Entrance region flow of blood in concentric annulus

Abstract

Flow characteristics of blood obeying Casson's stress-strain relation have been investigated in the entrance region of annuli. Application of momentum-integral technique to the governing equations of flow leads to the solution of a system of two nonlinear ordinary differential equations which has been solved numerically using Runge-Kutta method. Casson fluid possesses an yield value, therefore there is a plug core formation away from the walls. The problem has been analysed by considering the two boundary layer flow regions separated by the plug core formation. Variation of the boundary layer thickness, plug core velocity, pressure drop, entrance length and the correction factor for friction-loss have been determined for all admissible yield values and for all admissible values of the aspect ratio. Assigning particular values to the aspect ratio, the corresponding results for entrance region flow in a tube and parallel-plate channel have been obtained. Calculations have been made for yield value equal to zero to get the corresponding results for a Newtonian fluid. Comparisons have been made with the available numerical solution for a Casson fluid and also for a Bingham fluid for a particular yield value. The analysis may lead to a better understanding for the flow characteristics and anomalies of blood which may be of interest in the membrane oxygenators and may help in the diagnosis of cardiovascular diseases and possibly in their treatment.