Two-dimensional boundary-layer flow and heat transfer over a wedge: numerical and asymptotic solutions

Abstract

The two-dimensional laminar boundary-layer flow of a viscous fluid and heat transfer is analyzed at arbitrary values of the exponent wall temperature and Prandtl number. This study is known to occur in several important classes of boundary-layer flow. The fluid flow outside the boundary-layer is approximated by a power of the distance from a leading edge and the flow is on an impermeable wedge. The steady non-dimensional partial differential equations with the physical boundary conditions are converted to a system of ordinary differential equations. Two methods are employed: the full nonlinear equations are solved numerically using the Keller-box method, and in order to support these results, we solve the linear system in an asymptotic limit. Both approaches give good agreement with each other in predicting the wall shear stress, the temperature gradient, velocity and temperature profiles. Our results show that there is a mutual interaction between wedge surface and fluid and the coupling between momentum and thermal boundary layers. It is observed further that, both thermal and momentum boundary layer thicknesses are found to be thinner for accelerated flows and smaller values of the Prandtl number. The results on wall shear stress and temperature gradients are found to decrease initially and become flatter as the Prandtl number increases. The present work shows that the results have various technological applications involving these kinds of flow.