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The magnetohydrodynamic (MHD) flow under slip conditions over a shrinking sheet is solved analytically. The solution is given in a closed form equation and is an exact solution of the full governing Navier-Stokes equations. Interesting solution behavior & observed with multiple solution branches for certain parameter domain. The effects of the mass transfer, slip, and magnetic parameters are discussed. 相似文献
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An analytical solution to the famous Falkner-Skan equation for the magnetohydrodynamic (MHD) flow is obtained for a special case, namely, the sink flow with a velocity power index of -1. The solution is given in a closed form. Multiple solution branches are obtained. The effects of the magnetic parameter and the wall stretching parameter are analyzed. Interesting velocity profiles are observed with reversal flow regions even for a stationary wall. These solutions provide a rare case of the Falkner-Skan MHD ... 相似文献
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The magnetohydrodynamic(MHD) flow induced by a stretching or shrinking sheet under slip conditions is studied.Analytical solutions based on the boundary layer assumption are obtained in a closed form and can be applied to a flow configuration with any arbitrary velocity distributions. Seven typical sheet velocity profiles are employed as illustrating examples. The solutions to the slip MHD flow are derived from the general solution and discussed in detail. Different from self-similar boundary layer flows, the flows studied in this work have solutions in explicit analytical forms. However, the current flows require special mass transfer at the wall, which is determined by the moving velocity of the sheet. The effects of the slip parameter, the mass transfer at the wall, and the magnetic field on the flow are also demonstrated. 相似文献
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The unsteady viscous flow over a continuously shrinking surface with mass suction is studied. The solution is fortunately an exact solution of the unsteady Navier-Stokes equations. Similarity equations are obtained through the application of similarity transformation techniques. Numerical techniques are used to solve the similarity equations for different values of the mass suction parameters and the unsteadiness parameters. Results show that multiple solutions exist for a certain range of mass suction and unsteadiness parameters. Quite different flow behaviour is observed for an unsteady shrinking sheet from an unsteady stretching sheet. 相似文献
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An analytical solution to the famous Falkner-Skan equation for the magnetohydrodynamic (MHD) flow is obtained for a special
case, namely, the sink flow with a velocity power index of −1. The solution is given in a closed form. Multiple solution branches
are obtained. The effects of the magnetic parameter and the wall stretching parameter are analyzed. Interesting velocity profiles
are observed with reversal flow regions even for a stationary wall. These solutions provide a rare case of the Falkner-Skan
MHD flow with an analytical closed form formula. They greatly enrich the analytical solution for the celebrated Falkner-Skan
equation and provide better understanding of this equation. 相似文献
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A liquid film flow over a flat plate is investigated by prescribing the unsteady interface velocity. With this prescribed surface velocity, the governing Navier–Stokes(NS) equations are transformed into a similarity ordinary differential equation, which is solved numerically. The flow characteristics is controlled by an unsteadiness parameter S and the flow direction parameter Λ. The results show that solutions only exist for a certain range of the unsteadiness parameter, i.e., S≤1 for Λ =-1 and S≤-2.815877 for Λ = 1. In the solution domain,the dimensionless liquid film thickness β decreases with S for both the cases. The wall shear stress increases with the decrease of S for Λ =-1. However, for Λ =-1 the shear stress magnitude first decreases and then increases with the decrease of S. There are no zero crossing points for the velocity profiles for both the cases. The profiles of velocity stay either positive or negative all the time, except for the wall zero velocity. Consequently,the vertical velocity becomes a monotonic function. To maintain the prescribed velocity, mass transpiration is generally needed, but for the shrinking film case it is possible to have an impermeable wall. The results are also an exact solution to the full NS equations. 相似文献
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