EPA-600/R-92-203
ORNL/M-2426
OAK RIDGE
NATIONAL
LABORATORY
Literature Review: Heat Transfer
ESEBH^SSS^H Through Two-Phase Insulation
Systems Consisting of Powders
in a Continuous Gas Phase
David W. Yarbrough
MANAGED BY
MARTIN MARIETTA ENERGY SYSTEMS, INC.
FOR THE UNITED STATES
DEPARTMENT OF ENERGY
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EPA-600/R-92-203
ORNL/M-2426
LITERATURE REVIEW: HEAT TRANSFER THROUGH TWO-PHASE INSULATION
SYSTEMS CONSISTING OF POWDERS IN A CONTINUOUS GAS PHASE
David W. Yarbrough
Date Published: December 1992
NOTICE Thi« document contain* information of a preliminary nature.
It it subject to revision or correction »nd therefore does not represent a
final report.
Prepared for
U.S. Department of Energy
Office of Buildings Energy Research
and
Environmental Protection Agency
Office of Research and Development
Prepared by the
OAK RIDGE NATIONAL LABORATORY
Oak Ridge, TN 37831-6092
managed by
MARTIN MARIETTA ENERGY SYSTEMS, INC.
for the
U.S. DEPARTMENT OF ENERGY
Under Contract DE-AC05-840R21400
and
EPA Interagency Agreement DW89934975
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TABLE OF CONTENTS
LIST OF TABLES v
ABSTRACT 1
INTRODUCTION AND BACKGROUND 2
CALCULATION OF HEAT FLOW ACROSS GAS-POWDER COMPOSITES 4
Gas-Phase Thermal Conductivity 4
Radiative Transport 8
Heat Transport by Conduction 12
VACUUM PANEL INSULATIONS 14
SUMMARIZING DISCUSSION 15
REFERENCES 16
APPENDIX A: KEY REFERENCES FROM REVIEWS CITED IN TABLE 1 20
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LIST OF TABLES
Table 1. Reviews of the literature oil superinsulations and
heat transfer through powders 3
Table 2. Breakaway pressure at 300 K for air 5
Table 3. PxL for selected k^/k^ 6
Table 4. L/Dp as a function of void fraction, e 7
v
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Literature Review: Heat Transfer through Two-Phase Insulation Systems
Consisting of Powders in a Continuous Gas Phase
Davkl W. Yarbrough
Building Materials Group
Oak Ridge National Laboratory*
Oak Ridge, Tennessee 37831-6092
ABSTRACT
This review of the literature on heat flow through powders was motivated by the use of
fine powder systems to produce high thermal resistivities (thermal resistance per unit thickness).
The term "superinsulations" has been used to describe this type of material, which has thermal
resistivities in excess of 20 ft2-h-°F/Btu (3.52 Km2/W) per inch (2.54 cm) of insulation thickness.
The present report is concerned with superinsulations obtained using evacuated powders.
The literature review has shown that the calculation of heat flow through gas-powder
systems is highly developed. One major weakness in the calculational procedures is the absence
of structural features for the powders, which are invariably characterized as regular arrays of
spheres or cubes rather than random irregularly shaped particles. The effect of particle size
distribution on the shape and size of void spaces is not modeled, although it affects the thermal
conductivity of the gas. Calculations of thermal performance based on simplified descriptions of
the porosity distribution can be used to show the dependence of thermal resistance on interstitial
gas pressure. The literature reviewed in this report provides a basis for predicting the interstitial
gas pressure at which thermal conductivity begins to increase. The objective is to design filler
material for powder insulation systems with ultrafine void spaces that will permit pressure
increases without dramatic thermal conductivity increases.
•Research sponsored by the Office of Buildings Energy Research, Building Systems and
Materials Division, U. S. Department of Energy, under contract DE-AC05-840R21400 with
Martin Marietta Energy Systems, Inc. and the U.S. Environmental Protection Agency Office of
Research and Development under Interagency Agreement DW89934975.
1
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2
INTRODUCTION AND BACKGROUND
An effort is under way at the Oak Ridge National Laboratory (ORNL) to facilitate the
use of evacuated powder insulation in appliances such as refrigerators and freezers and in selected
building applications. The objective of the effort is to produce and demonstrate performance and
durability of very-high thermal resistivity systems to replace closed-cell foam products containing
environmentally unacceptable chemicals. Important tasks associated with the objective include
cost effective minimization of the heat transfer through a layer of fine powder with low interstitial
gas pressure and demonstration that the low interstitial pressure, which is a major factor in the
thermal performance, can be maintained for extended periods. In the case of appliance
insulation, the service life of the insulation should be 10 to 20 years, while in the case of building
insulations the service life should be at least 25 years and perhaps as much as 50 years.
Interest in two-phase dispersed systems dates back at least 100 years to Maxwell's
research.1 The early work focused on solid mixtures, but the resulting theory is applicable to
systems in which the continuous phase is a non-condensible gas or, more precisely, a gas above its
critical temperature. The transport of heat by the gas in a gas-solid composite can be a significant
part of the total heat flow. If the composite is to be used as an insulator, the gas-phase
conduction can be reduced by lowering the pressure (evacuation) and/or reducing the dimensions
of the gas phase regions (use fine powders).
