A numerical study is made of transient natural convective cool-down process of a fluid in a cylindrical container. The density-temperature relationship of the fluid is given by a quadratic function, with the maximum density rho(m) occurring at T-m. Cooling is accomplished by abruptly lowering the sidewall temperature, and the mean temperature passes through T-m in the course of cool-down. Numerical solutions are acquired to the fun, time-dependent Navier Stokes equations. The flow is governed by a properly defined Rayleigh number Rn, the density inversion factor gamma, the aspect ratio A, and the Prandtl number, Pr. Evolutions of the flow and temperature fields are analyzed. Based on the structures of the sidewall boundary layer al early times, three characteristic flow regimes are identified. The qualitative early-time behavior is determined by gamma. The intermediate-stage features for large gamma disclose the flow restructuring. When A or Ra is large, boundary layer waves are monitored for moderate Values of gamma. The analysis of time dependent heat transfer characteristics suggests that the coal-down process is divided into several transient phases. The relevant time scales for the overall cool-down process are estimated. The specific effects of Ra, gamma and A on each evolutionary stage are elaborated. (C) 1997 Elsevier Science Ltd.