Abstract
This paper attempts to explain theoretically the observed results that (1) the cells in steady convection approach a hexagonal form, and (2) the occurrence of ascent or descent in the middle of the cell depends on how the kinematical viscosity varies with temperature. The theory is based on non-linear equations and, of course, a variable coefficient of viscosity.It is found that, due to the variation of viscosity with temperature, the non-linear terms contain a second-order term which is destabilizing. This second-order term regulates the development and leads to a final motion composed of regular hexagons with ascent or descent in the middle of the cell according as the viscosity decreases or increases with temperature.The influence of a variable viscosity on Rayleigh's result concerning the initiation of convection is obtained as a by-product.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Reference10 articles.
1. Tippelskirch, H. V. 1956 Beitr. Phys. frei. Atmos. 29,37.
2. Pellew, A. & Southwell, R. V. 1940 Proc. Roy. Soc. A,176,312.
3. Bénard, M. 1901 Ann. Chim. Phys. 23,62.
4. Jeffreys, H. 1930 Proc. Camb. Phil. Soc. 26,170.
5. Graham, A. 1933 Phil. Trans. A,232,285.
Cited by
257 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