Abstract
Hydrodynamics of a conducting visco-elastic fluid in a porous medium sandwiched between two parallel plates, under the effect of the Lorentz force, for both moving and stationary wall boundary conditions, is considered in this paper. The non-linear momentum equation is solved analytically using the optimal homotopy analysis method (OHAM) and the effect of existing parameters in the physics of the problem is demonstrated on the dimensionless velocity profile and skin friction coefficient. The robustness of the analytical solution is checked by comparison with numerical results and plotting the residual errors. Results show that there is excellent agreement between numerical and analytical solutions. Furthermore, the error diagrams show that OHAM yields accurate results in all values of the different effective parameters, such as porous medium shape factor, Forchheimer number, visco-elastic parameter, Reynolds number and the parameters related to the Lorentz force.