Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures
Author:
G. K. Batchelor
Journal:
Quart. Appl. Math. 12 (1954), 209-233
MSC:
Primary 76.1X
DOI:
https://doi.org/10.1090/qam/64563
MathSciNet review:
64563
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Abstract: The two-dimensional convective motion generated by buoyancy forces on the fluid in a long rectangle, of which the two long sides are vertical boundaries held at different temperatures, is considered with a view to the determination of the rate of transfer of heat between the two vertical boundaries. The governing equations are set up; they reveal that the flow is determined uniquely by the Prandtl number $\sigma$, the Rayleigh number $A = g\left ( {{T_1} - {T_0}} \right ){d^3}/\left ( {{T_0}\kappa \nu } \right )$, and the ratio of the sides of the rectangle $l/d$. In the case of cavities used for thermal insulation of buildings, which is kept specially in mind throughout the paper, $A$ is usually about 1000 d$^{3}$ (where $d$ is in centimeters), and $l/d$ takes values between about 5 and 200.
Goldstein (Editor), Modern developments in fluid dynamics, Oxford, Vol. II, Chap. 14, 1938.
E. Love, The mathematical theory of elasticity, Cambridge, 1900.
Jakob, Heat Transfer, Wiley & Sons, Vol. I, Chap. 25, 1949.
Mull and H. Reiher, Gesundh.-Ing. Beihefte, Reihe 1, No. 28, 1930.
F. Pillow, The free convection cell in two dimensions, Aero. Res. Lab., Melbourne, Rep. A79 (1952).
Goldstein (Editor), Modern developments in fluid dynamics, Oxford, Vol. II, Chap. 14, 1938.
E. Love, The mathematical theory of elasticity, Cambridge, 1900.
Jakob, Heat Transfer, Wiley & Sons, Vol. I, Chap. 25, 1949.
Mull and H. Reiher, Gesundh.-Ing. Beihefte, Reihe 1, No. 28, 1930.
F. Pillow, The free convection cell in two dimensions, Aero. Res. Lab., Melbourne, Rep. A79 (1952).
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Article copyright:
© Copyright 1954
American Mathematical Society