Natural convection of water near its density maximum between horizontal cylinders

Ice‐melt rates in liquid‐filled cavities during explosive subglacial eruptions

“…The use of the coefficient of thermal expansion in equation () implies that the convecting fluid expands uniformly over the whole temperature range of interest. The behavior of water is anomalous: as water is warmed at 0.1 MPa from 0°C, it contracts initially until a maximum density is reached at 4°C [ Li et al ., ]. Thus, in principle, a convecting layer of warm water may be insulated from an overlying ice surface by a convectively stable layer of water.…”

Natural convective heat transfer of water near its density maximum in an eccentric horizontal annulus

“…From Fig. 4(d), it is found that the variation of the local Nusselt number between p/2 and 3p/2 is similar with that in narrow-gap concentric annulus [30]. The variation is more obvious than that between Àp/2 and p/2.…”

“…The co-rotating cell at the bottom of the annulus also disappears with the increase of the Rayleigh number. Furthermore, the stagnant region of the fluid flow at the top of the annulus is compressed with the increase of eccentricity, which is opposite to that of downward vertically eccentric annulus [30]. the mechanisms of oscillatory convection in annuli with upward vertical eccentricity are analogous to those in the horizontal concentric annulus.…”

“…Moreover, the physical properties of cold water are identical to those in Ref. [30]. The nonlinear density-temperature relation of water, which is proposed by Gebhart and Mollendorf [31], is adopted in the following form:…”

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.…”