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Exact Solution of Stokes’ First Problem for Second Grade Fluid on a Permeable Wall

Abdulhameed Mohammed, Rozaini Roslan, Muhathir Muhammad, Ishak Hashim


In this work, the Stokes’s first problem for second grade fluid on a permeable wall is considered. The governing equations were solved analytically for the exact solution by using the perturbation techniques and the Laplace transform method. The solution found is the first known solution of the Stokes’s first problem for second grade fluid when fluid transpiration is presented. Analysis of the result has shown that the second grade fluid exert a great influence on the general flow pattern, the injection provides opposite effect on the velocity field compare with suction and time provides positive improvement on the velocity field. The solution obtained was found in excellent agreement with related solution for Newtonian fluid.


Stokes’ first problem, Second grade fluid, Permeable wall.

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