Analytical approach to explore theory of creeping flow with constant absorption

Exploration of entire human body is now possible with the advancement in the field of biotechnology, biosensors and bio-inspired modeling. We model the flow of a fluid between parallel plates for a couple stress fluid in order to incorporate polar effects on the flow. The stream function is used to transform the governing equations to system of ordinary differential equations. The analytical solutions are found for velocity components, pressure distribution, the axial flow rate, the mean pressure drop and the shear stress. The effect of couple stress parameter on the velocity, pressure and the shear stress has been investigated through graphs. We have also used the data from the renal tubule of a rat kidney in our analytical results to study the effect of the couple stress parameter on the mean pressure drop across the slit of the rat’s renal tubule. •Flow of a non-Newtonian fluid through a porous walled channel is studied.•Flow in the proximal renal tubules of a kidney can be explored with this model.•Theoretical analysis is documented in detail.•Numerical simulations are incorporated for creeping flow.