UNSTEADY CONVECTIVE DIFFUSION IN VISCOELASTIC FLUID FLOWING THROUGH ATUBE

The longitudinal dispersion of passive contaminant molecules released in unsteady viscoelastic fluid flowing through a tube is examined. A f inite difference implicit scheme is adopted to solve the Aris integral moment equations arising from the unsteady convective-diffusion equat ion for all time period. Here it is shown how the injected material sp read due to the shear effect in the viscoelastic fluid caused by the c ombined action of periodic flow and lateral diffusion about its mean p osition, centre of gravity of mass moves and the mean concentration di stribution approaches to Gaussianity, when the contaminant is initiall y uniform over the cross-section of the tube and the Peclet number is large. The analysis reveals that for viscoelastic fluid the dispersion coefficient changes cyclically with a double frequency period and rea ches asymptotically a stationary state after a certain time as in the case of a Newtonian fluid, and its increases with the viscoelastic par ameter. Further, it shows that there is a remarkable similarity betwee n the mean concentration distribution of solute in a Newtonian and non -Newtonian fluid. (C) 1997 Elsevier Science Ltd.