This paper reports the development of a methodology for calculating the flow of upper convected Maxwell fluids using a finite-volume based method. The algorithm was developed for a general non-orthogonal collocated grid, and the pressure-velocity-stress coupling was addressed by a special interpolation technique inspired by Rhie and Chow’s (1982) method. The differencing schemes are second order accurate and calculations were carried on for a two-dimensional entry channel flow in order to assess the performance of the method. The interpolation technique specially devised for the stresses was found to work well and the results of the simulation compared favourably with those of the literature (Eggleton et al, 1996). Convergence was attained for Deborah and Reynolds numbers identical to those reported in the literature for a similar flow problem using other numerical methods.

Viscoelasticity was responsible for the development of very intense normal stresses, which were tractive in the wall region. As a consequence the viscoelastic fluid was forced to move away from the wall, in a more intense way than with Newtonian fluids, thus reducing locally the shear rates and the role of viscosity in redeveloping the flow.

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