|
|
 |
| |
|
|
|
Analytical Solutions of Incompressible Couple Stress Fluid Flows |
|
|
|
PP: 1009-1014 |
|
|
|
doi:10.18576/amis/130614
|
|
|
|
Author(s) |
|
|
|
Imran Siddique,
Yousra Umbreen,
|
|
|
|
Abstract |
|
|
| In the present article, we intend to solve the Stokes first and
second problems for an incompressible couple stress fluid under
isothermal conditions. The solutions of the considered problems are
obtained by the Laplace transform (LT) as for the time
variable $t$ and the sine Fourier transform (FT) as for the $y$-variable.
It ought be noticed that by suitable manipulations of the inverse
integral transforms, fluid velocity expressions are written as the
sum of steady-state (post-transient solution) and
transient solutions. Further, we wish to give a comparison of the
obtained results and the results obtained by Devakar and Lyengar \cite{1}
by using the four inverse Laplace transform algorithms (Stehfests,
Tzous, Talbot, Fourier series) in the space time domain utilizing a
numerical methodology. Moreover, velocity profiles are plotted and
considered for different times and different values of couple stress
Reynolds number. At the end, the outcomes are introduced through graphs
and in tabular forms. |
|
|
|
|
|
|
|
