Theoretical analysis of the liquid thermal structure in a pool fire

Abstract

This article presents a theoretical work on liquid heat-up in the case of a pool fire. It is assumed that the convective currents occurring within the upper layer of the liquid are induced by Rayleigh–Bénard instabilities that are caused by in-depth radiation. The upper layer depth has been estimated based on the analytical solution of a one-dimensional Fourier’s equation for the temperature with a source term for in-depth radiation. The model has been assessed against experimental data for a 9-cm-diameter methanol steady-state pool fire and three different liquid depths (18, 12 and 6 mm). The general trend, that is, increase in the upper layer depth as the bottom boundary temperature increases, is well captured. In order to ensure that the well-mixed upper layer is at a temperature near the boiling point (as suggested by the experimental data), an improvement is proposed based on a radiative heat balance integral method. In addition to the above, a novel methodology is developed for the calculation of the ‘effective’ thermal conductivity as a means to circumvent detailed calculations of heat transfer within the liquid.