The motivation for this literature review was the use of evacuated fine powder systems to
produce high thermal resistivities (thermal resistance per unit thickness, R*). The term
"superinsulations" has been used to describe this type of material, which has thermal resistivities in
excess of 20 ft2-h-°F/Btu (3.52 K-m2/W) per inch (2.54 cm) of insulation thickness.
The use of evacuated powders is one method of producing a superinsulation. Multi-layer
evacuated insulation made from high reflectance-low emittance foils is another, and evacuated
fibrous insulations represent a third. "Hie present paper is concerned with superinsulations
obtained using evacuated powders. Riede and Wang2 as early as 1960 mention the commercial
use of evacuated perlite or Santocel to produce R* greater than 80 at cryogenic temperatures.
These authors also report R* of 3333 ft2-h-°F/Btuin. at a T mean of -99.5°F and pressures
less than 1.0 micron for an opacified powder. Vacuum panels as superinsulations were discussed
in 1967 by Grunert and Notaro3 and a U.S. patent describing the use of fine silica powder was
issued in 1979.4
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Six reviews that represent important stages in the development of vacuum insulations are
listed in Table 1. These reviews demonstrate the considerable interest that has existed in this
class of superinsulations in recent years and represent valid starting points for work in this area.
The technical references from the reviews in Table 1 have been reproduced in Appendix A.
Table 1. Reviews of the literature on superinsulations
and heat transfer through powders
Year
Reference
Title/Author
Number of
References
1967
5
Thermal Insulation Systems - A Survey!
Glaser, Black, Lindstrom, Ruccia, and Wechler
6
1975
6
Investigation of the Effective Thermal Conductivity of
Gas-Filled Fiber-Powder Insulation Systems for Residential
and Commercial Structures!
Rogers
131*
1977
7
Thermal Conductivity of Granular Materials - A Review!
Crane, Vachon, and Khader
65*
1988
8
Advanced Evacuated Thermal Insulations: The State of
the Art/
Fine
42*
1988
9
Thermal Radiation in Packed and Fluidized Beds!
Tien
76*
1989
10
Recent Advances in Thermal Superinsulations!
Buttner, Kreh, and Fricke
14*
'References to patents and non-technical discussions have not been included.
The transfer of heat through a particulate bed containing a stagnant gas is generally
discussed in terms of three mechanisms.11 These are: (1) radiation through the void fraction, (2)
conduction through a series of solid and gas elements, and (3) conduction through the solid
phase. The three mechanisms are taken to result in additive heat flows that are often represented
as "thermal conductivities,"
ka - f kgd + k^BaHon W
The three stated mechanisms and Eq. (1) are not totally consistent. Radiative transport through
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the solid particles (as well as the void space) occurs, and the steady-state heat flow across planes
perpendicular to the overall heat flow direction is not distributed among the mechanisms the same
way for every plane. The notation used in Eq. (1), however, is useful in that most of the
theoretical discussion of heat flow across gas-solid systems involves a calculation of a heat flow
that depends on the thermal conductivities of the two materials with an added term for radiation.
The radiative term then must include radiation across voids and radiation through particles.
CAIjCULATION of the heat flow across gas-powder composites
Gas-Phase Thermal Conductivity
The primary reason for this review is an interest in evacuated powder systems.
Calculational methods that have been developed for solids dispersed in a fluid are applicable
provided that the correct value for the fluid (gas) phase thermal conductivity is used. The
thermal conductivities of gases that do not form hydrogen bonds are a very weak function of
pressure at pressures near or above one atmosphere.12 The chemical species that make up air do
not form hydrogen bonds, dimers, or polymers. In small volumes such as the interstitial region
between fine powders, the rate of gas molecule collisions is limited by the dimensions of the
spaces occupied by the gas phase. When the dimensions of the gas phase region are of the same
order of magnitude as the mean free path length in the gas phase, the gas phase is no longer a
continuum, and the thermal conductivity of the gas decreases as pressure decreases. The
condition under which this occurs is generally taken to be a Knudsen number greater than three
(Kn > 3).13
Kn = tJL (2)
where lg is the molecular mean free path, and L is a characteristic dimension for the gas phase.
In the case of spherical particles, the characteristic length is commonly taken to be the particle
diameter, Dp. The molecular mean free path in cm is given by Eq. (3) as a function of T
(temperature, K), P (pressure in atmospheres), and o (the collision diameter of the gas-phase
species, cm).14
tg = 3.065 x 10"23 Tl(a2F) (3)
If Kn > 3 is taken as a criterion for the Knudsen gas regime, a prediction can be made of
the pressure region in which the apparent thermal conductivity of the gas-solid composite
decreases as the interstitial gas pressure is reduced, the "breakaway" point The assignment of a
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5
critical Knudsen number such as Knc = 3, and the identification of a "characteristic length, L," in
the gas are somewhat arbitrary. Equation (4) predicts the breakaway pressure, PB, in terms of
Knc, L, and the collision diameter of the interstitial gas, o.
