Critical Rayleigh Numbers for Natural Convection of Water Confined in Square Cells With L/D From 0.5 to 8

Abstract

An experimental study of heat, transfer modes in water heated from below was conducted using test cells of square cross section, 0.5 X 0.5 in., and heights of 1.25 to 4 in.Heat transfer was unidirectional and parallel to gravity.Tests both included and excluded the maximum density region of 4 deg C. Ice was present above the liquid during certain runs.The three modes of heat transfer, conduction and laminar and turbulent natural convection, were characterized by temperature profiles, fusion-front velocities and positions, and fluid flow patterns.Transitions between modes occur at well-defined critical Rayleigh numbers ivhich are distinct functions of the L/D of the liquid.The critical values are not affected by the presence of ice, motion of the fusion front, or the temperatures of the warm and cold boundaries, if the Rayleigh number is calculated as described.

Study of buoyancy driven heat transport in silicone oils and in liquid nitrogen in view of cooling applications

“…Here, the heater geometry is different and the walls are not perfect. The latter shifts the instability appearance but has small effect as long as the horizontal to vertical ratio is large (∼ 10) [26,27], which is the case here. Since, our setup did not allow us to accurately measure this threshold, we kept the cited value Ra c = 1707 as the threshold reference.…”

The thermal structure of the anoxic trough in Lake Untersee, Antarctica

“…From Fig. 3b, density values varied by about 0.002 kg m -3 (hence Δρ/ρ~2 × 10 -6 ) over a range of~1 m. Equations (1) and(2) yielded R a~1 0 8 , five orders of magnitude higher than the limit for heat transport due exclusively to molecular heat diffusion in horizontal layers with horizontal length scale much larger than the vertical length scale (Heitz & Westwater 1971). R a also exceeded the limit for transition from laminar natural convection to turbulent natural convection (10 5 -10 6 ).…”

“…When density inversions are very small, conduction is the mode of heat transfer (e.g. Heitz & Westwater 1971). To provide a numerical estimate of the strength of convection, the Rayleigh number (R a ) was computed:…”

Millimeter‐Wave Heating in In Vitro Studies: Effect of Convection in Continuous and Pulse‐Modulated Regimes

“…For convection of fluid between solid boundaries, the critical Ra number is calculated to be 1708.8 [Jeffreys, ]. For other combinations of boundaries, the critical Ra number is < 1708.8 [Heitz and Westwater, ]. The Grashof number is defined by the ratio of the buoyant forces on the fluid to the viscous forces.…”