Author:
Liang S. F.,Vidal A.,Acrivos Andreas
Abstract
Numerical solutions to the Boussinesq equations containing a temperature-dependent viscosity are presented for the case of axisymmetric buoyancy-driven convective flow in a cylindrical cell. Two solutions, one with upflow and the other with downflow at the centre of the cell, were found for each set of boundary conditions that were considered. The existence of these two steady-state régimes was verified experimentally for the case of a cylindrical cell having rigid insulating lateral boundaries and isothermal top and bottom planes.Using a perturbation expansion it is also shown that only one of these solutions remains stable in the subcritical régime. This, however, seems to be confined to a very narrow range of Rayleigh numbers, beyond which, according to all the evidence presently at hand, both solutions are equally stable for those values of the Rayleigh and Prandtl numbers for which axisymmetric motions occur.Finally, certain fundamental differences between the problem considered here and that of thermal convection in a layer of infinite horizontal extent are briefly discussed.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Reference13 articles.
1. Thermal instability in a horizontal fluid layer: effect of boundary conditions and non-linear temperature profile
2. Palm, E. 1960 On the tendency towards hexagonal cells in steady convection J. Fluid Mech. 8,183–92.
3. Mitchell, W. T. & Quinn, J. A. 1966 Thermal convection in a completely confined fluid layer A.I.Ch.E. J. 12,1116–24.
4. Hurle, D. T. J. , Jakeman, E. & Pike, E. R. 1967 On the solution of the Bénard problem with boundaries of finite conductivity Proc. Roy. Soc. A 296,469–75.
5. Palm, E. , Ellingsen, T. & Gjevik, B. 1967 On the occurrence of cellular motion in Bénard convection J. Fluid Mech. 30,651–661.
Cited by
77 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献