PB = 310.56 x 27a2 xKnexL (4)
T: (K)
o: A
L: (im
PB: Pa
If the accommodation coefficient between gas molecules and solid particles, a, is one, then
the conductivity of the interstitial gas, kr can be expressed in terms of the atmospheric pressure
value, k° , as follows:15
kg = k; x Lj{L + ig) = *;/(! + Kn) (5)
A breakaway pressure can be estimated from Eqs. (4) and (5) by assigning the value 0.9 to the
ratio kg/kj . This assignment gives Knc = 0.11 and permits a calculation of PB at 300 K using a =
3.62 A, the effective collision diameter for air.16
PB = 64633/L (6)
L: jim
PB: Pa
The 10% reduction in interstitial-gas thermal conductivity chosen as the criterion for
Eq. (6) would result in a smaller reduction in the overall apparent thermal conductivity, perhaps
5%. A 5% change in the apparent thermal conductivity is observable with current measurement
technology. Table 2 contains breakaway pressures for air at 300 K for five values of the
characteristic length. The PB listed in Table 2 shows the increase in breakaway pressure as the
characteristic length decreases.
Table 2. Breakaway pressure at 300 K for air
L(jxm) PB (Pa) PB (torr)
1000 6.46 x 10' 0.48
100 6.46 x 102 4.8
10 6.46 x 10* 48
1 6.46 x 104 480
0.1 6.46 x 10s 4800
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Masamune and Smith11 use Eq. (7) due to Kennard17 to discuss the effect of pressure on
the thermal conductivity of the interstitial gas.
*« = V f1 * -T? (-^-) (4-)]1
* { fia Y + 1 %<3 PL Pr t
(7)
k Boltzmann constant, 1.3806 x 10'16 erg/K
a accommodation coefficient
Y heat capacity ratio, Cp/Cv
Pr Prandtl number, Cpji&
There should be an observable increase in k, as pressure increases when kj is about 10% of
k, + k„. Equation (8) follows from Eq. (7) for air at 300 K, a = 1.0, y = 1.40 and Pr = 0.71.18
kjkj = P x Lf(P x L + 644.28) (8)
P pressure, ton
L thickness, pm
Table 3 contains a few values for P x L calculated from Eq. (8).
Table 3. P x L for selected
kg/k° P x L (torr x ^m)
0.90 5798.5
0.50 6443
0.10 71.6
0.01 6.5
If kg/kg = 0.01 is taken to be the beginning of a significant contribution of the interstitial
gas thermal conductivity to k,, the pressure at which this happens can be estimated from Eq. (9)
for air.
P = 65/L (9)
Apparent thermal conductivity data reported by Yarbrough et al19 for perlite shows the
beginning of the k, increase with pressure in the range 0.38 to 1.13 torr for particulate beds with
mean particle diameters of 12.8 and 20.9 jim. Equation (9) predicts pressures of 0.51 and
0.31 torr, respectively, thus showing a degree of agreement between theory and experiment.
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Results obtained by Hunter et al,20 however, for 0.02 to 0.03 powders show ka increasing with
pressure around 10 Pa. This discrepancy could be accounted for by effective particle diameters
much greater than single particle diameters due to agglomeration. An increase in k, for fine
perlite and silica powders as interstitial pressures increase above 10 Pa has also been observed by
Christiansen et al.21 Cunnington and Tien22 report apparent thermal conductivities at 300 K for
80 [im-diameter spheres that increase as pressure rises above 10 Pa. The Cunnington and Tien
observation is consistent with Eq. (9).
Masamune and Smith11 used results from Fisher,23 Rose24, and Kunii and Smith25 to obtain
the following relationship between L and the diameter of solid phase spheres with void fraction e.
L = Df x n x £
C « (sec e - l)2 (1 - (tt/2 - 6) tan 0)
—"H)
n = 6.93 - (25.509 e - 0.260)
Table 4 contains values for the ratio L/Dp obtained from Eq. (10). The variable L, which is
important in the calculation of interstitial gas phase thermal conductivity, decreases as the void
fraction decreases. This decrease in L would result in a decrease in kg at a given interstitial
pressure. Bala et al26 have shown, however, that decreasing the void fraction of metallic powders
Table 4. L/Dp as a function of void fraction, e
e L/DP
0.260 0.07471
0.300 0.08416
0.350 0.1007
0.400 0.1272
0.450 0.1806
0.476 0.2434
in the range 0.82 > e > 0.45 results in an increase in the overall thermal conductivity due, no
doubt, to increased solid phase and particle-to-particle conduction.
Pradhan and Saxena27 studied the thermal conductivity of MgO and Af203 powders as a
function of pressure and discussed their results using Eq. (11). The k, data obtained for MgO and
A{203 show k, increasing steeply with interstitial gas pressures near 100 Pa. This pressure is
consistent with the perlite data cited above. Pradhan and Saxena do not give particle-size
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K = k; x pup + pc)
k° = apparent thermal conductivity at atmospheric pressure (H)
Pc = pressure at which ka « 0.5 k°
information so further comparisons can not be made. Equation (11) is limited in application since
it does not have the correct low pressure limit.
