Viscous oscillatory exponentially stratified flow through Rectangular Narrow Channels

Abstract

The research work in this article proposes a mathematical model and its results to the flow which is oscillatory and vertically exponential density stratified viscous fluid induced by constant suction through one side of the channel. The region of the flow is assumed to be narrow rectangular shaped formed by two parallel plates of which the right-hand side plate is porous and the fluid is taken out through this plate inducing the flow with constant velocity. The mathematical system explaining the above problem is formed using narrow channel approximation and solved using variable separable similarity solution and were interpreted through graphs for various parameter involved in the system. The stratification is considered to be exponentially distributed in the vertical direction and the results reveal that the flow in the vertical direction is mainly affected by the stratification parameter and significant comparisons are established with the case of linearly distributed density stratification. Further for second-degree approximation, the exponential stratification reduces to the results of linear stratification results, which are already available in the literature.