Effect of polymer additives and viscous dissipation on natural convection in a square cavity with differentially heated side walls

Abstract

This study presents an extensive numerical investigation on how the addition of polymer molecules into a Newtonian solvent would tend to influence the natural convection heat transfer phenomena in a differentially heated square cavity. The rheological behaviour of the resulting polymer solution is modelled based on the FENE-P viscoelastic constitutive equation, which along with other governing equations, namely, mass, momentum, and energy equations, have been solved using the open source CFD code OpenFOAM over the following ranges of conditions: Rayleigh number, 103 ≤ Ra ≤ 106; Weissenberg number, 1 ≤ Wi ≤ 100; polymer extensibility parameter, 10 ≤ L2 ≤ 500, polymer viscosity ratio, 0.5 ≤ β ≤ 0.9 and for a fixed value of the Prandtl number of Pr = 7. At low values of the Rayleigh number, the average Nusselt number gradually increases with the Weissenberg number. However, at high values of it, the average Nusselt number first increases steeply up to a critical value of the Weissenberg number, and beyond that, it remains almost constant as the Weissenberg number further increases. The average Nusselt number is seen to decrease with the increasing values of both the polymer extensibility paramter and polymer viscosity ratio. The viscous dissipation tends to deteriorate the heat transfer rate in comparison to that seen in the absence of it; however, the extent of this deterioration is found to be independent on the values of Wi, L2 and β. Furthermore, a detailed discussion of the results in terms of the streamline profiles, isotherm contours, distribution of local Nusselt number, variation of velocity components, etc., is also presented. Finally, from an application standpoint, a simple correlation for the average Nusselt number is presented, which can be used for the interpolation of the present results for the intermediate values of the governing parameters in a new application.