Transport of Jeffrey fluid in a rectangular slit of the microchannel under the effect of uniform reabsorption and a porous medium

This research explores the transport of a Jeffrey fluid through a permeable slit of microchannel under the effect of a porous medium and constant reabsorption.Physical laws of fluid mechanics are used to study the flow in a cross-sectional area of a narrow slit which generates a highly nonlinear system of partial differential equation with nonhomogeneous boundary conditions.To solve the complex boundary value problem;a recursive(Langlois)approach is used and explicit expressions for velocity,pressure,stream function,flux,shear stress and fractional reabsorption are calculated.It is noticed that the flow rate at the centre line of slit and shear stress on the walls of slit decay due to the presence of porous medium and viscoelastic fluid parameters.It is also quantitatively observed that more pressure is required for the fluid flow when the slit is filled with a porous medium and reabsorption on the walls is constant.The mathematical results of the present research have significant importance in the field of biofluid mechanics and medical industry,therefore the application of a diseased rat kidney is also included in this research:and reabsorption velocities in the case of a diseased and a healthy rat kidney are calculated with the effects of a porous medium and constant re-absorption.

Metachronal propulsion of non-Newtonian viscoelastic mucus in an axisymmetric tube with ciliated walls

Cilia-induced flow of viscoelastic mucus through an idealized two-dimensional model of the human trachea is presented.The cilia motion is simulated by a metachronal wave pattern which enables the mobilization of highly viscous mucus even at nonzero Reynolds numbers.The viscoelastic mucus is analyzed with the upper convected Maxwell viscoelastic formulation which features a relaxation time and accurately captures normal stress generation in shear flows.The governing equations are transformed from fixed to wave(laboratory)frame with appropriate variables and resulting differential equations are perturbed about wave number.The trachea is treated as an axisymmetric ciliated tube.Radial and axial distributions in axial velocity are calculated via the regular perturbation method and pressure rise is computed with numerical integration using symbolic software MATHEMATICA^(‘TM’).The influence of selected parameters which is cilia length,and Maxwell viscoelastic material parameter i.e.relaxation time for prescribed values of wave number are visualized graphically.Pressure rise is observed to increase considerably with elevation in both cilia length and relaxation time whereas the axial velocity is markedly decelerated.The simulations provide some insight into viscous-dominated cilia propulsion of rheological mucus and also serve as a benchmark for more advanced modeling.