This section on gas-phase thermal conductivity can be summarized as follows. The
relationship between kg and interstitial gas pressure is well established, but contains quantities that
are not easily evaluated. The accommodation coefficient and the characteristic length and its
dependence on void fraction or porosity are factors that must be estimated or arbitrarily assigned.
If the particles in the gas-solid composite have a given shape and arrangement, such as spheres
arranged on a cubic lattice, then an average spacing can be estimated. The characteristic length,
L, can be viewed as a parameter to be determined from k, measured as a function of pressure.
Useful estimates of k, can be obtained using a = 1 and L equal to the mean particle diameter,
especially in the case of uniformly sized particles. A key issue in the discussion of kg at reduced
pressure is the true particle size. Very small particles often agglomerate to form much larger
effective diameter particles.
Radiative Transport
Heat flow per unit area in the positive x direction across a particulate bed by radiation,
qp is commonly expressed in terms of a radiative conductivity, kr defined by Eq. (12).
Expressions for qr can, therefore, be rearranged to give kj. The radiative heat flow, qr has been
discussed by a number of authors.1417,20'28"39 The radiative conductivity and qr are proportional to
the cube of a mean radiant temperature defined by either Eq. (13a) or (13b), the difference being
the constant in the k, equation.
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9
ft « 4 (Jf + if) (T2 - 7\) (13a)
4
if = (1? +lf) (T2 + T,) (13b)
The "diffusive" approximation for k,. requires the refractive index, n, and an effective extinction
coefficient, E^,10,28'37'40 that is related to optical thickness, x0, by Eq. (14).28
<14)
The expression for k, is Eq. (15a) when Tr is defined by Eq. (13a) and Eq. (15b) when Tr is
defined by Eq. (13b) and oB is the Stefan-Boltzmann constant.
kr = 16n2aaltpE^ (15a)
kr = 4ttzo gftfiEtf (15b)
An estimate for Ee(f or t0 can be obtained from measurements of k, as a function of Tr with a fit
to Eq. (16) if n is known.
kr = a + £7? (16)
= 16n2o/3p or 4n2o/3p (17)
The radiative heat flow has also been written in terms of the radiative properties of the materials
making up the system.32'36 Black et al32 express q, in terms of an absorption coefficient, o„ a
scattering coefficient, av and the number of radiation shields in the powder bed, n, having
emittance, e.
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_ m)oai - if) (lg)
(oa + 2a Jd + ij/e - 1
This equation could be applied to evacuated powder-filled panels by setting n = 0. Equation (18)
would also be useful for evaluating the effect of a buried radiation shield.
Rogers and Williamson33 lists 15 equations and the corresponding references in which k,. is
proportional to oT 3. The proportionalities typically involve radiative properties, void fraction,
and particle diameter. Godbee and Ziegler28 (cited as Ref. 79 in Rogers and Williamson33) gives
k, in terms of readily available property information.
k. - 4n2e^ - ljz>po7? (19)
r
f solid fraction (volume fraction of the solid)
n refractive index
e emittance of particle surface
Equation (19) is valid for solid materials with zero transmission since It, = 0 when f = 1.
Laubitz29 (cited as Ref. 67 in Rogers6) proposes Eq. (20) for radiation across cubic voids while
Bosworth30 (cited as Ref. 90 in Rogers6) gives an expression for that contains no dependence
on solid fraction.
£ = 4e f- - — + /-"l D al2 (20)
f fm p r
kr = 4/3 Dp
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Equation (15) seems to be the best candidate for predicting k,. or correlating thermal data
by using n2/Eeff as an adjustable parameter. Equation (19) provides a k, prediction given the solid
fraction and the particle size, f, and would be useful for analyzing experimental data or predicting
the sensitivity of to Dp or f. The use of an expression for k,. in terms of Eeff could be useful for
the evaluation of opacifiers since the magnitude of Erfr is a direct measure of the effectiveness of
an opacifier.
A reduction in can be accomplished by decreasing Dp or increasing f. Changing the
particle size or volume fraction solid results, however, in an increase in conductive transport. In
general, there is an optimum f for a given Dp (i.e., minimum kj. The addition of an opacifier to
reduce k, without a compensating increase in conductive transport is desirable. The use of
opacifiers to reduce k, by increasing the effective extinction coefficient has been discussed by
numerous authors.2,6'20,21,32*36 The strategy is to select a candidate opacifier that has low IR
transmission at wave lengths where the primary powder has low absorption (high transmission).
Riede and Wang2 found that about 30% of the heat transport across evacuated perlite was
by radiation with the remainder being solid conduction. The addition of opacifiers to perlite
would, therefore, have limited benefit. Si02 on the other hand has significant transmission except
for a narrow band from 8 to 10 yin. As a result, the addition of copper or aluminum powder to
Santocel, a silica aerogel, reduced the low temperature k, to about 20% of the non-opacified case.
