Accounting for temperature-dependent properties in viscoelastic duct flows

A numerical and theoretical study is conducted to evaluate the effect of temperature-dependent properties on the hydrodynamic and thermal characteristics of viscoelastic fluid flow. The theological constitutive equation of the fluid under consideration follows a common form of the PTT model, which embodies both influences of elasticity and shear-thinning in viscosity. A large number of simulations were carried out for a developing channel flow with an imposed constant wall temperature by varying the parameters controlling elasticity (Weissenberg number) and viscous dissipation (Brinkman number). The resulting Nusselt number and friction factor were determined from the numerical results, for both conditions of constant and temperature-dependent properties. The properties that were allowed to vary with temperature were the viscosity, thermal conductivity, specific heat and relaxation time of the PTT model. From the results it was possible to determine how the usual correlations for Nu and C-f have to be modified, following the property-correction method, in order to represent variable-property flow of this viscoelastic fluid. An alternative method to account for variable properties, based on the definition of an equivalent temperature to be used with the constant property Nu and C-f expressions, is also proposed and shown to be less sensitive to the influence of viscous dissipation. The corrections are highly non-linear and strongly depend on epsilonWe(2) and Br especially when viscous dissipation is weak. (C) 2003 Elsevier Ltd. All rights reserved.