Flow analysis in permeable channel with variable wall reabsorption

Abstract

An analytical investigation is made to determine the flow of viscous fluid in a permeable channel. The mathematical model is developed by using the continuity and momentum equations. The fluid reabsorption across the walls is taken as the hyperbolic functions of wall permeability along the channel. Two different cases are considered, such as fluid reabsorption across the wall varies as a (1) sine and (2) cosine hyperbolic functions along the channel. The flow equations are solved for velocity components, mass flow rate, wall shear stress, pressure distribution, fractional reabsorption and leakage flux using the appropriate form of stream function. The results are compared with the literature and the impact of the hyperbolic reabsorption parameter is studied graphically. Using the data of rat kidney, a table is constructed for different fractional reabsorption values, i.e. , , and to quantify the values of hyperbolic reabsorption parameter and pressure drop. The results reveal that higher fractional reabsorption can be achieved by increasing the hyperbolic reabsorption parameter for the first case, while in the second case, all the fluid is reabsorbed across the walls before reaching the end of the channel. It is found that the transverse velocity at the walls increases with increasing hyperbolic reabsorption parameter for both the reabsorption cases.