Exact analysis of unsteady convective diffusion in Casson f luid flow in an annulus – Application to catheterized artery P. Nagarani, Deshmukhi, G. Sarojamma, Tirupati, and G. Jayaraman, New Delhi, India Received December 9, 2005 Published online: April 14, 2006 Ó Springer-Verlag 2006 Summary. 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. 1 Introduction The study of diffusion in an annulus has attracted the attention of researchers due to its applications in chromatography, heat transfer and physiological fluid dynamics. In chemical engineering, the dispersion of a gaseous tracer is studied by injecting the tracer into a flowing stream of a second gas where the tracer gas can also be exchanged by diffusion with the stationary gaseous zone held in a porous solid. This model resembles the one used to evaluate the effective diffusivity of gases in porous solids that are packed in the tubular chromatographic column. These models have been used for the construction of high performance liquid chro- matography instruments to study the effective diffusivity of liquids [1]. The annular chro- matographic method is used for separation of metals, sugars and proteins [2]–[4]. In this method of chromatography, a slowly rotating annular bed is used with a continuous supply of eluent. The studies on natural convective heat transfer in annular regions have applications in nuclear reactors, recovery of geothermal energy and exothermal chemical reaction [5], [6]. Aris [7] studied the dispersion of a solute in a coaxial annular region by considering the two phases of flow with velocities and diffusion coefficients varying only with radial dis- tance. It was shown that the apparent axial diffusion coefficient, at large times, contained the convective and diffusive components consisting of weighted averages of contributions Acta Mechanica 187, 189–202 (2006) DOI 10.1007/s00707-006-0316-9 Acta Mechanica Printed in Austria