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.

Abstract

Entrance region flow in concentric annuli with rotating inner wall for Bingham non-Newtonian fluid has been studied numerically. The inner cylinder is assumed to be rotating with a constant angular velocity ω and the outer cylinder to be stationary. Finite difference analysis is used to obtain the velocity components U, V, W and the distribution of pressure P along the radial direction R. With Prandtl's 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. The development of the axial velocity profile, radial velocity profile, tangential velocity profile and pressure distribution in the entrance region have been analyzed. Comparison of the present results with the results available in literature for various particular cases has been done and found to be in agreement. Mathematical Subject Classification: 76U05

A finite difference analysis of the entrance region flow heat transfer of Herschel-Bulkley fluids in concentric annuli with rotating inner wall has been carried out. The analysis is made for simultaneously developing hydrodynamic and thermal boundary layer in concentric annuli with one wall being isothermal and other one being adiabatic. The inner cylinder is 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, pressure drop and temperature variations along the radial direction. Computational results are obtained for various values of aspect ratio, flow index, Prandtl's number and Herschel-Bulkley number. Comparison of the present results with the results available in literature for various particular cases has been done and found to be in agreement.