International Journal of Heat and Mass Transfer
Effective thermal conductivity of various filling materials for vacuum insulation panels
Introduction
A recent survey shows that 48% of the total energy consumption in the USA is made in buildings [1]. Needless to say, high performance thermal insulation is increasingly required to reduce energy consumption and/or to save valuable space. A superior thermal insulation can be achieved by so called vacuum insulation panel (VIP). Evacuated insulation enables a VIP to have about 10 times higher thermal resistance than the conventional insulators such as polystyrene or polyurethane foams. Similarly to a conventional Dewar flask or Thermos flask, a VIP makes use of vacuum to suppress the heat transfer due to gaseous conduction. While the Dewar flask has cylindrical shape made of glass or stainless steel wall, the flat type VIP must have a core material which withstands the atmospheric pressure and a gas-tight envelope maintaining the inside vacuum level. The core material has to be porous to easily evacuate and to have minimum conduction heat transfer effect. For this reason, materials in the form of powders, foams and fibers are used as the VIP core material [2]. In addition to the above conventional insulation materials, artificial structures such as staggered beams or honeycomb are proposed for the VIP’s filling material [3], [4].
Thermal transport in a VIP occurs via solid conduction, gaseous conduction and radiation. The solid conduction depends on the structure and material properties of the core. The gaseous conduction by residual gases depends on the gas pressure which increases with time by infusion of atmospheric gases and outgassing of the inner material. Thermal radiation depends on the structure and optical properties of the core. The total effective conductivity keff of the VIP can be determined by summation of the solid conductivity ks, the gaseous conductivity kg and the radiative conductivity kr as
Separate study of each contribution is required to improve the thermal insulation performance of the VIP. However, experimental separate measurement of these contributions is not easy because any of them cannot be fully eliminated. So, a theoretical study on the separate heat transfer mechanisms of the VIP is very instrumental for improving the thermal performance of a VIP.
Numerous studies on the heat transfer mechanisms of the non-evacuated conventional insulators have been conducted. For instance, Chan and Tien [5] analyzed conductance of packed spheres in vacuum. Also, an analytical model for predicting the effective thermal conductivity of packed beds of spheres is developed by Turyk and Yovanovich [6]. Thermal transport mechanisms in closed-cell foam insulations are described by Kuhn et al. [7]. For the fibrous insulation, heat transfer mechanisms are calculated theoretically and compared with the experimental data by Bankvall [8]. However, few studies on the thermal transport mechanisms of the various evacuated insulators are found in the literature.
The aim of this paper is a theoretical investigation of the thermal transport mechanisms with special emphasis on the solid conductivity for various VIP core structures including powder, foam, fiber and the staggered beam core. The solid conductivity is determined via a theoretical model. The gaseous and the radiative conductivities are derived by using separate theoretical models. With the above calculated results, the three heat transfer effects in VIPs are scrutinized in depth.
Section snippets
Powder insulation
Powders are often used as the filling material in vacuum for cryogenic applications. Materials such as perlite or silica are formed into fine granular particles. It is difficult to completely describe the effective solid conductivity due to the randomness of the packed bed structure. Instead, two cases are investigated using two different models. Firstly, a loose simple cubic arrangement of packed spheres is considered as a typical model (Fig. 1(a)). And then, a hexagonal close-packed model is
Gaseous conduction
Thermal transport in VIPs also occurs due to residual thin gas in the internal space. Thermal conductivity of gas is independent of pressure as far as the gaseous conduction may be treated as a continuum. This phenomenon is the result of the inverse relation between pressure and mean free path [17]. However, thermal conduction by gas is significantly reduced when the mean free path of gas molecules is about equal to or greater than the distance over which heat is transported. The mean free path
Radiative conductivity
Radiation at low pressure is another important heat transfer mechanism for VIPs. Radiation from a hot surface is attenuated via scattering and absorption/emission of the core structure. Two approaches are generally considered to describe the radiation heat transfer in thermal insulations structures, following Petrov [21].
The first approach is based on the radiative transfer equation (RTE). It can be solved numerically if the spectral and temperature dependencies of the absorption coefficient
Practical examples and discussions
The theoretically calculated solid conductivities ks of the various insulation materials for VIP are shown in Table 1. Note that the actual measurement reports exceptionally smaller solid conductivity for spherical powder, and thus, it calls for further investigation. As mentioned earlier, the discrepancy has been interpreted in terms of the increased porosity and the surface roughness effect. Suffice it to mention that actual ks for the silica powder-filled VIP is roughly one tenth of the
Conclusion
Heat transfer mechanisms with powder, foam, fiber and staggered beam as the VIP’s filling material have been investigated theoretically. The solid conductivity is obtained using simplified models. The effective solid conductivity is related with the porosity, pure solid conductivity and mechanical properties of the material. The fiber and staggered beam core are recommended in the aspect of the solid conduction due to the tortuously long thermal path. The gaseous conductivity at low pressure is
Acknowledgments
The authors gratefully acknowledge the financial support of several projects: Energy, Environment, Water, and Sustainability (EEWS) program funded by the Korea Advanced Institute of Science and Technology (KAIST), the Brain Korea 21 (BK21) program funded by Ministry of Education, Science and Technology (MEST) and the Manpower Development Program for Energy & Resources funded by the Ministry of Knowledge and Economy (MKE).
References (32)
Vacuum insulating panel
Vacuum
(1995)- et al.
Thermal transport in polystyrene and polyurethane foam insulations
Int. J. Heat Mass Transfer
(1992) - et al.
Thermal conductivity of silica powders at temperatures from 10 to 275 K
J. Non-Cryst. Solids
(1995) - et al.
Vacuum insulation panel – from research to market
Vacuum
(2008) Combined radiation and conduction heat transfer in high temperature fiber thermal insulation
Int. J. Heat Mass Transfer
(1997)- et al.
Spectral transmission and reflection properties of high temperature insulation materials
Int. J. Heat Mass Transfer
(1984) - et al.
Radiative heat transfer in insulation with random fibre orientation
Int. J. Heat Mass Transfer
(1990) - et al.
Radiative heat transfer through opacified fibers and powders
J. Quant. Spectrosc. Radiat. Transfer
(1983) - et al.
Improving energy efficiency in existing buildings
ASHRAE J.
(2008) - G. Kawaguchi, K. Nagai, Vacuum insulation spacer, US Patent No. 4409770,...