Series Solution of Non-similarity Boundary-Layer Flows Over a Porous Wedge

Abstract

Solution of non-similarity boundary-layer flows over a porous wedge is studied. The free stream velocity U w (x) ∼ a x m and the injection velocity V w (x) ∼ b x n at the surface are considered, which result in the corresponding non-similarity boundary-layer flows governed by a nonlinear partial differential equation. An analytic technique for strongly nonlinear problems, namely, the homotopy analysis method (HAM), is employed to obtain the series solutions of the non-similarity boundary-layer flows over a porous wedge. An auxiliary parameter is introduced to ensure the convergence of solution series. As a result, series solutions valid for all physical parameters in the whole domain are given. Then, the effects of the physical parameters on the skin friction coefficient and displacement thickness are investigated. To the best of our knowledge, it is the first time that the series solutions of this kind of non-similarity boundary-layer flows are reported.

Flow of a Second Grade Fluid over a Stretching Surface with Newtonian Heating

“…It also gives us huge freedom to choose the initial guess and the linear operator for various problems. This method has been successfully applied to various nonlinear problems including [25][26][27][28][29][30][31][32][33][34][35]. The effect of Newtonian heating (NH) on the flow and heat transfer in the non-Newtonian fluids has not been reported so far.…”

Predictor homotopy analysis method and its application to some nonlinear problems

“…The HAM has been successfully applied to many nonlinear problems, such as 2-dimensional steady slip flow in microchannels [4], calculus of variations [5], Chen system [6], thin film flows of a third order fluid [7]. The powerful analytical method HAM has been already successfully applied to various complicated problems in science and engineering [8][9][10][11][12] and very recently in [13][14][15][16][17][18][19][20][21][22][23][24][25]. Also by traditional HAM the multiple solutions of some problems have been obtained [26][27][28].…”

Boundary layer flow of a Jeffrey fluid with convective boundary conditions

“…Second, to provide an analytic solution of the resulting nonlinear system. A series of solutions of mathematical problems is derived by homotopy analysis method [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. The convergence of obtained solution is ensured and the graphical results for the pertinent parameters are plotted and discussed.…”