Natural Convection in a Horizontal Layer of Water Cooled From Above to Near Freezing

Abstract

Natural convection in horizontal layers of water cooled from above to near freezing was studied analytically. The water was confined laterally and underneath by rigid insulators, and the upper horizontal surface was subjected to: (1) a constant 0C temperature, rigid conducting boundary, and (2) a free, water to air convection boundary condition, in which the convective heat transfer coefficient was held constant at values of 5.68 W/m2 · K and 284 W/m2 · K (1.0 and 50.0 Btu/hr ft2F) and the temperature of the ambient air was maintained at 0C. The ratios of the width to the depth of the rectangular water layers under consideration were W/D = 1, 3, and 6. Initially the water is assumed to be at a uniform temperature of either 4C or 8C, and then the upper surface boundary condition was suddenly applied. It was observed in all cases for which the initial water temperature was 4C, that the water remained stagnant and became thermally stratified. Heat transfer application of either of the surface boundary conditions to water initially at 8C produced large convective eddies extending from the bottom to the top of the layer of water. As the liquid layer cooled further, two distinct horizontal regions appeared, the 4C isothermal line separating the two. This produces a region of hydrodynamic instability in the fluid since the maximum density fluid (4C) is physically located above the less dense fluid in the lower portion of the cavity. The large eddies which appeared initially were confined to the hydrodynamically unstable region bounded by the 4C isotherm and the bottom of the cavity. The action of viscous shearing forces upon the stable water above the 4C isotherm produced a second “layer” of eddies. An alternating direction implicit finite difference method was used to solve the coupled system of partial differential equations. The paper presents transient isotherms and streamlines and a discussion of the effect of maximum density on the flow patterns.

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

“…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. Another study with a bearing on the subject discussed here is the numerical investigation carried out by Forbes and Cooper [16] on transient natural convection of water initially at either 4°C or 8°C, confined laterally and underneath by rigid insulators, with the upper surface maintained at a constant 0°C temperature. Also, in this case, the physical properties were assumed as constant, incorporating the buoyancy effects by invoking the Boussinesq approximation.…”

Cooling process of water in a horizontal circular enclosure subjected to non-uniform boundary conditions

“…Cooling a horizontal layer of water from above was accomplished by Forbes and Cooper [4]. Vasseur and Robillard [5] studied cooling process of water with 0 C boundary imposed on the vertical and horizontal walls.…”

Unsteady MHD Heat Transfer in Couette Flow of Water at 4°C in a Rotating System with Ramped Temperature via Finite Element Method

“…The effects of 4 o C on the natural convective heat transfer and temperature distribution with initial temperatures at 4 o C and 8 o C were reported by Forbes and Cooper [1] who cooled water from the top with either a rigid boundary condition at constant temperature or a free water-air surface with a constant convective heat transfer coefficient. We known that for a fluid like water or air at ordinary temperature and atmospheric pressure the variation  of the density with the variation T   of the temperature is given by T     From the above it is apparent that for low temperature variations, natural convection in water near 4°C would be different from that at 20°C [2].…”