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Cellular convection with liquid-film flow

Published online by Cambridge University Press:  12 April 2006

E. James Davis  and
C. K. Choi
E. James Davis
Affiliation:
Department of Chemical Engineering, Clarkson College of Technology, Potsdam, New York 13676
C. K. Choi
Affiliation:
Department of Chemical Engineering, Clarkson College of Technology, Potsdam, New York 13676
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Abstract

This paper is a theoretical and experimental investigation of the onset of the buoyancydriven longitudinal roll cells that occur when a liquid layer flows over a heated horizontal plate. Linear stability theory is applied under the assumption that the spatially developing temperature profile can be treated locally, that is at each axial position, as being ‘frozen’. Using the film thickness as the length scaling factor, the critical Rayleigh numbers associated with the onset of longitudinal rolls are found to be considerably lower than measured values. A modified local stability analysis using the thermal boundary-layer thickness as the scaling factor is shown to agree with experiments. Predicted wavenumbers and the position of the onset of cellular convection are in agreement with wavenumbers measured by flow-visualization techniques. The position of the onset of cellular convection is also obtained from heat-transfer measurements at the heated surface. In the asymptotic limit of a linear undisturbed temperature profile the classical solutions of the Rayleigh-Bénard problem for the critical Rayleigh number and wavenumber are recovered, the only effect of the flow being the structure of the secondary flow that occurs when the system is unstable. Amplification theory is also compared with experimental data for the position at which the thermal effects of the convection are detectable and for the wavenumbers measured by flow visualization. The thermal amplification ratio $\overline{Nu}$ and a velocity-disturbance amplification ratio $\overline{w}$ are used to interpret the onset of discernible cellular convection. The data are not consistent with any single amplification ratio over the range of Rayleigh numbers studied (103 < Ra < 3 × 105), and the theoretical and experimental results suggest that a band of wavenumbers rather than a single wavenumber is encountered when cellular convection occurs.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 81 , Issue 3 , 13 July 1977 , pp. 565 - 592
Copyright
© 1977 Cambridge University Press

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