The lowest k, was observed at near 50 wt % metal powder. The thermal resistivity
(ft2-h •°F/'Btu) at T = -99.5° F of the evacuated system was increased from 83 to 378, a factor of
4.6. Hunter et a!20 also studied metal powders as opacifiers for very fine silica powders such as
Cab-O-Sil to achieve better than an order-of-magnitude reduction in k, at T = -121° F. An
optimum mixture was 50 wt % aluminum of particle size less than 44 jim. The Si02 particle sizes
were in the range 0.02 to 0.03 |im, so the large aluminum powder would effectively be floating
radiation shields in a relatively transparent medium.
Power34 achieved significant reductions in k, at T = -121°F by mixing aluminum powder
with silica-aerogel (Santocel-A). The addition of fine aluminum powder to coarse Santocel-A did
not result in a k, decrease due presumably to increased solid conduction. The addition of coarse
aluminum powder to fine Santocel-A under vacuum increased R* from 75.9 ft2-h-°F/Btu-in. to
515.1 ft2-h-°F/Btuin. at T = -201°F. The largest R* reported was at a 50/50 wt % mixture of
6 pm Santocel-A and 6 jtm aluminum. Power's paper includes infrared transmission data for the
powder mixtures that show a strong correlation between reduced apparent thermal conductivity
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12
and reduced transmission for wavelengths from 1 to 15 jim. Infrared transmission measurements
provide for a quick evaluation of candidate opacifiers. Buried radiation shields formed from
aluminum foil or aluminum coated mylar have been shown to be effective with evacuated fiber
systems for reducing k,.23
The use of carbon black, finely divided carbon, to increase absorption has been discussed
in the literature for over 80 years.37,38 Decreases in k, of silica powders due to the addition of
finely divided carbon have been reported by Bosworth,30 Black et al,32 Rogers and Williamson,33
and Johnson and Hollweger.36 Glaser and Reiter34 examined the effect of adding carbon particles
to perlite.
Black et al32 report thermal resistivities as high as 303 ft2-h-°F/Btu-in. for silica and
carbon powder mixtures. The temperature, pressure, and composition yielding the high thermal
resistivity are not stated. The text of the paper, however, suggests significant carbon content,
perhaps as high as 60 wt %. Rogers and Williamson33 studied mixtures of Cab-O-Sil (M-5) and
carbon black and mixtures of perlite and Cab-O-Sil. The reason for mixing particles like perlite
and silica is to block as many transmission wavelengths as possible. Rogers and Williamson report
the best result to be for a 50/50 wt % mixture of Cab-O-Sil and carbon black. Glaser and
Reiter35 measured k, for a 60 wt % perlite - 40 wt % carbon mixture at T = -120°F and P = 10'2
microns. The result, ka = 0.004 Btuin./ft2-hr-°F corresponds to a thermal resistivity of
250 ft2-hr-°F/Btu-in.
Caps et al31 have obtained transmission data that show Fe304 and TiOi have near zero
transmission in wavelength ranges where transmission occurs through SiO^ Fe^, TiO^ or
mixtures would, therefore, be candidates for SiO, opacification. Relatively small (1-5 wt %)
amounts of Fe304, Fe^, Cr203, SiC, or MgO added to Si02 significantly reduces the optical
thickness. It has also been shown that decreasing the particle size of the opacifier further
decreases the optical thickness. The optical thickness was observed to decrease for Fe304
concentrations to 17 wt %. The effect of these opacifiers on the thermal resistivity was not
determined so the increase in solid conductivity cannot be assessed.
Heat Transport by Conduction
Equations for the calculation of heat flux through two-phase systems have been in the
literature for about 120 years. Rogers and Williamson39 lists 35 models for the heat flux published
during the period 1873-1970. Most of these models involve the gas phase thermal conductivity,
which is a function of the interstitial pressure and porosity and the thermal conductivity of the
solid phase material. The models involve regularly shaped particles, such as spheres on cubes,
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arranged on lattices to produce typical elements. Later papers, such as that published by Godbee
and Ziegler28 include a shape factor. Invariably, the models involve structured parameters, such
as particle diameter, or characteristic lengths that are not readily available for particle systems
containing a distribution of particle shapes and sizes. Rogers also reviewed four additional papers
dealing with solid conduction. The models are not particularly useful for making a priori
calculations since material parameters are needed. The equations that are available provide a
basis for analyzing data. Crane et al7 compared measured k, with k, calculated using previously
published models. Derivations between calculated and measured k, exceeded ±20%.
Buttner et al10,40 propose an empirical approach where the conductive terms are
independent of temperature and radiative transport varies as Tr3 [as shown in Eq. (16)]. The
conduction terms (represented by a) are obtained as a function of external pressure, Pext- A
correlation where k, increases as Pext,/3 k proposed. The experimental data cited, however, are
for systems that compress as the external pressure is increased. The Pext10 dependence is
uniquely related to particle-to-particle contact resistance.
