Three-dimensional numerical simulation of natural convection of water near its density maximum in a horizontal annulus

Correlations for Transient Thermal Convection of Water Near Its Density-Inversion Point in a Square Enclosure Heated From Below

“…T s s (18) in which ρ ∆ is the difference between the water densities at 4°C and 0°C, while all the other physical properties are evaluated at the density-inversion temperature of 4°C. The standard deviations of the errors are 1.8% for equation ( 12), and 2.2% for equation (13). Once the value of h Nu is known, the average Nusselt number of the cooled top wall at steady-state, ,…”

“…Later investigations were performed numerically on square cavities by Zubkov and Kalabin [8], on cubic enclosures by Zubkov et al [9], and on shallow cylindrical containers by Li et al [10], in all of which the heating-from-below condition was implemented in the hypothesis of constant physical properties, except for the density in the buoyancy force term of the momentum equation. Additionally, partly related studies are those recently conducted by Li and colleagues using annular enclosures having more or less complex configurations [11][12][13][14][15]. Primary aim of all these cited works was to show the existence of multiple stable steady-state or periodically-oscillating flow pattern solutions, while no special attention was devoted to the transient regime.…”

Eccentricity effect on bifurcation and dual solutions in transient natural convection in a horizontal annulus

“…Fattahi et al [5] simulated the natural and mixed convection heat transfer problems by lattice Boltzmann model based on double-population approach. Yuan and Li [6,7] investigated the natural convective heat transfer of water near its density maximum in an eccentric horizontal annulus. Yi et al [8] investigated the natural convection in eccentric annulus over a wide range of Rayleigh numbers using the dissipative particle dynamics method with energy conservation (eDPD).…”

Penetrative convection of water in cavities cooled from below

“…In particular, defined the density inversion parameter as θ inv = (4°C − t c ) / (t h − t c ), where t h and t c are the temperatures of the heated and cooled walls in Celsius degrees, Zubkov and colleagues assigned θ inv = 0.5 imposing t c = 0−3°C, whereas Li and co-workers fixed θ inv = 0.3, again imposing t c = 0−3°C. A number of partly related studies were recently performed by Li and colleagues on horizontal annular enclosures having more or less complex geometric configurations [11][12][13][14][15][16]. Primary aim of all these cited works was to determine the existence of multiple stable steady-state or periodically-oscillating flow pattern solutions.…”