An analysis of the flow of a power law fluid due to ciliary motion in an infinite channel

Abstract

The propulsion mechanics of cilia-induced flow is studied through a mathematical model. The problem of two-dimensional motion of a power law fluid inside a channel with ciliated walls is considered. The characteristics of ciliary systems are determined by the dominance of viscous effects over inertial effects using the long-wavelength approximation. Solutions for the longitudinal, transverse, and resultant velocities are obtained. The pressure gradient and volume flow rate for different values of the power law index are also calculated. The flow properties for the power law fluid are determined as a function of the cilia and metachronal wave velocity. The viscous and power law fluid are compared and discussed graphically.

Exact solution of cilia induced flow of a Jeffrey fluid in an inclined tube

“…Cilia motion in Newtonian and non-Newtonian fluids is a current topic of interest. Different studies exit in literature in which the cilia induced flow in different geometries and stresses are discussed (Siddiqui et al 2010, 2014a, b2015; Akbar et al 2014, 2016). The exact analytical results obtained by Siddiqui et al.…”

Adomian decomposition solution for propulsion of dissipative magnetic Jeffrey biofluid in a ciliated channel containing a porous medium with forced convection heat transfer

“…In recent years rheological hydrodynamics with cilia effects have stimulated some attention. Interesting studies in this regard include Siddiqui et al (who used the Ostwald‐de Waele power law model), Maqbool et al (who considered the fractional Burgers model for ciliated propulsion in a tilted vessel) and Siddiqui et al (who simulated the epididymal fluid through the ductus efferentes of the male reproductive track by considering the viscous fluid model and Carreau fluid model, respectively, in metachronal wave of cilia motion in an asymmetric tube). Akbar et al studied the hydromagnetic viscoplastic metachronal propulsion with multiple slip effects.…”

Analysis of a channel and tube flow induced by cilia

“…4 we have presented the velocity profile relative to the change in which depends on the mean radius and the length of the cilia. The effect of this parameter on the flow has been reported by Siddiqui et al [20] and Maiti and Pandey [21] and the references therein. Our numerical technique proved to be more accurate to obtain the threshold value of this radius and cilia length dependent parameter.…”

“…We have considered the numerical integration after calculating the numerical results for the velocity and pressure. This reduced the complexity to deal with the pressure gradient ( 1 0 dp dx dx for channel geometry, 1 0 dp dz dz for tube geometry) and the volume flow rate ( 1 0 udy for channel geometry, 1 0 r udr for tube geometry), which was reported by Siddiqui et al [20] and Maiti and Pandey [21] while solving the problem analytically. The pumping performance of the fluid can be better understood with the help of the numerical technique.…”