Local Non-Similar Solutions for Boundary Layer Flow over a Nonlinear Stretching Surface with Uniform Lateral Mass Flux: Utilization of Third Level of Truncation

Abstract

The present study aims to examine the effects of uniform lateral mass flux on the boundary layer flow induced by a non-linearly stretching surface. For uniform mass flux, the boundary layer flow does not conform to a similarity solution. The problem may be resolved by the similarity solution only when the transverse velocity at the boundary of the porous stretching surface is of the form vw∼xp−12. In other words, the flow becomes non-similar; to date, this has not been reported in the literature. That is why, in the current study, the local-similarity approximation up to the third level of truncation is utilized to solve the problem. The pseudo-similarity variable, stream function and transformed streamwise coordinate are defined such that the continuity equation is identically satisfied, and the momentum equation reduces to a non-similar dimensionless boundary layer equation. We derived the non-similar equations of the first, second and third levels of truncations and compared the numerical results obtained from different levels of truncations. In order to find numerical solutions to these equations, the built-in MATLAB routine, known as bvp4c, is used. Further, all non-similar terms that appear in the momentum equations are retained without any approximations. The approximations are introduced only in the subsidiary equations and relative boundary conditions. For the case of suction, the rate of increase in the numerical values of skin friction coefficient obtained from the first level of truncation with increasing velocity index parameter is found to be underestimated, while overestimation is found in the case of injection. The numerical results that were obtained from the third level of truncations are plotted against the embedding physical parameters and are then discussed.