Thermal conductivity of porous materials
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tsu Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi, 466-8555 Japan
Hideaki Matsubara Japan Fine Ceramics Center, Atsuta, Nagoya, 456-8587 Japan
Pierre Elser and Urs T. Gonzenbach De Cavis Ltd., 8093 Zürich, Switzerland (Received 20 March 2013; accepted 31 May 2013)
Incorporation of porosity into a monolithic material decreases the effective thermal conductivity. Porous ceramics were prepared by different methods to achieve pore volume fractions from 4 to 95%. A toolbox of analytical relations is proposed to describe the effective thermal conductivity as a function of solid phase thermal conductivity, pore thermal conductivity, and pore volume fraction (mp). For mp , 0.65, the Maxwell–Eucken relation for closed porosity and Landauer relation for open porosity give good agreement to experimental data on tin oxide, alumina, and zirconia ceramics. For mp . 0.65, the thermal conductivity of kaolin-based foams and calcium aluminate foams was well described by the Hashin Shtrikman upper bound and Russell’s relation. Finally, numerical simulation on artificially generated microstructures yields accurate predictions of thermal conductivity when fine detail of the spatial distribution of the phases needs to be accounted for, as demonstrated with a bio-aggregate material.
I. INTRODUCTION
Porous materials have found important applications as filters, catalytic supports, and thermal insulators. With present day concerns of energy saving in high temperature industrial processes and buildings, the development of new thermal insulators has become the object of much recent research. Heat transfer through a solid material is essentially controlled by its thermal conductivity in the steady state and by a combination of thermal conductivity and specific heat capacity in transient situations. Given the lower value of the thermal conductivity of air compared with a solid phase, the incorporation of porosity into a material decreases significantly its effective conductivity. The aim of this paper is to examine the effect of pore volume fraction on the effective thermal conductivity of a porous material composed of an assembly of joined particles such as crystallites. When a porous nonmetallic solid is subjected to a thermal gradient, heat transfer involves vibrational conduction in the solid phase, conduction by colliding gas molecules in the pore phase, and radiation either through a semi-transparent solid phase or across large pores. For pore sizes less than 5 mm, corresponding to the a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2013.179 2260
J. Mater. Res., Vol. 28, No. 17, Sep 14, 2013
http://journals.cambridge.org
Downloaded: 30 Nov 2014
materials discussed here, convection heat transfer can be neglected.1 Taking the case of a polycrystalline ceramic material, the solid phase thermal conductivity depends on: (i) the intrinsic thermal conductivity of the grains and (ii) the thermal resistance due to interfaces called grain boundaries. In the temperature range of i
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