Entrance Region Flow in Concentric Annuli with Rotating Inner Wall for Herschel–Bulkley Fluids

Abstract

A finite difference analysis of the entrance region flow of Herschel-Bulkley fluids in concentric annuli with rotating inner wall has been carried out. The analysis is made for simultaneously developing hydrodynamic boundary layer in concentric annuli with the inner cylinder assumed to be rotating with a constant angular velocity and the outer cylinder being stationary. A finite difference analysis is used to obtain the velocity distributions and pressure variations along the radial direction. With the Prandtl boundary layer assumptions, the continuity and momentum equations are solved iteratively using a finite difference method. Computational results are obtained for various non-Newtonian flow parameters and geometrical considerations. A significant asymmetry is found in the entrance region which is gradually reduced as the flow develops. For smaller values of aspect ratio and higher values of Herschel-Bulkley number the flow is found to stabilize more gradually. Comparison of the present results with the results available in literature for various particular cases has been done and found to be in agreement.

Entrance Region Flow Heat Transfer in Concentric Annuli with Rotating Inner Wall for Herschel-Bulkley Fluids

“…In the case of stationary cylinders, the results in our analysis are matching with the results of Kandasamy et al [10]. Also, in the case of non-thermal part these results match with the results of Kandasamy and Srinivasa Rao [12]. From this study, the following can be concluded.…”

“…The temperature distribution along radial direction have been plotted for different axial positions with N =0.3, 0.8, n=0.8, 1, 1.2 and Y h =0, 10. The effects of non-Newtonian characteristics and geometrical parameters on velocity profiles and pressure drop have been extensively discussed elsewhere [12]. Here the temperature distributions during the rotation of the inner wall of the annuli have been shown in Fig.…”

“…Recently, Kandasamy and Srinivasa Rao [12], [13] have investigated the entrance region flow in concentric annuli with rotating inner wall for Herschel Bulkley and Bingham fluids.…”

Entrance Effects of Blood Model Casson Fluid in the Concentric Rings with Inner Ring Rotation

“…Analytical solution in the entrance region blood flow in a concentric annuli has been obtained by [3] assuming the blood to obey Casson model. Recently [7,10] analyzed the entrance effects of non-Newtonian flow in the concentric rings. The problem of Casson fluid in the concentric rings to the flow of the inlet region has been studied in the present work.…”

Entrance region flow in concentric annuli with rotating inner wall for Bingham fluid

“…Sayed-Ahmed and Hazem [4] applied a finite difference method to study the laminar flow of a Power-Law fluid in the concentric annuli with rotating inner wall. Recently, Kandasamy and Srinivasa Rao [5] investigated entrance region flow in concentric annuli with a rotating inner wall for Herschel-Bulkley Fluids. The constitutive equation for Bingham fluid is given by Bird et al [6]…”