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

An experimental study of heat transfer modes in water heated from below was conducted using test cells of square cross section, 0.5 × 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 which 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. The L/D was varied from 0.5 to 8 and the critical Rayleigh numbers varied from about 1700 to 10⁸.