Details

In this paper, we present a ‘simplified’ approach for the numerical modelling of the convective currents that occur within a liquid fuel in the case of a pool fire and which are induced by in-depth thermal radiation. This approach is based on the concept of ‘effective’ thermal conductivity, which is calculated herein based on the analytical solution of a steady-state one-dimensional heat conduction equation including a source term for in-depth radiation. This solution leads to a temperature profile which displays a horizontal liquid layer (of a given depth) that is bounded by a temperature that is higher at its bottom than its top. This thermal structure generates Rayleigh-Bénard instabilities which enhance heat transfer within the liquid. This effect is modeled via an increase of the ‘actual’ thermal conductivity of the liquid by a dimensionless heat transfer number, namely the Nusselt number. The Nusselt number is calculated based on the ‘classical expression’ of the Rayleigh number for the case of a ‘horizontal cavity heated from below’. The paper provides the details of the derived solution for the ‘effective’ thermal conductivity along with examples of application to several fuels.