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 th...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.展开更多
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 eq...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.展开更多
We study the viscous flow over an expanding stretching cylinder.The solution is exact to the Navier–Stokes equations.The stretching velocity of the cylinder is proportional to the axial distance from the origin and d...We study the viscous flow over an expanding stretching cylinder.The solution is exact to the Navier–Stokes equations.The stretching velocity of the cylinder is proportional to the axial distance from the origin and decreases with time.There exists a unique solution for the flow with all the studied values of Reynolds number and the unsteadiness parameter.Reversal flows exist for an expanding stretching cylinder.The velocity decays faster for a larger Reynolds number and a more rapidly expanding cylinder.展开更多
We investigate a viscous flow over a cylinder with stretching and torsional motion.There is an exact solution to the Navier–Stokes equations and there exists a unique solution for all the given values of the flow Rey...We investigate a viscous flow over a cylinder with stretching and torsional motion.There is an exact solution to the Navier–Stokes equations and there exists a unique solution for all the given values of the flow Reynolds number.The results show that velocity decays faster for a higher Reynolds number and the flow penetrates shallower into the ambient fluid.All the velocity profiles decay algebraically to the ambient zero velocity.展开更多
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 ...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.展开更多
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 cl...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.展开更多
The boundary layer flow of power-law fluids over a shrinking sheet with mass transfer is revisited.Closed-form analytical solutions are found and presented for special cases.One of the presented solutions has an algeb...The boundary layer flow of power-law fluids over a shrinking sheet with mass transfer is revisited.Closed-form analytical solutions are found and presented for special cases.One of the presented solutions has an algebraic decay behavior.These analytical solutions might offer valuable insight into the nonlinear boundary layer flow for power-law fluids.展开更多
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 appl...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.展开更多
文摘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.
文摘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.
文摘We study the viscous flow over an expanding stretching cylinder.The solution is exact to the Navier–Stokes equations.The stretching velocity of the cylinder is proportional to the axial distance from the origin and decreases with time.There exists a unique solution for the flow with all the studied values of Reynolds number and the unsteadiness parameter.Reversal flows exist for an expanding stretching cylinder.The velocity decays faster for a larger Reynolds number and a more rapidly expanding cylinder.
基金by the NC Space Grant and the MeadWestvaco Corporation on projects of investigating liquid atomization of swirl atomizers.
文摘We investigate a viscous flow over a cylinder with stretching and torsional motion.There is an exact solution to the Navier–Stokes equations and there exists a unique solution for all the given values of the flow Reynolds number.The results show that velocity decays faster for a higher Reynolds number and the flow penetrates shallower into the ambient fluid.All the velocity profiles decay algebraically to the ambient zero velocity.
文摘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.
文摘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.
文摘The boundary layer flow of power-law fluids over a shrinking sheet with mass transfer is revisited.Closed-form analytical solutions are found and presented for special cases.One of the presented solutions has an algebraic decay behavior.These analytical solutions might offer valuable insight into the nonlinear boundary layer flow for power-law fluids.
文摘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.
