Periodic permeable free convective 3-dimensional flow of a second grade fluid with slip effect

Abstract

This study addresses the development of a mathematical model and theoretical analysis of a free convective three-directional flow of an incompressible second-grade fluid through a highly porous medium bounded by a vertical infinite plate in slip flow regime subjected to a constant suction. The free stream velocity is rumored to be constant while permeability of the medium is presumed to be periodic. It is well known that the assumption of either time dependent or constant permeability of a porous medium leads to two-dimensional flows, of course, the flow comes to be three-dimensional due to variation in permeability of the porous medium. Approximate solutions of velocity and temperature fields, heat flux and skin friction are established by applying the regular perturbation technique. Results are discussed and visualized graphically in the light of physical parameters emerging in the mathematical model of the physical phenomenon with carefully selected and viable data. The significance of current study reveals that presence of slip parameter reduces the thickness of boundary layer causing the enhancement in the main flow velocity component. With increasing permeability parameter fluid velocity is decelerated whereas it is accelerated with increasing Grashof number. With increasing non-Newtonian parameter, a similar response is noted as for the permeability parameter. It is also noted that permeability parameter, Prandtl number, Grashof number and elastic parameter provide mechanism to control the skin friction. In addition, Reynolds number also plays a vital role to control the skin friction. Furthermore, Reynolds number significantly boosts the coefficient of heat transfer, and Prandtl number causes to reduce the thermal boundary layer thickness.