Exact analysis of unsteady convective diffusion in Casson fluid flow in an annulus – Application to catheterized artery

Abstract

The dispersion of a solute in the flow of a Casson fluid in an annulus is studied. The generalized dispersion model is employed to study the dispersion process. The effective diffusion coefficient, which describes the whole dispersion process in terms of a simple diffusion process, is obtained as a function of time, in addition to its dependence on the yield stress of the fluid and on the annular gap between the two cylinders. It is observed that the dispersion coefficient changes very rapidly for small values of time and becomes essentially constant as time takes large values. In non–Newtonian fluids the steady state is reached at earlier instants of time when compared to the Newtonian case and the time taken to reach the steady state is seen to depend on the values of the yield stress. It is observed that a decrease in the annular gap inhibits the dispersion process for all times both in Newtonian as well as in non–Newtonian fluids. When the yield stress is 0.05, depending upon the size of the annular gap (0.9–0.7) the reduction factor in the dispersion coefficient varies in the range 0.58–0.08. The application of this study for understanding the dispersion of an indicator in a catheterized artery is discussed.