Unsteady Laminar Boundary Layer Forced Flow in the Region of the Stagnation Point on a Stretching Flat Sheet
This paper analyses the unsteady, two-dimensional stagnation point flow of an incompressible viscous fluid over a flat sheet when the flow is started impulsively from rest and at the same time, the sheet is suddenly stretched in its own plane with a velocity proportional to the distance from the stagnation point. The partial differential equations governing the laminar boundary layer forced convection flow are non-dimensionalised using semi-similar transformations and then solved numerically using an implicit finitedifference scheme known as the Keller-box method. Results pertaining to the flow and heat transfer characteristics are computed for all dimensionless time, uniformly valid in the whole spatial region without any numerical difficulties. Analytical solutions are also obtained for both small and large times, respectively representing the initial unsteady and final steady state flow and heat transfer. Numerical results indicate that the velocity ratio parameter is found to have a significant effect on skin friction and heat transfer rate at the surface. Furthermore, it is exposed that there is a smooth transition from the initial unsteady state flow (small time solution) to the final steady state (large time solution). Keywords—Forced flow, Keller-box method, Stagnation point, Stretching flat sheet, Unsteady laminar boundary layer, Velocity ratio parameter.
Impulsive Stretching of a Surface in a Viscous Fluid
The induced transient viscous flow due to a suddenly stretched surface is studied. After a similarity transform, the unsteady Navier--Stokes equation is solved by several methods, including perturbation for small times, numerical integration, and asymptotic analysis for large times. It is found that the validity of the small-time series can be greatly extended and the approach to steady state is exponential.
Unsteady mixed convection flow in the stagnation region of a heated vertical plate due to impulsive motion
Abstract The unsteady mixed convection in the stagnation flow on a heated vertical plate is studied where the unsteadiness is caused by the impulsive motion of the free stream velocity and by sudden increase in the surface temperature (heat flux). The short time as well as the long time solutions are included in the analysis. Both prescribed surface temperature and prescribed surface heat flux conditions are considered. The partial differential equations governing the flow and the heat transfer have been solved numerically using an implicit finite difference scheme. Also, the asymptotic behaviour of the solution for large value of the independent variable is examined when the flow becomes steady. There is a smooth transition from the small-time solution to the large-time solution. The surface shear stress and the heat transfer increase with time and buoyancy parameter. The heat transfer increases with the Prandtl number, but the surface shear stress decreases.