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Analysis of unsteady stagnation‐point flow over a shrinking sheet and solving the equation with rational Chebyshev functions
Author(s) -
Foroutan Mohammadreza,
Ebadian Ali,
Najafzadeh Shahram
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4185
Subject(s) - mathematics , laminar flow , mathematical analysis , chebyshev filter , boundary value problem , boundary layer , algebraic equation , stagnation point , nonlinear system , heat transfer , mechanics , physics , quantum mechanics
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.