A theoretical model is proposed for the situation in which the rate of spread of flame across the surface of a liquid is controlled by the necessity to preheat the liquid in advance of the flame. In this model the flame is represented by a moving strip source of heat and the liquid by an anisotropic solid. The contributions of convection currents to the preheating of the liquid are represented by 'effective thermal conductivities'. Heat conduction theory then leads to expressions relating rate

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... f spread of flame and horizontal and vertical temperature varia tions in the liquid to the characteristics of the flame and the liquid. Several points of qualitative resemblance between the predictions of this theoretical model and relevant experimental data are established, and these are used to determine values of horizontal and vertical ' effective thermal conductivities ' and of heat flux from the flame to the liquid, the significance of which is discussed. The model predicts a region in which the spread of flame would not be possible because of excessive heat loss. This region was not entered experimentally for reasons which are discussed. I n t r o d u c t io n