The effect of heating rate on the stability of stationary fluids

Author:

Currie I. G.

Abstract

A horizontal fluid layer whose lower surface temperature is made to vary with time is considered. The stability analysis for this situation shows that the criterion for the onset of instability in a fluid layer which is being heated from below, depends on both the method and the rate of heating. For a fluid layer with two rigid boundaries, the minimum Rayleigh number corresponding to the onset of instability is found to be 1340. For slower heating rates the critical Rayleigh number increases to a maximum value of 1707·8, while for faster heating rates the critical Rayleigh number increases without limit.Two specific types of heating are investigated in detail, constant flux heating and linearly varying surface temperature. These cases correspond closely to situations for which published data exist. The results are in good qualitative agreement.

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Reference9 articles.

1. Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability .Oxford University Press.

2. Soberman, R. K. 1959 Onset of convection in liquids subject to transient heating from below Phys. Fluids 2,131–38.

3. Goldstein, A. W. 1959 Stability of a horizontal fluid layer with unsteady heating from below and time dependent body forces.NASA Tech. Rep. no. R-4.

4. Chandra, K. 1938 Instability of fluids heated from below.Proc. Roy. Soc A164,231–42.

5. Spangenberg, W. G. & Rowland, W. R. 1961 Convective circulation in water induced by evaporative cooling Phys. Fluids 4,743–50.

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