Critical Rayleigh number of an error function temperature profile with a quasi-static assumption
Kerr, O. (2016). Critical Rayleigh number of an error function temperature profile with a quasi-static assumption.
Abstract
When a semi-infinite body is heated from below by a sudden increase in temperature (or cooled from above) an error function temp erature profile grows as the heat diffuses into the fluid. The stability of such a profile is investigated using a large-wavelen gth asymptotic expansion under the quasi-static, or frozen-time, approximation. The critical Rayleigh number for this layer is f ound to be Ra=√(1/2) based on the length-scale √(κ t) where κ is the thermal diffusivity and t the time since the onset of heating.
| Publication Type: | Article |
|---|---|
| Additional Information: | Copyright the author, 2017. |
| Subjects: | Q Science > QA Mathematics |
| Departments: | School of Science & Technology > Mathematics |
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Official URL: http://arxiv.org/abs/1609.05124
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