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Convection in a radiating gas

Published online by Cambridge University Press:  28 March 2006

John Gille  and
Richard Goody
John Gille
Affiliation:
Harvard University
Richard Goody
Affiliation:
Harvard University
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Abstract

We have made a theoretical and experimental study of the effect of radiative transfer on the onset of convection by means of comparative experiments in dry air and ammonia contained between horizontal aluminium plates maintained at different temperatures.

The first effect of radiative transfer is to distort the linear, diffusive profile in the initial, pre-convective state. A non-grey theory is developed and is shown to predict the non-linear profiles profiles with satisfactory accuracy. The change of radiative flux with pressure of ammonia is also predicted and confirmed. This constitutes the first successful attempt to confirm the methods used in atmospheric studies in controlled experiment.

A non-grey theory of the onset of convection is developed, separating effects associated with the distortion of the static state and the dissipative effect of radiative transfer on temperature fluctuations.

Experiments indicate that the critical Rayleigh number in ammonia can be greatly increaesd over the best value for air (Rac = 1786); the maximum observed being Rac = 4870. Theory and experiment are shown to agree within reasonable limits.

This work confirms the validity of methods which are of great importance to astrophysics and atmospheric physics.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 20 , Issue 1 , September 1964 , pp. 47 - 79
Copyright
© 1964 Cambridge University Press

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References

Benedict, W. S., Plyer, E. K. & Tidwell, E. D. 1958 Vibration rotation bands of ammonia. I. The combination bands v2 +(v1, v3). J. Res. N.B.S. 61, 123–147.Google Scholar
Bleaney, B. & Penrose, R. P. 1948 Collision broadening of the inversion spectrum of ammonia. III. The collision cross-section for self-broadenign and for mixtures with non-polar gases. Proc. Phys. Soc. 60, 540–549.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford: Clarendon Press.
Chapman, S. & Cowling, T. G. 1952 The Mathematical Theoryof Non-Uniform Gases. Cambridge University Press.
Van Cleave, A. B. & Maass, O. 1935 The variation of the viscosity of gases with temperature over a large temperature range. Canad. J. Res. 13, 140–148.Google Scholar
Croft, J. F. 1958 The convective region and temperature distribution above a horizontal heated surface. Quart. J. R. Met. Soc., 84, 418–427.Google Scholar
Foley, H. M. & Randall, H. M. 1941 Fine structure in the far infrared spectrum of NH3. Phys. Rev. 59, 171–173.Google Scholar
Franck, E. U. 1951 Zur Temperaturabhängigkeit der Wärmeleitfähigkeit einiger Gase. Z. Elektrochem., 55, 636–643.Google Scholar
Friberg, S. 1927 über die Dispersion des Lichtes in gasformigen Körpern innerhalb des ultravioletten Spektrums. Z. Physik, 41, 378–384.Google Scholar
Garing, J. S., Nielsen, H. H. & Rao, K. N. 1959 The low frequency vibration-rotation bands of the ammonia molecule. J. Mol. Spectroscopy, 3, 496–527.Google Scholar
Gerhard, S. L. & Dennison, D. M. 1933 The envelopes of infrared absorption bands. Phys. Rev. 43, 197–204.Google Scholar
Goody, R. M. 1956 The influence of radiative transfer on cellular convection. J. Fluid Mech., 1, 424–435.Google Scholar
Goody, R. M. 1964 Atmospheric Radiation. I. Theoretical Basis. Oxford: Clarendon Press.
Hadni, A. 1953 Structure fine des raies de rotation de l'ammoniac de J' = 14 a J' = 18. Compt. Rend., Paris, 237, 317–318.Google Scholar
Hansler, R. L. & Oetjen, R. A. 1952 The infrared spectrum of HCl, DCl, HBr, and NH3 in the region from 40-140. J. Chem. Phys. 21, 1340–1343.Google Scholar
Hirschfelder, J. O., Curtiss, C. F. & Bird, R. B. 1954 Molecular Theory of Gases and Liquids. New York: Wiley.
Hottel, H. C. 1954 Heat Transmission, ed. McAdams, W. H., Chapter IV. New York: McGraw-Hill.
Kaplan, L. D. & Eggers, D. F. 1956 Intensity and linewidth of the 15-micron CO2 band, determined by a curve of growth method. J. Chem. Phys. 25, 876–883.Google Scholar
Kennard, R. B. 1941 Temperature distribution and heat flux in air by interferometry. Temperature. Its Measurement and Control in Science and Industry, pp. 685–706. New York: Reinhold.
Landholt-Bornstein 1962 Zahlenwerte und Funktionen, 1962, 6th edition. Berlin: Springer.
Mason, E. A. & Monchick, L. 1962 Heat conductivity of polyatomic and polar gases. J. Chem. Phys. 36, 1622–1639.Google Scholar
McKean, D. C. & Schatz, P. N. 1956 Absolute infrared intensities of vibration bands in ammonia and phosphine. J. Chem. Phys. 24, 316–325.Google Scholar
National Bureau of Standards 1955a Circular 564. Tables of thermal properties of gases. Washington, D.C.: U.S. Department of Commerce.
National Bureau of Standards 1955b Circular 561. Reference Tables for Thermocouples. Washington, D.C.: U.S. Department of Commerce.
Malkus, W. V. R. 1954 Discrete transitions in turbulent convection. Proc. Roy. Soc. A, 225, 185–195.Google Scholar
Osborne, N. S., Stimson, H. F., Sligh, T. S. Jr., & Crague, C. S. 1924 Specific heat of superheated ammonia vapor. Sci. Papers Nat. Bur. Standards, 20, 65–110.Google Scholar
Pellew, A. & Southwell, R. V. 1940 On maintained convective motion in a fluid heated from below. Proc. Roy. Soc. A, 176, 312–343.Google Scholar
Pierson, R. H., Fletcher, A. N. & Gantz, E. St. C. 1956 Catalogue of infrared spectra for qualitative analysis of gases. Anal. Chem. 28, 1218–1239.Google Scholar
Port, F. J. Jr., 1940 Heat Transmission by Radiation from Gases. Sc.D. Thesis, Dept. of Chemical Engineering, Masschusetts Institute of Technology.
Silveston, P. L. 1958 Wärmedurchgang in waagerechten Flüssigkeitsschichten. Forsch. Ing. Wes. 24, 29–32 and 59–69.Google Scholar
Slawsky, Z. I. & Dennison, D. M. 1939 The centrifugal distortion of axial molecules. J. Chem. Phys. 7, 509–521.Google Scholar
Spiegel, E. A. 1957 On smoothing temperature fluctuations by radiative transfer. Ap. J., 126, 202–207.Google Scholar
Spiegel, E. A. 1960 The convective instability of a radiating fluid layer. Ap. J., 132, 716–728.Google Scholar
Sutton, O. G. 1951 On the stability of a fluid heated from below. Proc. Roy. Soc. A, 204, 297–309.Google Scholar
Thompson, H. W. 1941 The free energy of methyl cyanide and equilibrium constants of some relatd reactions. Trans. Faraday Soc., 37, 344–352.Google Scholar
Townsend, A. A. 1958 The effects of radiative transfer on turbulent flow of a stratified fluid. J. Fluid Mech., 4, 361–375.Google Scholar
Wright, N. & Randall, H. M. 1933 The far infrared absorption spectra of ammonia and phosphine gases under high resolving power. Phys. Rev. 44, 391–398.Google Scholar