Modeling the Effect of Infrared Opacifiers on Coupled Conduction-Radiation Heat Transfer in Expanded Polystyrene

Heat transfer properties of two expanded polystyrene (EPS) samples of similar density, one without (white) and one with graphite opacifier particles (gray), are compared. Tomographic scans are used to obtain cell sizes of the foams. Using established models for closed-cell polymer foams, the extinction coefficient and the effective thermal conductivity are obtained. The effect of opacifiers is modeled using (1) an effective refractive index for the polystyrene walls within a cell model for the EPS and (2) a superposition of extinction due to a particle cloud upon extinction predicted by the cell model, where particles are modeled as oblate spheroids, or equivalent volume, surface, or hydraulic diameter spheres. Modeled effective conductivities are compared with measurements done on a guarded hot-plate apparatus at sample mean temperatures in the range from 0 °C to 40 °C. Typically, cells of the gray EPS are about 40% larger than those of the white EPS and the cell walls in the gray EPS are thicker. The refractive index mixing model and the model with graphite opacifier particles as oblate spheroids overpredict extinction, however, the mean error in the effective conductivity predicted by the oblate spheroids model is only 2.7%. Equivalent volume/surface sphere models underpredict extinction, but still yield a low mean error in effective conductivity of around 4%. While the oblate spheroids model has a lower mean error, the computationally less expensive equivalent volume or equivalent surface models can also be recommended to model the inclusions.