stretching/shrinking sheet. The thermal conductivity and viscosity is considered to be vary linearly with temperature. By applying suitable similarity transformations, the constitutive equation of Carreau fluid along with energy and transport equations transformed to set of ordinary differential equations. The obtained problem is solved analytically by Homotopy Analysis Method (HAM). As increasing magnetic force, skin friction and heat transfer rate are decreased in the stretching case, while opposite effects are seem in the shrinking case. Similarly, increase in the Lewis number leads to a reduction in the concentration profile. furthermore, increasing the power index and the Weissenberg number leads to an increase in skin friction and a heat transfer rate in the case of stretching, while both are reduced in case of shrinking For validity purpose the problem is also solved numerically using BVP4C (Matlab routine). Analysis of results show that analytical and numerical solutions are in excellent agreement. Furthermore, the impacts of different fluid parameters such as the Weissenberg number We2, Magnetic parameter M2, Suction parameter s, Prandtl number Pr, Lewis number Le, Stretching/ Shrinking parameter B and the heat flux constants on the velocity, temperature and concentration profiles are investigated graphically.