Applications of the Numerical Inversion of the Laplace transform to unsteady problems of the third grade fluid

In this article, we have effectively used the Numerical Inversion of Laplace transform to study some time dependent problems of the third grade fluid. To do so, we have considered three different types of unsteady flows of the third grade fluid, namely(a)Unsteady flow over a flat rigid plate with porous medium.(b)Unsteady MHD flow in a porous medium.(c)Unsteady MHD flow in a non-porous space with Hall currents.The solution to the governing equation in each case is obtained by using the standard Laplace transform. However, to transform the obtained solutions from Laplace space back to the original space, we have used the Numerical Inversion of the Laplace transform. Graphical results for each case have been presented to show the effects of different parameters involved and to show how the fluid flow evolves with time.