Masamune and Smith11 have a model for an assembly of uniform spheres. Their result
[shown as Eq. (22)] is combined with 0 and e expressed in terms of the void fraction in the
particulate bed. The model is self contained, since no adjustable parameters are involved. The
model is useful for making estimates of the variation of k, with void fraction.
Chu and Tseng41 have taken an approach like that of Buttner. They measure conductivity
terms at low temperatures where radiation transport is small. The difference between the linear
conduction expression obtained at low temperatures and the total heat transport at high
temperature is attributed to radiation and expressed as a function of Tr3.
Luikov et al42 developed one of the more comprehensive models for heat flow across
particle beds. Their model involves characteristic lengths associated with cubic elements. It is a
series-parallel analog based on a cubic array of uniform spherical particles. Comparisons have
been made of measured and calculated k, values. The biggest percent differences between
measured and calculated k, occur at low k, where differences of ±30% occur, presumably with
structural factors treated as adjustable parameters. Terms are included for contact resistance and
(1-ge) (1-5)
_0 + (1-0)
~ (1-«€)*, +
(22)
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14
the resistance of oxide films on particles. Rogers and Williamson33 have commented on Luikov's
model, observing up to 50% difference between measured and calculated values.
Crane and Vachon43 and Crane et al7 discuss simple geometric models that tend to predict
selected data sets to within about 20%. Similarly, Levy44 has modified the Maxwell-Eucken
equation. The preceding three papers do not provide guidance concerning structural effects. A
relatively recent work by Cunnington and Tien22 is unique in that the void fraction of the primary
particles is considered. The model was built around hollow spheres, but could provide a starting
point for treating porous agglomerations.
VACUUM PANEL INSULATIONS
There has been commercial interest in developing evacuated insulations over the last two
decades. Fine,® for example, listed nine U.S. patents (1979(1), 1980(1), 1983(1), 1984(1), 1985(1),
1987(4)], and one German patent [1985(1)] that describe advanced (evacuated) concepts. The
period from 1984 to the present saw research activity at ORNL directed toward the development
of advanced insulations for appliances, primarily refrigerators.4549 The ORNL effort was focused
on the development of low-cost evacuated panels for use in refrigerators. Methods of evaluating
thermal performance were developed and refined and a study of evacuated perlite-filled panel
insulation being used in Japanese-built refrigerators was completed. A number of low-to-medium
cost silica, perlite, and silica + carbon powders were studied.8 Kollie et al50 reviewed the work
done at ORNL prior to 1991 and added a comprehensive study of the use of powder-filled
evacuated panels in portable coolers.
Strong et alis reviewed the concept of a fiat evacuated thermal insulation in 1960. Their
discussion was slanted toward the use of a fibrous filler material, but there was mention of the use
of fine powders. The concept of using an evacuated powder system for high thermal resistance is
attributed to Smolukowski37 in 1910. Emphasis was placed in these early papers on the thermal
resistances that could be achieved, while the question of the life expectancy of an evacuated panel
was not an issue. Strong et al51 produced a second paper on flat panel vacuum insulation in 1960.
The emphasis in this second paper was the use of fibers as filler material, although mention was
made of sand, crushed glass, and foam.
Grunert and Notaro3 discussed the importance of the encapsulating material in
maintaining the vacuum required to achieve high thermal resistance values. Use of flat evacuated
panels in refrigerators was considered, and panel lifetimes were discussed in terms of years.
There is evidence of Soviet interest in powder-filled evacuated panels in 1975.52
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SUMMARIZING DISCUSSION
This review of the literature on heat flow through powders has shown wide-ranging
interest in the subject for over a century. The use of evacuated powders for high thermal
resistance has been under consideration for over 80 years, primarily for cryogenic applications.
The calculation of heat flow or thermal resistance through idealized gas-powder systems is
highly developed. The calculational procedures have been checked against a modest number of
data sets with agreements in the range ±20%. One major weakness in the calculational
procedures is the absence of structural features for the powders. The powder systems are
invariably characterized as regular arrays of spheres or cubes rather than a random assembly of
irregularly shaped particles.
Gas phase conductivity calculations are on a firm foundation, but radiative transport
calculations are approximate. Particle-to-particle contact resistance is treated empirically. The
effect on particle-size distributions on the shape and size on void spaces is not modeled, although
it obviously affects the thermal conductivity of the gas.
The high thermal resistance that can be achieved with evacuated powders has been clearly
demonstrated. Calculations of thermal performance based on simplified descriptions of the
porosity or void-space distribution can be used to show the dependence of thermal resistance on
interstitial gas pressure. The challenge for bringing powder-filled evacuated panels to
commercialization lies primarily with the development of a packaging system that will maintain the
required low pressures for many years. The developmental work then should concentrate on
barrier material air-permeability and vacuum sealing technology.
The development of advanced filler materials must move forward in order to provide
panels that will exhibit high thermal resistance even though air leakage has occurred. The
literature reviewed in this paper provides a basis for predicting the interstitial gas pressure at
which thermal conductivity begins to increase. The objective is to design filler material with ultra-
fine void spaces that will permit pressure increases without dramatic thermal conductivity
increases.
