Effects of narrow channel approximation on viscous oscillatory density stratified fluid flow through rectangular channels

Viscous oscillatory density stratified fluid flow through rectangular channel with a porous wall is considered in this problem. The governing equations of motion are transformed into ordinary differential equations of constant coefficient by using variable separable transformation. Solutions are also obtained by considering the channel to be narrow by applying Lubrication approximation in the momentum equations. The solutions in both the cases are compared using graphical interpretations of velocity profiles, pressure and density distributions for various parameters associated with problem. The findings of the investigation reveals that the narrow channel approximation results in pressure dominated flow and stratification effects are observed in this case nearer to the boundaries. The analysis gives a considerable measure to control the flow along with the effects of various associated parameters.