LAUSR

Abstract Main objective of this frame work is to establish the modeling and simulation of mix convection flow along a vertically heated sheet filled with water. Two important mechanisms: magneto-hydrodynamics and porous medium are also considered within the restricted domain of the fluid flow. Temperature is controlled with the wall temperature and then mathematical model is constructed in the form of PDEs. To determine the similarity solution results are obtained via two different techniques. Numerically solutions are obtained with the help of shooting technique and then validate with the help of optimal homotopy analysis method (OHAM). Obtained analytical and numerical results are validated graphically. Effect of emerging parameters are plotted for velocity and temperature profiles. It is found that for mixed convection parameter ( ξ 0 ) , velocity profile depicts the increasing behavior for various values of power index m. However, for ξ > 0 , velocity profile shows the decreasing behavior with respect the parameter m. Temperature distribution in the restricted domain depicts the decreasing behavior for both m and ξ .