2016 International Symposium on Nanofluid Heat and Mass Transfer in Textile Engineering and 5th International Symposium on Nonlinear Dynamics

Journal: Nonlinear Science Letters A
(ISSN 2519-9072(Online), ISSN 2076-2275 (Print))          Vol. 2 No. 1
Extended Homotopy Perturbation Method and the Flow past a Nonlinearly Stretching Sheet
M. Rentoul, P. D. Ariel
Department of Mathematical Sciences
Trinity Western University, Langley, BC, Canada, V2Y 1Y1
Email: DAriel@twu.ca
Abstract: The extended homotopy perturbation method is applied to compute the flow of a viscous, incompressible fluid past a stretching sheet for which the stretching velocity is nonlinearly varying with the distance from a coordinate axis or the origin. Three problems are considered: (i) when the stretching velocity is proportional to some power of the distance from a coordinate axis, (ii) when the stretching velocity varies exponentially with the distance from a coordinate axis, and (iii) when the stretching is done radially with velocity that is proportional to the distance from the origin. It is shown that the boundary value problems characterizing all the three problems stem from the same prototype equation containing a parameter ε, the value of which distinguishes one problem from the others. There is an excellent agreement between the results obtained by the extended homotopy method and the exact numerical solution.

Keywords: Stretching sheet, homotopy perturbation method, nonlinear stretching, Ackroyd's method, numerical solution

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