Core variation in the entrance region flow of herschel- Bulkley fluid in an annuli

The entrance region flow in channels constitutes a problem of fundamental interest in engineering applications such as nuclear reactors, polymer processing industries, haemodialyzers and capillary membrane oxygenators. In such installations, the behavior of the fluid in the entrance region may play a significant part in the total length of the channel and the pressure drop may be markedly greater than for the case where the flow is regarded as fully developed throughout the channel. Recently, there has been an increasing interest in problems involving materials with variable viscosity such as Bingham materials, Casson fluids and Herschel-Bulkley fluids which are characterized by an yield value. The entrance region flow of a Herschel- Bulkley fluid in an annular cylinder has been investigated numerically without making prior assumptions on the form of velocity profile within the boundary layer region. This velocity distribution is determined as part of the procedure by cross sectional integration of the momentum differential equation for a given distance z from the channel entrance. Using the macroscopic mass balance equation the core thickness has been obtained at each cross section z of the annuli for specific values of Herschel -Bulkley Number, flow behavior index and various value of aspect ratio.