NATURAL CONVECTION IN A HORIZONTAL WATER LAYER WITH MAXIMUM DENSITY AT 4°C
This paper is concerned with the heat transfer characteristics in a horizontal water layer having a maximum density at 4°C. A bottom cold plate is fixed at 0°C considered ice layer, and heat is generated in a top warm plate to estimate heat flux in water layer. Heat transfer coefficient in the water layer indicates a maximum value at 3.6°C slightly less than 4°C of the top warm plate temperature Th. Heat transfer in the water approaches gradually to heat conduction with increasing Th. The results obtained are expressed by ordinary dimensionless variables of Nu-Ra for the range of Th < 7°C. For Th < 7°C, the heat transfer can be expressed by a newly introduced relation of Nu-Ramod including a modified volumetric expansion coefficient of water βmod having a positive value.
natural convection, Benard cells, horizontal water layer, maximum density, numerical solution, modified dimensionless variable.
Received: June 1, 2021; Accepted: July 28, 2021; Published: September 24, 2021
How to cite this article: M. Sugawara and M. Tago, Natural convection in a horizontal water layer with maximum density at 4°C, JP Journal of Heat and Mass Transfer 24(1) (2021), 1-18. DOI: 10.17654/HM024010001
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
1] Y. Katto, Heat Transfer, Yokendo, Japan, 1974, p. 173 (in Japanese).[2] Masahiro Sugawara, Shoichiro Fukusako and Nobuhiro Seki, Experimental studies on the melting of a horizontal ice layer, Bulletin of the JSME 18(121) (1975), 92-98.[3] N. Seki, S. Fukusako and M. Sugawara, A criterion of onset of free convection in a horizontal melted water layer with free surface, J. Heat Transfer 99 (1977), 92-98.[4] M. Sugawara and M. Tago, An application of Neumann’s solution for freezing of water in an adiabatic rectangular cavity, JP Journal of Heat and Mass Transfer 18(1) (2019), 73-108.[5] R. Kobayashi, Instabilität einer von unten erwärmten Flüssigkeitsschicht bei gleichzeitiger Berücksichtigung von Oberflächenspannung und Auftriebskraft, ZAMP 18 (1967), 845-851.[6] D. A. Nield, Surface tension and buoyancy effects in cellular convection, J. Fluid Mech. 19 (1964), 341-352.
