Stokes problem for the generalized Navier-Stokes equations

The generalized Navier-Stokes equations for incompressible viscous flows through isotropic granular porous medium are considered. First Stokes problem is solved applying Laplace transform with respect to time variable and evaluating the inverse transform integrals by the residue calculus. The derived analytical solution includes the classic one as a particular case, that is, it can be obtained from the generalized solution by putting the porosity parameter equal to 1. The use of the derived exact solutions for benchmarking purposes is described.