Analysis of unsteady stagnation-point flow over a shrinking sheet and solving the equation with rational Chebyshev functions

作者：Foroutan Mohammadreza^*; Ebadian Ali; Najafzadeh Shahram

来源：Mathematical Methods in the Applied Sciences, 2017, 40(7): 2610-2622.

DOI：10.1002/mma.4185

• boundary layer flow
• rational Chebyshev functions
• dual solutions
• spectral methods
• stagnation-point flow

This paper investigates the nonlinear boundary value problem, resulting from the exact reduction of the Navier-Stokes equations for unsteady laminar boundary layer flow caused by a stretching surface in a quiescent viscous incompressible fluid. We prove existence of solutions for all values of the relevant parameters and provide unique results in the case of a monotonic solution. The results are obtained using a topological shooting argument, which varies a parameter related to the axial shear stress. To solve this equation, a numerical method is proposed based on a rational Chebyshev functions spectral method. Using the operational matrices of derivative, we reduced the problem to a set of algebraic equations. We also compare this work with some other numerical results and present a solution that proves to be highly accurate.

• 出版日期2017-5