Effective Thermal Conductivity Of Foams Research Articles

Computational design of isotropic and anisotropic ultralow thermal conductivity polymer foams

Current state-of-the-art commercial polymer thermal insulation foam exhibits a thermal conductivity of 24 mW⸳m−1⸳K−1 (equivalently thermal resistivity of R-6/in.), similar to that of static air. To further optimize building energy efficiency, achieving even lower thermal conductivity is needed, which is, however, highly challenging. This paper presents computational evidence that demonstrates the feasibility of achieving an ultra-low thermal conductivity of less than 14.4 mW⸳m−1⸳K−1 (equivalently R-10/in.) using isotropic and anisotropic foam cell designs. For the isotropic design, we have identified analytical effective medium approximation (EMA) models within the accuracy of ±5% as finite element analysis (FEA) in predicting the effective thermal conductivity of foams with various porosities and filler gases. For the anisotropic design, we have developed and validated new EMA models against FEA in predicting the effective thermal conductivity of general anisotropic cuboids and Voronoi foams. For both isotropic and anisotropic designs, the design spaces for 18, 16, and 14.4 mW⸳m−1⸳K−1 (equivalently R-8, R-9 and R-10/in.) using various filler gases are obtained. It is found that polymer foams can be improved to achieve ultralow thermal conductivity by reducing CO2 concentration, reducing radiation, increasing porosity, and using anisotropic pore geometry. These findings contribute to the development of highly efficient thermal insulation materials, enhancing building energy efficiency and promoting sustainable construction practices.

Influence of boundary conditions on computation of the effective thermal conductivity of foams

Accurate numerical simulation of the effective thermal conductivity (ETC) of 3D pore-scale foam models requires a judicious choice of boundary conditions, as the computational domains are often smaller than the representative volume element, giving rise to considerable edge effects. Within the finite element homogenization framework, a set of mixed boundary conditions are considered alongside the usual uniform and periodic boundary conditions. Validity criteria and order relations, demonstrated from entropy-based principles, are numerically verified on unit cell-based geometries, random virtual periodic foams, and non-periodic tomography-reconstructed foams of equivalent microstructure. A statistical treatment based on the integral range provides confidence intervals for the estimated ETC. For foam samples with random homogeneous porosity, the mixed boundary conditions are shown to fulfill the macrohomogeneity condition and thus provide thermodynamically valid ETC estimates. For periodic foams with irregular microstructure, the ETC is very slightly underestimated under the mixed boundary conditions. For non-periodic geometries, it is shown that periodic boundary conditions–commonly viewed as the reference–underestimate the ETC due to boundary geometry mismatch, while the mixed boundary conditions give a more accurate and precise estimate.

Modeling heat conduction in open-cell metal foams by means of the Three-Dimensional Thermal Fin theory

Their relatively high thermal conductivity makes metal open-cell foams promising heat transfer enhancers for lightweight applications. Conduction occurs through both solid and fluid phases, depending on the material and the microstructure. The effective conductivity of a foam is predicted by means of analytical and numerical methods, based on both idealized and realistic foam geometries, as well as by empirical correlations based on experiments. In this paper, a new model for the prediction of the effective thermal conductivity of foams is proposed. The proposed Three-Dimensional Thermal Fin (TTF) theory is based on the Electrochemical Fin (ECF) theory previously applied to the analysis of ion and electron transport through nanoporous materials. It has computational time two - three times shorter than those of current numerical techniques, such as finite-element methods. Starting from a tomography-reconstructed metallic open cell foam, the 3-D structure is modeled as a network. Conventional fin heat transfer scaled equations, applied to each part of the network, allow for the evaluation of the temperature distribution and heat rates. The effective thermal conductivity of the metal foam is then derived. The proposed model is validated by comparison with experimental results as well as with predictive models from the open literature and a finite-element based model.

Thermal conductivity of rigid foam insulations for aerospace vehicles

The present work describes measurements of the effective thermal conductivity of NCFI 24-124 foam, a spray-on foam insulation used formerly on the Space Shuttle external fuel tank. A novel apparatus to measure the effective thermal conductivity of rigid foam at temperatures ranging from 20K to 300K was developed and used to study three samples of NCFI 24-124 foam insulation. In preparation for measurement, the foam samples were either treated with a uniquely designed moisture absorption apparatus or different residual gases to study their impact on the effective thermal conductivity of the foam. The resulting data are compared to other measurements and mathematical models reported in the literature.

Estimation of effective thermal conductivity enhancement using foam in heat exchangers based on a new analytical model

Thermal performance of open-cell metal foam has been investigated under low Reynolds number by comparing the heat transfer coefficient and thermal conductivity for the flow through a packed channel of high porosity metal foam to that of an open channel. In the case of Al-Air at porosity 0.971, the ratio of heat transfer coefficients is estimated to be 18.5 when the thermal conductivity ratio of foam matrix to fluid conductivity is 130. This demonstrates that the useusing of foam in the structure of conventional air coolers increases effective thermal conductivity, heat transfer coefficient and thermal performance considerably. To overcome the drawbacks of previous models, a new model to describe the effective thermal conductivity of foam was developed. The model estimates effective thermal conductivity based on a non-isotropic tetrakaidecahedron unit-cell and is not confined only to isotropic cases as in previous models. Effective thermal conductivity is a function of foam geometrical characteristics, including ligament length (L), length of the sides of horizontal square faces (b), inclination angle that defines the orientation of the hexagonal faces with respect to the rise direction (θ), porosity, size, shape of metal lump at ligament intersections and heat transfer direction. Changing dimensionless foam ligament radius or height (d) from 0.1655 to 0.2126 for Reticulated vitreous foam -air (RVC-aAir) at θ=π/4 and dimensionless spherical node diameter (e) equal to 0.339, raises effective thermal conductivity by 31%. Moreover, increasing θ from π/4 to 0.4π for RVC-aAir at d=0.1655 and e=0.339 enhances effective thermal conductivity by 33%.