Mixed convection in the stagnation point flow adjacent to a vertical surface in a viscoelastic fluid

An analytic technique, namely the homotopy analysis method (HAM), is applied to study the steady mixed convection in two-dimensional stagnation flows of a viscoelastic fluid around heated surfaces for the case when the temperature of the wall varies linearly with the distance from the stagnation point. The two-dimensional boundary layer equations governing the flow and thermal fields are reduced by appropriate transformations to a set of two ordinary differential equations. These equations are solved analytically using the HAM in the buoyancy assisting and opposing regions. It is found that, as for the Newtonian flow case, a reverse flow region develops in the buoyancy opposing flow region, and dual solutions are found to exist in that flow regime for a certain ranges of the buoyancy and viscoelastic parameters.