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REFERENCES
1. J. C. Maxwell, Electricity and Magnetism, Vol. 1, 3rd ed., Oxford University Press,
London, 1892.
2. P. M. Riede and D.IJ. Wang, "Characteristics and Applications of Some Superinsulations,"
Adv. in Cryogenic Engr. 6, 209-215 (1960).
3. W. E. Grunert and F. Notaro, "Vacuum Panel Insulation Systems," Adv. in Cryogenic
Engr. 13, 690-700 (1967).
4. P. Pelloux-Gervais and D. Goumy, "Insulating Material with Low Thermal Conductivity,
Formed of a Compacted Granular Structure," U.S. Patent 4,159,359 (June 26, 1979).
5. P. E. Glaser, I. A. Black, R. S. Lindstrom, F. E. Ruccia, and A. E. Wechler, "Thermal
Insulations Systems - A Survey," NASA SP-5027, 73-81 (1967).
6. D. B. Rogers, "Investigation of the Effective Thermal Conductivity of Gas-Filled Fiber-
Powder Insulation Systems for Residential and Commercial Structures," Ph.D.
Dissertation, Vanderbilt University, Nashville, TN (1975).
7. R. A. Crane, R. I. Vachon, and M. S. Khader, "Thermal Conductivity of Granular
Materials - A Review," Proc. of the Seventh Symposium on Thermophysical Properties,
109-123 (1977).
8. H. Alan Fine, "Advanced Evacuated Thermal Insulations: The State of the Art," J.
Thermal Insulation 12, 183-208 (1989).
9. C. L. Tien, "Thermal Radiation in Packed and Fluidized Beds," Trans. ASME 110.
1230-1242 (1988).
10. D. Buttner, A Kreh, and J. Fricke, "Recent Advances in Thermal Superinsulations," Hiph
Temps - High Press 21. 39-50 (1989).
11. S. Masamune and J. M. Smith, Thermal Conductivity of Beds of Spherical Particles," Ind.
and Engr. Chem - Fundamentals 2(2). 136-143 (1963).
12. J. O. Hirschfelder, C. F. Curtis, and R. Byron Bird, Molecular Theory of Gases and
Liquids. John Wiley & Sons, Inc., New York, p. 615 (1954).
13. ibid 6, Sect. II-C-2.
14. D. W. Yarbrough, D. L. McElroy, and F. J. Weaver, "Models for Heat Transport through
Assemblies of Uniform-Diameter Hollow Spheres," ORNI/TM-11397, Oak Ridge National
Laboratory (April 1991), also ibid 12, page 10.
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17
15. H. M. Strong, F. P. Bundy, and H. P. Bovenbeck, "Flat Panel Vacuum Thermal
Insulation," J. of AppI. Phvs. 31(1), 43 (1960).
16. L. Holborn and J. Otto, Z. Phvzik 10. 367 (1922).
17. E. H. Kcnnard, Kinetic Theory of Gases. McGraw-Hill Publishing Company, New York
(1938).
18. Robert H. Perry and Cecil H. Chilton, Chemical Engineer's Handbook. Fifth Edition,
McGraw-Hill Book Company, New York, 3-216 (1973).
19. D. W. Yarbrough, R. S. Graves, F. J. Weaver, and D. L. McElroy, The Thermal
Resistance of Perlite-Based Evacuated Insulations for Refrigerators," ORNL/CON-215,
Oak Ridge National Laboratory (September 1986).
20. B. J. Hunter, R. H. Kropschot, J. E. Schrodt, and M. M. Fulk, "Metal Additives in
Evacuated-Powder Insulation," Adv. in Cryogenic En p. 6, 146-156 (1960).
21. R. M. Christiansen, H. Hollingsworth, Jr., and H. N. Marsh, Jr., "Low-Temperature
Insulating Systems," Adv. in Cryogenic Engr. 6, 171-178 (1960).
22. G. R. Cunnington, Jr., and C. L. Tien, "Heat Transfer in Microsphere Insulation in the
Presence of a Gas," Thermal Conductivity 15. V. V. Mirkovich, ed., Plenum Press,
325-333 (1978).
23. R. A. Fisher, J. Act. Sci. 16, 492 (1926).
24. W. Rose, J. AppI. Phvs. 29, 687 (1958).
25. D. Kunii and J. M. Smith, AIChEJ. 6, 71 (1960).
26. K. Bala, P. R. Pradhan, N. S. Saxena, and M. P. Saxena, "Effective Thermal Conductivity
of Copper Powders," J. Phvs. D: Annl. Phvs. 22. 1068-1072 (1989).
27. P. R. Pradhan and N. S. Saxena, "Interstitial Pressure Dependence of Effective Thermal
Conductivity and Diffusivity of MgO and Af203," Indian J. Phvs. 63A. 532-549 (1989).
28. H. W. Godbee and W. T. Ziegler, "Thermal Conductivities of MgO, Al203, and Zr02
Powders to 850° C II Theoretical, J. AppI. Phvs. 37(1) 40-55 (1966).
