Thermal conductivity estimates of intumescent chars by direct numerical simulation

The effective thermal conductivity of fully expanded intumescent chars is estimated numerically using the finite element method. Digital images are used in conjunction with information regarding total porosity from bulk and helium density measurements to construct the FE model, where one pixel of the image corresponds to one element in the model. In order to account for micro-porous inclusions (at resolutions below the digital images), a thermal conductivity sub-model is employed. This is necessary in order to restrict the number of elements in the model to a reasonable size (∼10⁷ or fewer). Corrections to account for assumed 3D structure from the observed 2D image and also radiation augmentation across pores are also used in order to obtain better estimates of effective thermal conductivity. Calculations are compared to experimental values for a wide range of temperatures and surprisingly good agreement is found, given the severe assumptions adopted in the model.