A numerical study of nanofluid natural convection in a cubic enclosure with a circular and an ellipsoidal cylinder

In this paper we develop a numerical method and present results of simulations of flow and heat transfer of nanofluids. We consider a heated circular and elliptical cylinder in a cooled cubic enclosure. Natural convection, which drives the flow, and heat transfer are simulated for different temperature differences and enclosure inclination angles. Steady laminar regime is considered with Rayleigh number values up to a million. Al2O3, Cu and TiO2 nanofluids are considered, as well as pure water and air for validation purposes. Properties of nanofluids are considered to be constant throughout the domain and are estimated for different nanoparticle volume fractions (0.1 and 0.2). In order to simulate nanofluids, an in-house numerical method was developed based on the solution of 3D velocity-vorticity formulation of Navier-Stokes equations. The boundary element method is used to solve the governing equations. In the paper, special consideration is given to the estimation of the boundary value of vorticity on an arbitrary curved surface. The results show highest heat transfer enhancement in the conduction dominated flow regime, where the enhanced thermal properties of nanofluids play an important role. When convection is the dominant heat transfer mechanism, the using nanofluids yields a smaller increase in heat transfer efficiency. Comparison of 2D and 3D results reveals consistently lower heat transfer rates in the 3D case. As the enclosure is tilted against gravity, the flow symmetry around an elliptical cylinder is lost and the overall heat transfer increases. (C) 2015 Elsevier Ltd. All rights reserved.