Numerical simulation of the non-isothermal flow of a nonlinear viscoelastic fluid in a rectangular channel
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AbstractAn orthogonal collocation finite element program was used to numerically model the hydrodynamically and thermally developing flow of a nonlinear viscoelastic fluid. The temperature dependence of the rheological parameters was imposed using an Arrhenius-like exponential relationship. The flow was creeping, at the earlier stages of thermal development and wall cooling was imposed. The maximum Weissenberg number for which convergence was achieved was NWe = 0.46. A bifurcation branch was found to emanate from NWe = 0.4 and extend from NWe = 0.16 to NWe = 0.65. The existence of solution multiplicity was associated with an increase in the hyperbolic character of the governing equations at NWe = 0.4. Since no change of type has been found to occur in the isothermal case, this irregularity in the behaviour of the solution was attributed to the temperature dependence of the fluid properties. The solution profiles in the neighborhood of the change of type as well as at the termination point are free of numerical error, suggesting that the above mentioned irregularities are inherent to the continuous rheological problem and not to its discretized counterpart.

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