pure and applied geophysics

, Volume 71, Issue 1, pp 132–148 | Cite as

The effect of radiative heat loss on steady cellular convection

  • Durga Ray


In the atmosphere there may be layers undergoing cellular convection with a much larger heat flux through the base of the layer than through the top. This may be either because there is a steady loss of heat by radiation from the body of the fluid or because the temperature is everywhere rising. In this latter case the temperature gradients could remain constant so that the mechanics would be the same as if the heat were being lost and the temperature kept steady. The fluid is considered incompressible as in the classical theory of cellular convection, and we determine the critical Rayleigh number for the onset of convection and the width to height ratio of the cells as functions of the heat loss. The problem, is in some respects analogous to that of the motion of a viscous fluid between rotating cylinders but in this case there are two non-dimensional-numbers-the Rayleigh number (g α βh4/K v) and a number representing the ratio of the heat loss by radiation to the heat flux. It is found that the critical Rayleigh number is decreased and the cells widened as had already been found for the case of a fluid with transfer coefficients having a spatial variation, with free boundaries, but the cells are made more narrow if the boundaries are rigid.


Radiation Atmosphere Convection Heat Flux Temperature Gradient 
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Copyright information

© Birkhäuser Verlag 1968

Authors and Affiliations

  • Durga Ray
    • 1
  1. 1.Mathematics DepartmentUniversity of IllinoisChicagoUSA

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