Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures

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 , the Rayleigh number <!-- MATH $A = g\left( {{T_1} - {T_0}} \right){d^3}/\left( {{T_0}\kappa \nu } \right)$ --> , and the ratio of the sides of the rectangle . In the case of cavities used for thermal insulation of buildings, which is kept specially in mind throughout the paper, is usually about 1000 d (where is in centimeters), and takes values between about 5 and 200.