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Analytical solutions of a coupled nonlinear system arising in a flow between stretching disks. (English) Zbl 1277.76024
Summary: We consider the axi-symmetric flow between two infinite stretching disks. By using a similarity transformation, we reduce the governing Navier-Stokes equations to a system of nonlinear ordinary differential equations. We first obtain analytical solutions via a four-term perturbation method for small and large values of the Reynolds number \(R\). Also, we apply the homotopy analysis method (which may be used for all values of \(R\)) to obtain analytical solutions. These solutions converge over a larger range of values of the Reynolds number than the perturbation solutions. Our results agree well with the numerical results of Fang and Zhang. Furthermore, we obtain the analytical solutions valid for moderate values of \(R\) by use of homotopy analysis.

MSC:
76D99 Incompressible viscous fluids
65N99 Numerical methods for partial differential equations, boundary value problems
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