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Analytical solution for time-dependent flow of a third grade fluid induced due to impulsive motion of a flat porous plate. (English) Zbl 1321.35188

Summary: The aim of the present communication is to discuss the analytical solution for the unsteady flow of a third grade fluid which occupies the space \(y>0\) over an infinite porous plate. The flow is generated due to the motion of the plate in its own plane with an impulsive velocity \(V(t)\). Translational symmetries in variables \(t\) and \(y\) are utilized to reduce the governing non-linear partial differential equation into an ordinary differential equation. The reduced problem is then solved using homotopy analysis method (HAM). Graphs representing the solution are plotted and discussed and proper conclusions are drawn.

MSC:

35Q51 Soliton equations
35B35 Stability in context of PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
76S05 Flows in porous media; filtration; seepage
76A05 Non-Newtonian fluids

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