Steady laminar MHD flow of visco-elastic fluid through a porous pipe embedded in a porous medium

An attempt has been made to study the effect of elasticity, suction/injection, porous matrix, inlet flow Reynolds number on the flow of a visco-elastic (Walters B′) fluid through a porous pipe. The novelty of the study is to consider the entire flow domain without boundary layer approximation in the governing equations vis-à-vis the fully developed solutions of the velocity field are obtained. Further, we have discussed the viscous and non-conducting flow as particular cases by omitting the effect of elasticity and magnetic field. It is interesting to note that elasticity property of the fluid in presence of porous matrix and suction reduces the skin friction at the plate which is a desirable outcome of the present study.