The Landau method is used to determine the heat transfer to the upper and lower surfaces of a volumetrically heated layer of molten fuel for various fixed values of the upper and lower surface temperatures. To use the Landau method, the Stuart shape assumption is imposed and solutions to the linearized stability problem are used. The results are generalized in terms of two Nusselt numbers (upper and lower surface heat transfer) which are presented as a function of the Rayleigh number based on the internal heat generation rate for various values of an external Rayleigh number based on the surface to surface temperature difference. Results are also presented for a molten UO2 layer for various typical values of decay heat. Comparison is made with experiment, where possible, and found to be good.

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