Buoyancy-driven convection of water near its density maximum with partially active vertical walls P. Kandaswamy * , S. Sivasankaran, N. Nithyadevi UGC-DRS Centre for Fluid Dynamics, Department of Mathematics, Bharathiar University, Coimbatore 641 046, India Received 31 December 2005; received in revised form 20 July 2006 Available online 23 October 2006 Abstract Transient natural convection of cold water around its density maximum in a square cavity is studied numerically. Nine different posi- tions of the active zones are considered. The governing equations are solved using Control volume method with power low scheme. The results obtained for various values of parameters are presented graphically in the form of streamlines and isotherms. It is found that the average Nusselt number behaves non-linearly as a function of Grashof number. The heat transfer rate is decreased in the density max- imum regions. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Transient convection; Partially active walls; Square cavity; Density maximum 1. Introduction The buoyancy-driven convection in a fluid-filled cavity is a topic of interest for many researchers, due to its wide ranging of applications in cryogenic industry, cooling problems, crystal growth techniques, space applications, etc. Free convection arises in a fluid due to the density vari- ations caused by the temperature differences of the system. In most of the analysis pertaining to the convection of water in enclosures, a linear temperature–density relation- ship was taken. But in practice this will never happen as the density of water varies with temperature in a nonlinear fashion, attaining its maximum density around 4 °C. Ho and Tu [1] experimentally and numerically investi- gated the natural convection of water near its maximum density at high Rayleigh numbers. They observed oscilla- tory convection flow and temperature fields in the enclo- sure and provide a good agreement with the measured time period of the cyclic traveling wave motion of the maximum density contour. Kandaswamy and Kumar [2] studied the natural convection of water near its density maximum in the presence of uniform magnetic field. They observed that the effect of the magnetic field on the natural convection is to inhibit the heat transfer rate. The effect of density inversion on steady natural convection heat trans- fer of cold water is studied by Lin and Nansteel [3]. They found convection is reduced due to the density maximum. Mahidjiba et al. [4] investigated onset of convection in a horizontal anisotropic porous layer saturated with water near 4 °C. It is found that the onset of motion dependent permeability ratio and inversion parameter. Michalek et al. [5] made a numerical benchmark study on natural convection for anomalous density variation of water, and compare performance of four different numerical methods. Convection in water above ice penetrates into the stably stratified region above the density maximum at 4 °C stud- ied by Moore and Weiss [6]. They found steady convection occurs at Rayleigh numbers below the critical value predicted by linear theory. Pantokratoras [7] studied natu- ral convection of water near the density extremum along a vertical plate with sinusoidal surface temperature variation. It is found that there is an inner boundary layer near the plate with periodic characteristics. Tong and Koster [10] 0017-9310/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2006.08.013 * Corresponding author. Tel.: +91 422 2426764; fax: +91 422 2422387. E-mail address: pgkswamy@yahoo.co.in (P. Kandaswamy). www.elsevier.com/locate/ijhmt International Journal of Heat and Mass Transfer 50 (2007) 942–948