Fractional generalized Burgers' fluid flow due to metachronal waves of cilia in an inclined tube

In this study, the cilia-induced flow is discussed for fractional generalized Burgers' fluid in an inclined tube. The mathematical model of fractional generalized Burgers' fluid flow is obtained under the long-wavelength approximation. It is found that thickness of flow region increases with the increase in relaxation time; thus, a large amount of pressure gradient is required for fluid flow, whereas the retardation time assists to decrease the thickness of the flow region, and therefore, less amount of pressure gradient is required for the fluid flow during the recovery stroke. The presence of fractional order derivatives in the generalized Burgers' model provides the large amount of frictional force when compared with generalized Burgers' fluid in the presence of parameters α = β = 1. Fractional Adomian decomposition method is used to calculate the pressure gradient. Results for stream function, axial velocity, pressure gradient, pressure rise, and frictional force are constructed and then plotted graphically to note the effects of various interesting parameters.