Natural convection occurs in enclosures as a result of gradients in density, which are in turn due to variations in temperature or concentration. The rate of heat transfer is usually characterized by a Nusselt number as a function of a Rayleigh number, the Prandtl number, the geometry, and the boundary and initial conditions. The Nusselt and Rayleigh numbers are ordinarily based on the external temperature difference and the dimension of the enclosure in the direction of heat transfer, with some exceptions as noted below. The other variables in these groups are defined as in Section 174.

Catton (1978) provides a recent, comprehensive, and interpretive review of natural convection in enclosures. Ostrach (1972 and 1975) discusses cylindrical and rectangular enclosures in somewhat greater detail. Koschmieder (1974) has reviewed Bénard-type convection and Buchberg et al. (1976) applications of natural convection in solar collectors. Churchill and Ozoe (n.d.) have utilized theoretical and experimental results for asymptotic conditions to develop correlating equations for heat transfer in rectangular and cylindrical enclosures for a wide range of conditions with special attention to the effect of the angles of inclination and rotation.

In this section a description of the fluid motion is provided and correlations are recommended for heat transfer for conditions of primary practical importance. Referral to the references cited herein and in the above reviews is suggested for derivations and further details.

Experimental results for natural convection in enclosures are generally less accurate than for forced convection owing to difficulty in repressing and evaluating the heat fluxes through and along the nonisothermal walls. As a consequence, discrepancies between various sets of data are not completely resolved. Also, the time scale of experiments, particularly with liquids, is sometimes insufficient to attain the true stationary state.

Theoretical results are limited in accuracy and scope owing to the inherent three dimensionality of the velocity and temperature fields in all enclosures with two or three finite dimensions. This three dimensionality affects the transitions from one mode of circulation to another. If one or the other aspect ratio is near unity, the three dimensionality affects the rates of circulation and heat transfer significantly. Even so, the many two- dimensional and the few three-dimensional solutions provide a useful basis for the interpretation, correlation, and extrapolation of the experimental values.