Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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.


References [Enhancements On Off] (What's this?)

  • [S] Goldstein (Editor), Modern developments in fluid dynamics, Oxford, Vol. II, Chap. 14, 1938.
  • [A] E. Love, The mathematical theory of elasticity, Cambridge, 1900.
  • [M] Jakob, Heat Transfer, Wiley & Sons, Vol. I, Chap. 25, 1949.
  • [W] Mull and H. Reiher, Gesundh.-Ing. Beihefte, Reihe 1, No. 28, 1930.
  • [A] F. Pillow, The free convection cell in two dimensions, Aero. Res. Lab., Melbourne, Rep. A79 (1952).

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DOI: https://doi.org/10.1090/qam/64563
Article copyright: © Copyright 1954 American Mathematical Society


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