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Onset of thermal instability in a horizontal layer of fluid with modulated boundary temperatures

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Abstract

Thermal instability in a horizontal layer of fluid, with the boundary temperatures modulated sinusoidally in time, is studied. The amplitude of modulation is assumed small and is used as an expansion parameter. It is shown that an exact solution can be obtained, even when the boundaries are considered to be rigid. When only the lower boundary temperature is modulated, for small values of the Prandtl number modulation is always stabilizing, while for large values it can be stabilizing or destabilizing depending on the modulation frequency. When both boundary temperatures are modulated in phase, modulation is destabilizing for low modulation frequency, but for higher modulation frequency stabilization occurs for low values of the Prandtl number. When the two boundary temperatures are modulated out of phase the modulation always has a stabilizing effect.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur, 721302, West Bengal, India

    V. R. K. Raju & S. N. Bhattacharyya

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  1. V. R. K. Raju
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  2. S. N. Bhattacharyya
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Correspondence to S. N. Bhattacharyya.

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Raju, V.R.K., Bhattacharyya, S.N. Onset of thermal instability in a horizontal layer of fluid with modulated boundary temperatures. J Eng Math 66, 343–351 (2010). https://doi.org/10.1007/s10665-009-9305-z

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  • DOI: https://doi.org/10.1007/s10665-009-9305-z

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