Asymptotic and numerical solutions of three‐dimensional boundary‐layer flow past a moving wedge

Abstract

We consider a laminar boundary‐layer flow of a viscous and incompressible fluid past a moving wedge in which the wedge is moving either in the direction of the mainstream flow or opposite to it. The mainstream flows outside the boundary layer are approximated by a power of the distance from the leading boundary layer. The variable pressure gradient is imposed on the boundary layer so that the system admits similarity solutions. The model is described using 3‐dimensional boundary‐layer equations that contains 2 physical parameters: pressure gradient (β) and shear‐to‐strain‐rate ratio parameter (α). Two methods are used: a linear asymptotic analysis in the neighborhood of the edge of the boundary layer and the Keller‐box numerical method for the full nonlinear system. The results show that the flow field is divided into near‐field region (mainly dominated by viscous forces) and far‐field region (mainstream flows); the velocity profiles form through an interaction between 2 regions. Also, all simulations show that the subsequent dynamics involving overshoot and undershoot of the solutions for varying parameter characterizing 3‐dimensional flows. The pressure gradient (favorable) has a tendency of decreasing the boundary‐layer thickness in which the velocity profiles are benign. The wall shear stresses increase unboundedly for increasing α when the wedge is moving in the x‐direction, while the case is different when it is moving in the y‐direction. Further, both analysis show that 3‐dimensional boundary‐layer solutions exist in the range −1<α<∞. These are some interesting results linked to an important class of boundary‐layer flows.

Computational and asymptotic methods for three-dimensional boundary-layer flow and heat transfer over a wedge

“…The flow in three-dimensional flow is mainly dominated by potential flows U ¼ U 1 x and V ¼ V 1 y, which are further superposed into Uðx; yÞ ¼ U 1 x þ V 1 y, so that the condition on c can be removed [10], and was extended for the applied magnetic field in the boundary-layer flow [11]. Furthermore, that the outer mainstream flows were approximated by a power of distances from the leading boundary-layer edge, in the form Uðx; yÞ ¼ U 1 ðx þ yÞ m and V ¼ V 1 ðx þ yÞ m , where m is a constant [12] which will provoke significantly a different flow structure. We have extended the above work along with heat transfer over moving wedge possessing the horizontal velocity behaviors, we focus on the effects of pressure gradient on three-dimensional boundary-layer flows and heat transfer.…”