An existence theorem for the flow of a non-newtonian fluid past an infinite porous plate |
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Affiliation: | 1. Department of Mathematical Sciences, University of South Africa, Florida, 0003, South Africa;2. Department of Mathematics and Applied Mathematics, North-west University, Potchefstroom, 2520, South Africa;1. Department of Mathematics, COMSATS Institute of Information Technology, Attock 43600, Pakistan;2. UGC Professor, Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh |
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Abstract: | Non-Newtonian fluid mechanics affords an excellent opportunity for studying many of the mathematical methods which have been developed to analyse non-linear 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 non-linear differential 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. |
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