This paper is concerned with convection generated by uniformly distributed internal heat sources. By a numerical method it is found that the planform is down-hexagons for infinite Prandtl numbers and Rayleigh numbers up to at least ten times the critical value. The motion is also studied for finite Prandtl numbers and small supercritical Rayleigh numbers by using an amplitude expansion. It follows that a small subcritical regime exists. Moreover, it also follows that for Prandtl number less than 0.25, the stable planform is up-hexagons. In section 3 a necessary condition is derived in order to obtain a hexagonal planform when the coefficients in the differential equations are a function of the vertical coordinate z.

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This paper is concerned with thermal convection in a horizontal fluid layer bounded below and above by two rigid planes of constant and equal temperature. The convection is generated by uniformly distributed internal heat (cool) sources. Stable hexagons are found for Rayleigh numbers up to 3.6 times the critical value~ down-hexagons when the fluid is internally heated, and up-hexagons when the fluid is internally cooled. Moreover, a subcritical region,where the hexagons may exist, is also found.

The conditions for obtaining thermal convection in dry snow are examined. It is shown that thermal convection will occur in dry snow layers with strong vertical temperature gradients and large air permeabilities (i.e., old snow). Thermal convection will lower the insulating power of the snow and increase the flux of water vapor through the snow layer. The magnitude of the heat and mass flux in convection is computed for several values of the Rayleigh number.