Computational thermal conductivity in polyurethane mixed cell foam: Numerical boundary effects and hybrid model

Abstract

The effective thermal conductivity is the most useful characteristic property to distinguish between two or more insulation materials. It is always the same by using different boundary conditions or different representative elementary volume sizes. The objective of this paper is to set variational formulations of different types of boundary conditions Dirichelet boundary condition (EBC), Neumann boundary condition (NBC), Mixed boundary condition (MBC) and Periodic boundary condition (PBC). Then effective thermal conductivity are investigated by scale effect study of the representative elementary volume size of the different categories of Polyurethane foam, closed cell foam, open cell foam and mixed cell foam. The apparent conductivity remain the same for MBC, PBC and EBC in the case of closed and open unit cell foam. The effective thermal conductivity for the different categories of PU foam converge as the REVs sizes increase. A comparative study with numerical, analytical and experimental thermal conductivity is performed in order to validate the results. A hybrid model is proposed in order to overcome the computational cost of the investigation of the effective thermal conductivity of mixed cell foam.

Keywords

• Multi-scale modeling
• Computational thermal conductivity
• Boundary conditions
• Numerical homogenization