Exact solutions of MHD Stoke’s problems for an incompressible couple stress fluid
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Date
2020
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UMT Lahore
Abstract
In this dissertation we intend to solve the MHD Stokes rst and second problems for an incompressible couple stress uid under isothermal conditions. The solutions of the studied problems are obtained by means of the Laplace transform with respect to the time variable t and the sine Fourier transform with respect to the y-variable. It should be noted that by convenient manipulations of the inverse integral transforms, uid velocity expressions are written as the sum between the steady-state solution (post-transient solution) and the transient solutions. Solutions of some known results from literature are recovered as limiting cases. Semi analytical solutions of these problems are also established by using the Laplace inversion numerical algorithms (Honig Hardies, Stehfest s, Tzou s, Talbot, Fourier series). Further we compare our obtained analytical and numerical results in graphical and tabular forms. Furthermore, we give a comparison of the obtained results in limiting cases with the results obtained by Devakar and Lyengar [1]. Moreover, velocity pro les are plotted and studied for di⁄erent times and di⁄erent values of couple stress Reynolds number and magenetic parameter. At the end, the results are presented through graphs and in tabular forms.