Generalized three-dimensional flow due to a stretching sheet. (English) Zbl 1047.76019

Ariel, P. Donald

ZAMM, Z. Angew. Math. Mech. 83, No. 12, 844-852 (2003).

Summary: The three-dimensional steady, laminar flow due to stretching of a sheet is considered. The governing equations of motion admit a similarity solution. By drawing an analogy with the flow due to a rotating disk it is demonstrated that the resulting boundary value problem admits a solution in terms of series of exponentially decaying functions. The solution is highly efficient and very accurate, as it eliminates the need of replacing numerical infinity in the range of integration by a finite value. Two perturbation solutions are also developed when the primary flow corresponds to the two-dimensional case and the axisymmetric case. In each case the expansion is obtained up to the second degree term of the perturbation parameter. Finally, an approximate solution is derived, which is very simple and highly accurate.

MSC:

76D99

Incompressible viscous fluids

Keywords:

stretching sheet; boundary value problem; Ackroyd’s method; principle of strained coordinate; approximation using minimization of residuals