Heat transfer behavior of Reiner-Rivlin fluids in rectangular ducts

Numerical studies are reported for the fully developed heat transfer behavior of elastic non-Newtonian fluids in steady laminar flow through rectangular ducts. The Reiner-Rivlin formulation with finite values of the second normal stress coefficient is used to model the flow. The limiting case of zero secondary normal stress difference corresponds to a purely viscous power-law fluid. Finite difference methods are developed to obtain the heat transfer results for the H2 thermal boundary condition for different combinations of heated and adiabatic walls. The influence of the second normal stress coefficient, the Reynolds number, the Peclet Number and the aspect ratio on the heat transfer are considered. It is found that the secondary flow, which is associated with the presence of second normal stresses, results in a significance increase in the heat transfer, especially for aspect ratios of 0.5 and 1.0. The general behavior of the Nusselt number predicted for the Reiner-Rivlin fluid is found to be in good agreement with experimental results reported for viscoelastic fluids.