© 1958 by Oxford University Press
HEAT TRANSFER BY LAMINAR FREE CONVECTION IN ENCLOSED PLANE GAS LAYERS
( Department of Theoretical Mechanics, University of Bristol )
A numerical method based on the use of orthogonal polynomials is given for the solution of two simultaneous partial differential equations which govern the heat transfer by laminar free convection in enclosed horizontal, oblique, and vertical gas layers. The heat transfer through the enclosed gas layer depends only on the Rayleigh number A = g(T1-T0)d3/(T0kv), the Prandtl number 
= v/k, the aspect ratio of the rectangular cell 
= l/d, the angle of inclination ø of the hot and cold walls to the vertical, and finally the temperature distribution in the remaining two walls or border strips.
Preliminary thermal results are given for air taking = 0·73, = 1, ø = 0 and A = 5× 102, 103, 2·5× 103, 5× 103, and 104, and the temperature distribution along the border strips to be T = T0+(T1-T0)y/d. A comparison of the theoretical prediction of the heat transfer across the cell with the experimental data of Mull and Reiher (1), as correlated by Jakob (2), can only be made in the region A = 104. Calculated results and empirical formulae obtained by Jakob agree favourably in this region considering that all the measurements of Mull and Reiher were made for large values of the aspect ratio and virtually non-conducting border strips.
Streamlines and isothermals have been plotted for A = 104 which clearly indicate the existence of an isothermal core in the cavity having constant vorticity, as postulated by Batchelor (3).