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.

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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.

Item Type: Article
Additional Information: Copyright the author, 2017.
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
URI: http://openaccess.city.ac.uk/id/eprint/17472

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