Heat transfer enhancement in laminar flow of viscoelastic fluids through a rectangular duct

Abstract

An investigation on convective heat transfer with viscoelastic fluids in a rectangular duct is carried out to analyze the influence of secondary flow on heat transfer enhancement on account of non-zero second normal-stress differences. The duct has an aspect ratio of 2, constant heat flux at the walls and the three dimensional numerical simulations use a finite-volume method. The numerical results are compared with the experimental heat transfer data of Hartnett and Kostic [1] and the influence of natural convection on the heat transfer process is also addressed. The viscoelastic fluid is described by the Phan-Thien-Tanner constitutive equation with non-zero second normal-stress difference ( N2 ! 0 ). The simulations show an enhancement of heat transfer for viscoelastic fluids, quantified by increased levels of the local and mean Nusselt numbers. The origin of this enhancement is the fluid rheology, particularly the shear-thinning nature of the viscoelastic fluid and the existence of the secondary flow induced by the non-zero second normal stress differences. In addition, the correct prediction of the experimental results of Hartnett and Kostic [1], requires the inclusion of buoyancy, but this mechanism essentially distorts the secondary flow unless there are much larger temperature differences and/ or weaker second normal stress differences than tested. In the present simulations, buoyancy did not change the global heat transfer, but merely redistributed it, because the buoyancyinduced secondary flow was weaker than the !2 - induced secondary flow. For these reasons, the effect of buoyancy decreases with an increase of N2.