Abstract
The method of energy is used to discuss the stability of time-dependent diffusive temperature profiles in fluid layers subject to impulsive changes in surface temperature.Bounds for the ratio of disturbance energy production to dissipation are found to be parametric functions of time because the basic temperature develops through diffusion. This time dependence leads to the demarcation of regions of stability in a Rayleigh number-time plane and the interpretation of these regions is given. Numerical results are presented for the cases of impulsive heating and cooling of initialty isothermal fluid layers. New global stability results which give the Rayleigh number below which the diffusive solution to the Boussinesq equations is unique are reported for these cases.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Reference26 articles.
1. Joseph, D. D. 1971 In Instability of Continuous Systems IUTAM Symp. Herrenalb 1969 (ed. H. Leipholz ).Springer.
2. Yih, C.-S. 1968 J. Fluid Mech. 31,737.
3. Conrad, P. W. & Criminale, W. O. 1965a Z. angew. Math. Phys. 16,233.
4. Rosenblat, S. & Herbert, D. M. 1970 J. Fluid Mech. 43,385.
5. Joseph, D. D. 1965 Arch. Rat. Mech. Anal. 20,59.
Cited by
80 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