Analytical Investigation of Laminar Viscoelastic Fluid Flow over a Wedge in the Presence of Buoyancy Force Effects

Abstract

An analytical strong method, the homotopy analysis method (HAM), is employed to study the mixed convective heat transfer in an incompressible steady two-dimensional viscoelastic fluid flow over a wedge in the presence of buoyancy effects. The two-dimensional boundary-layer governing partial differential equations (PDEs) are derived by the consideration of Boussinesq approximation. By the use of similarity transformation, we have obtained the ordinary differential nonlinear (ODE) forms of momentum and energy equations. The highly nonlinear forms of momentum and energy equations are solved analytically. The effects of different involved parameters such as viscoelastic parameter, Prandtl number, buoyancy parameter, and the wedge angle parameter, which is related to the exponent $m$ of the external velocity, on velocity and temperature distributions are plotted and discussed. An excellent agreement can be seen between the results and the previously published papers for $f^{\prime \prime }(0)$ and ${\theta }^{\prime }(0)$ in some of the tables and figures of the paper for velocity and temperature profiles for various values of viscoelastic parameter and Prandtl number. The effects of buoyancy parameter on the velocity and temperature distributions are completely illustrated in detail.