THREE DIMENSIONAL NATURAL CONVECTION OF THE WATER LAYER IN A VERTICAL CAVITY WITH THE MAXIMUM DENSITY
This paper is concerned with the three dimensional heat transfer in a vertical water layer that is calculated numerically by the PHOENICS Code. The thickness of the water layer is 2.5cm, and the length and depth are both 25cm. The vertical warm plate generates heat per unit volume to set the mean temperature of its plate Th and the temperature of the cold plate Tc is fixed at 0°C considering the melting of ice. The Nusselt number, Nu, of 3D is generally larger than Nu of 2D in a range of However, the ratio of increases with decreasing Th and marks the maximum of about 2.38 at The ratio decreases with decreasing from to
natural convection, comparison of 3D-Nu and 2D-Nu, vertical water layer, maximum density
Received: May 15, 2024; Accepted: June 8, 2024; Published: August 5, 2024
How to cite this article: M. Sugawara and M. Tago, Three dimensional natural convection of the water layer in a vertical cavity with the maximum density, JP Journal of Heat and Mass Transfer 37(4) (2024), 445-456. https://doi.org/10.17654/0973576324031
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:[1] Shoichiro Fukusako, Masahiro Sugawra and Nobuhiro Seki, Onset of natural convection and heat transfer in the melting of a horizontal ice layer (Review, in Japanese), Journal of the Japan Society of Mechanical Engineers 80-702 (1977), 445-450.[2] Masahiro Sugawara, Shoichiro Fukusako and Nobuhiro Seki, Experimental studies on the melting of a horizontal ice layer, Bulletin of the JSME 18-1218 (1975), 92-98.[3] Y. Katto, Heat Transfer (in Japanese), Yokendo, Japan, 1974, p. 173.[4] M. Sugawara, H. Inaba and N. Seki, Effect of maximum density of water on freezing of a water-saturated horizontal porous layer, Journal of Heat Transfer 110 (1988), 155-159.[5] M. Sugawara and M. Tago, Melting from below of a horizontal ice plate in rectangular cavity, JP Journal of Heat and Mass Transfer 35 (2023), 21-40.[6] M. Sugawara and M. Tago, Melting from above of a horizontal ice plate in an adiabatic cavity, JP Journal of Heat and Mass Transfer 29 (2022), 137-162.[7] M. Sugawara and M. Tag, Natural convection in a horizontal water layer with maximum density at 4°C, JP Journal of Heat and Mass Transfer 24 (2021), 1-18.[8] M. Sugawara and M. Tago, Three dimensional natural convection in a horizontal water layer with the maximum density, JP Journal of Heat and Mass Transfer 37-2 (2024), 159-170.[9] M. Sugawara and M. Tago, Melting of an ice plate in the inclined rectangular cavity with heat generating plate, JP Journal of Heat and Mass Transfer 36 (2023), 181-195.[10] 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 (2019), 73-108.[11] H. S. Carslaw and J. C. Jaeger, Conduction of heat in solid, 2nd ed., Oxford at the Clarendon Press, 1959, p. 286.
