Comparison of Models for Heat Transfer in High-Density Fibrous Insulation

Abstract

This study evaluated different models for calculating the effective thermal conductivity of fibrous insulation by comparing predicted values with certified values of Standard Reference Material 1450c, Fibrous Glass Board. This comparison involved the coupled effects of radiation and conduction heat transfer. To support these comparisons, the fiber diameter distribution was measured using X-ray computed tomography, and this distribution was used in several heat transfer models considered in this paper. For the evaluation of the radiative heat transfer, the diffusion approximation, the Schuster-Schwarzschild approximation, and the Milne-Eddington approximation were considered. The conduction of the gas and the fibers was treated by the kinetic theory and a semi-empirical model, respectively. Two models were considered for the evaluation of the radiative properties: the large specular reflecting approach and the application of Mie theory for media composed of infinite cylinders.

Theoretical and Experimental Studies on Thermal Properties of Polyester Nonwoven Fibrous Material

“…Some of the models require the fractions of fibers that are parallel or perpendicular to the heat flow direction. The values of fractions can be easily calculated via the trigonometric function (see Equations (12) and (13). The volume fractions of air and fiber and the fractions of fiber orientation are listed in Table 6.…”

Effective thermal conductivity of fiberglass insulation

“…As we will discuss subsequently, the relative contributions of the conductive and radiative heat transfers is a strong function of the insulation density. So, the findings of the study by Carvajal et al 23 for a very high-density fibrous insulation may not be applicable to very low-density fibrous insulations. Although the review paper by Anh and Pásztory 24 does not deal with the modeling of heat transfer in the insulation, it is a good resource for understanding the various factors that influence the thermal conductivity of building materials.…”

“…9,13-24 Lee et al 19 and Stephenson 22 have provided reviews of literature, especially on the radiative heat transfer in fibrous media. More recently, Carvajal et al 23 have evaluated several models for heat transfer for predicting the effective thermal conductivity of a high-density fibrous glass board insulation (NIST Standard Reference Material 1450c) used for industrial insulation applications. The density of the insulation used in the study by Carvajal et al 23 was 155.5 kg/m 3 .…”

“…More recently, Carvajal et al 23 have evaluated several models for heat transfer for predicting the effective thermal conductivity of a high-density fibrous glass board insulation (NIST Standard Reference Material 1450c) used for industrial insulation applications. The density of the insulation used in the study by Carvajal et al 23 was 155.5 kg/m 3 . This corresponds to about .07 volume fraction of glass fiber in the insulation fiber.…”

“…Modeling of the coupled phenomena of conduction and radiation in the fibrous insulation is challenging even when simplifying assumptions are made regarding the fiber orientation, fiber diameter, and the optical constants (the refractive index n and the absorption index κ in the complex refractive index m = n − iκ ). Because of its importance, the topic of heat transfer in fibrous insulations (for building and other applications) has received considerable attention in literature 9,13–24 . Lee et al 19 .…”