Analysis of unsteady stagnation‐point flow over a shrinking sheet and solving the equation with rational Chebyshev functions |
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Authors: | Mohammadreza Foroutan Ali Ebadian Shahram Najafzadeh |
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Affiliation: | Department of Mathematics, Payame Noor University, Tehran, Iran |
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Abstract: | 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. Copyright © 2016 John Wiley & Sons, Ltd. |
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Keywords: | boundary layer flow rational Chebyshev functions dual solutions spectral methods stagnation‐point flow |
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