In order to understand the characteristics of natural convection of cold water near its density maximum between horizontal cylinders, a series of unsteady two-dimensional numerical simulations were conducted by using finite volume method. The radius ratio of horizontal cylinders ranged from 1.2 to 2.0, density inversion parameter from 0 to 1, and the vertical eccentricity from 0 to 1.0 for eccentric annulus. The results show that the flow pattern mainly depends on the density inversion parameter and Rayleigh number. The formation of small cell at the top or bottom of annulus corresponds to the Rayleigh-Benard instability within the converse density gradient layer. The width of annulus has slightly influence on the flow structure. However, the number of Benard cells decreases with the increase of the radius ratio. For the oscillatory flow at a large Rayleigh number, the vertical converse density gradient in the top of annulus or the horizontal density gradient in the middle of annulus plays an important role for the formation of oscillatory flow when the density inversion parameter is in a small or moderate range. But the vertical density gradient in the bottom of annulus and the horizontal density gradient in the middle of annulus work together for oscillatory flow when the density inversion parameter is high. Average Nusselt number on the inner wall increases with the increase of Rayleigh number and radius ratio. However, there exists the minimum value of average Nusselt number at a moderate density inversion parameter. The flow pattern in eccentric annulus has the characteristics of coupling flows in the narrow-gap at the bottom with in the large-gap at the top of annulus. With the increase of the eccentricity, heat transfer is enhanced and the average Nusselt number increases slightly. Based on the simulation results, the new heat transfer correlation has been proposed according to the multiple linear regression technique. (c) 2011 Elsevier Ltd. All rights reserved.