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.
Boundary layer development on a wedge impulsively set into motion
The problem of impulsively set into motion wedge type (Falkner–Skan) flows has been formulated in a new set of scaled coordinates. Both the short time solution and the solution for infinite time, the Falkner–Skan solution, are included in the new formulation of the problem. In addition a new scaling reduces the region of integration from the traditional infinite region to a finite region, thus reducing the time required for numerical computations.The solution for the impulsively started flat plate has been obtained and compared with existing solutions to this special case to verify the method of solution. The agreement between the present solution and existing solutions for the flat plate case is excellent. Solutions have also been obtained for a number of impulsively started Falkner–Skan type flows ranging from the two-dimensional stagnation point flow to the incipient separation flow.Flows which involve an adverse pressure gradient are considered in detail to determine what information can be gained fro...
Stretching a surface in a rotating fluid
SummaryA surface is stretched in a rotating fluid. The solution to the governing set of nonlinear differential equations depends on a parameter λ which is the ratio of the rotation rate to the stretching rate. Perturbation solutions for small and large λ compare well with exact numerical integration.