Abstract
The problem of the onset of convective motion in the fluid bounded by walls of finite thermal conductivity and finite thickness is investigated by linear analysis for two cases. In Case I we consider only the effect of the upper and lower walls, assuming the horizontal extent of fluid to be infinite. In Case II we consider only the effect of side walls with the upper and lower boundary conditions treatded in a conventional manner. In both cases, the governing equations are linearized with the Boussinesq approximation and the principle of exchange of stabilities is proved to be valid. The procedure of solving the eigenvalue probelms is described briefly.
In Case I, the effect of the thickness of the walls (h) is found to be almost the same as that in the limiting case h→∞ for h larger than the depth of the fluid. As the ratio of thermal conductivity of the walls to that of the fluid (ξ) decreases, the critical Rayleigh number is reduced and the horizontal sclae of motion becomes larger.
In Case II the effect of the thickness of the side walls is almost the same as that in the limiting case h→∞ for h larger than half the depth of the fluid layer. The effect of the lateral width of the fluid layer is shown very strong on the onset of motion. The calculated value of the critical Rayleigh number is compared with that obtained experimentally by Ukaji and Sawada (1969), and good agreement is obtained.
