An existence theorem for the flow of a non-Newtonian fluid past an infinite porous plate. (English) Zbl 0599.76013

Rajagopal, K. R.; Szeri, A. Z.; Troy, W.

Int. J. Non-Linear Mech. 21, 279-289 (1986).

Non-Newtonian fluid mechanics affords an excellent opportunity for studying many of the mathematical methods which have been developed to analyze nonlinear problems in mechanics.
The flow of an incompressible fluid of grade three past an infinite porous flat plate, subject to suction at the plate, is governed by a nonlinear differenial equation that is particularly well suited to demonstrate the power and usefulness of three such techniques. We establish an existence theorem using shooting methods. Next we investigate the problem using a perturbation analysis. It is not clear that the perturbation solution converges and thus may not be the appropriate solution for a certain range of a material constant (which is not the perturbation parameter).
Finally, we employ a numerical method which is particularly suited to the problem in question.

MSC:

76A05	Non-Newtonian fluids
76S05	Flows in porous media; filtration; seepage
76M99	Basic methods in fluid mechanics

Keywords:

incompressible fluid of grade three; infinite porous flat plate; nonlinear differenial equation; existence theorem; shooting methods; perturbation analysis