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Computation of Non-Isothermal Reversed Stagnation-Point Flow over a Flat Plate
Vai Kuong Sin; Chon Kit Chio
Source PublicationComputational Simulations and Applications
Author of SourceJianping Zhu
Other Abstract

The full Navier-Stokes equations are difficult or impossible to obtain an exact solution in almost every real situation because of the analytic difficulties associated with the nonlinearity due to convective acceleration. The existence of exact solutions are fundamental not only in their own right as solutions of particular flows, but also are agreeable in accuracy checks for numerical solutions. In some simplified cases, such as two-dimensional stagnation point flows, by introducing coordinate variable transformation, the number of independent variables is reduced by one or more. The governing equations can be simplified to the non-linear ordinary differential equations and are analytic solvable. The classic problems of two-dimensional stagnation-point flows can be analyzed exactly by Hiemenz Hiemenz (1911), one of Prandtl’s first students. These are exact solutions for flow directed perpendicular to an infinite flat plate. Howarth Howarth (1951) and Davey Davey (1961) extended the two-dimensional and axisymmetric flows to three dimensions, which is based on boundary layer approximation in the direction normal to the plane. The similarity solutions for the temperature field were studied by Eckert Eckert (1942). Case corresponding a step change in wall temperature or in wall heat flux in laminar steady flows at a stagnation point has been also investigated by several authors (see Chao et al. Chao & Jeng (1965), Sano Sano (1981) and Gorla Gorla (1988)). Further, Lok et al. Lok et al. (2006) investigated the mixed convection near non-orthogonal stagnation point flow on a vertical plate with uniform surface heat flux, where the results published are very good with present value of θ(0) for the constant wall temperature boundary condition. On the contrary, reversed stagnation-point flow over an infinite flat wall does not have analytic solution in two-dimensional steady state case. The aim of this study is to investigate the unsteady viscous reversed non-isothermal stagnation-point flow, which is started impulsively in motion with a constant velocity away from near the stagnation point. A similarity solution of full Navier-Stokes equations and energy equation are solved by applying numerical method. Studies of the reversed stagnation-point flow have been considered during the last few years, as this flow can be applied in different important applications that occur in oil recovery industry, as shown in Fig.

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Document TypeBook chapter
CollectionFaculty of Science and Technology
AffiliationUniversity of Macau Taipa, Macao SAR, China
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Vai Kuong Sin,Chon Kit Chio. Computation of Non-Isothermal Reversed Stagnation-Point Flow over a Flat Plate:IntechOpen,2011.
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