Homotopy analysis method for the heat transfer in a asymmetric porous channel with an expanding or contracting wall

The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the porous upper plate is investigated and an analysis is made to determine the heat and mass transfer. The unsteady Navier–Stokes equations are reduced to a generalization of the Proudman–Johnson equation retaining the effect of wall motion using a suitable similarity transformation. The analytical solution for stream function and heat transfer characteristics are obtained by employing homotopy analysis method. The effects of various physical parameters like expansion ratio, Prandtl number, Reynolds number on various momentum and heat transfer characteristics are discussed in detail.