Heat transfer in one-dimensional micro- and nano-cellular foams

Author-Highlights
• In polymer foams more than 30% of heat can be transferred by radiation.
• One-dimensional plane-parallel model of polymer foam is developed.
• Foams are treated as participating media with reflection on phase interfaces.
• Knudsen effect in foams with sub-micron cells is studied.
• Foam geometry is optimized with regard to insulating properties.

We investigate heat transfer in one-dimensional multi-layer models of polymer foams and determine their equivalent thermal conductivities. The proposed model considers the participating gas and solid phases, i.e., combined heat transfer by conduction and radiation in both phases and partial photon reflection on phase interfaces. A correction for possible non-Fourier heat conduction in small gas cells, occurring in nanocellular foams, is implemented by the reduction of gas thermal conductivity based on the Knudsen number. The developed model was used for the optimization of foam structure with respect to its insulation properties. We found that although radiation can account for more than one-third of the total heat flux, it can be reduced in foams with cell-sizes below 100μm and be almost nullified by decreasing the foam cell size to sub-micron range. The presented model is a starting point for the development of an advanced model of heat transfer in spatially three-dimensional polymer foams.