Analytical study of creeping flow of Maxwell fluid in a permeable slit with linear re-absorption

Abstract

This research presents the analytical study of the creeping flow of a Maxwell fluid in a permeable slit under the effect of linear reabsorption. Analysis of fluid leakage on the slit wall is carried out with the help of the law of conservation of momentum in the rectangular coordinates. The mathematical model in the form of the system of nonlinear partial differential equations is solved by the recursive approach explaining the hydrodynamic aspects of creeping Maxwell fluid flow. The expressions for the velocity field, hydrostatic pressure, stream function, leakage flux, and fractional reabsorption on the boundary of the slit are obtained from the mathematical model. Graphical analysis is also established to demonstrate the effects of emerging parameters due to linear reabsorption on slit boundary and relaxation time. It is analyzed that the horizontal and vertical velocity decelerates by the growing values of the relaxation parameter, but the reabsorption rate gives an increasing effect on the shear stress, volume flow rate, and vertical velocity. This analytical study will help the bioengineers in designing the medical tools with the required pressure and flow rate, therefore the application of this model for the hemodialyzer is also important.