29. M. J. Laubitz, "Thermal conductivity of Powders," Canadian J. of Phvs. 37 (1959).
30. R, C. L. Bosworth, Heat Transfer Phenomena. The Flow of Heat in Practical Systems.
John Wiley and Sons, New York (1952).
31. R. Caps, J. Fricke, and H. Reiss, "Improving the Extinction Properties of an Evacuated
High-Temperature Powder Insulation," High Temp.-High Press. 15. 225-232 (1983).
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18
32. I. A. Black, A. A. Fowle, and P. E. Glaser, "Development of High-Efficiency Insulation,"
Adv. in Cryogenic Engr. 6, 181-188 (1960).
33. D. B. Rogers and John W. Williamson, "Thermal Characteristics of Gas-Filled Fiber
Powder Insulation Systems," Thermal Conductivity 15. V. V. Minkovitch, ed., Plenum
Press, 317-323 (1978).
34. W. H. Power, "Improvement of Evacuated Aerogel Powder Insulation," Adv. in Cryogenic
Insulation 6, 42-49 (1960).
35. P. E. Glaser and A Reiter, "Thin-Wall Evacuated Heat Insulating Panels," A D. Little,
Inc., Cambridge, MA
36. C. L. Johnson and D. J. Hollweger, "Some Heat Transfer Considerations in Nonevacuated
Cyogenic Powder Insulation," Adv. in Cryogenic Engineering 12. 77-88 (1966).
37. M. Smolukowski, Buil. Int. de L'Academic des Sciences de Cracovie, Series A 129 (1910).
38. W. R. Smith and G. B. Wilkes, Ind. Engr. Chem 36, 111 (1944).
39. ibid 6, Chapter III.
40. D. Buttner, J. Fricke, and H. Reiss, "Thermal Conductivity of Evacuated Load-Bearing
Powder and Fiber Insulations Under Variable External Loads," High Temp.-High Press.
17, 333-341 (1985).
41. Hsin-Sen Chu and Chung Jen Tseng, "Thermal Performance of Ultra-fine Powder
Insulations at High Temperatures," J. of Thermal Insulation 12, 298-312 (1989).
42. A V. Luikov, A G. Shashkov, L. L. Vasiiov, and Yu. E. Fraiman, Thermal Conductivity
of Porous Systems," Int. J. Heat and Mass Transfer 11. 117-140 (1968).
43. R. A Crane and R. I. Vachon, "Effective Thermal Conductivity of Granular Materials,"
Thermal Conductivity 12. 99-101 (1972).
44. F. L. Levy," A Modified Maxwell-Eucken Equation for Calculating the Thermal
Conductivity of Two-Component Solutions or Mixtures," Int. J. of Refrig. 4 (4), 223-225
(1981).
45. D. L. McElroy, D. W. Yarbrough, G. L. Copeland, F. J. Weaver, R. S. Graves,
T. W. Tong, and H. A Fine, "Development of Advanced Thermal Insulation for
Appliances," ORNL/CON-159, Oak Ridge National Laboratory, Oak Ridge, TN (1984).
46. G. L. Copeland, D. L. McElroy, R. S. Graves, H. A. Fine, and T. W. Tong, "Insulations
with Low Thermal Conductivity," Thermal Conductivity 17. J. G. Hust, ed., Plenum Press,
New York, 367-377 (1985).
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19
47. D. W. Yarbrough, T. W. Tong, and D. L. McElroy, "Use of Fine Powders for High
Thermal Resistance," Hiph Temperature Science 19. 213-223 (1985).
48. D. W. Yarbrough, F. J. Weaver, R. S. Graves, and D. L. McElroy, "Development of
Advanced Thermal Insulation for Appliances, Progress Report for the Period July 1984
through June 1985," ORNL/CON-199, Oak Ridge National Laboratory, Oak Ridge, TN
(1986).
49. D. W. Yarbrough, R. S. Graves, F. J. Weaver, and D. L. McElroy, "The Thermal
Resistance of Perlite-Based Evacuated Insulations for Refrigerators," ORNL/CON-215,
Oak Ridge National Laboratory, Oak Ridge, TN (1986).
50. T. G. Kollie, D. L. McElroy, H. A. Fine, R. S. Graves, and F. J. Weaver, "A Review of
Vacuum Insulation Research and Development in the Building Materials Group of the
Oak Ridge National Laboratory," ORNL/TM-11703, Oak Ridge National Laboratory,
Oak Ridge, TN (1991).
51. H. M. Strong, F. P. Bundy, and H. P. Bovenkerk, "Flat Panel Vacuum Thermal
Insulation," J. AddI. Phvs. 31 (1), 39-50 (1960).
52.
S. B. Milman and M. G. Kaganer, "Heat Transfer by Radiation in Vacuum-Powder
Insulation Studied by Infrared Spectroscopy," Inzh.-Fiz. Zh. 28 (1), 40-45 (1975).
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20
APPENDIX A: KEY REFERENCES FROM REVIEWS CITED IN TABLE 1
1967 NASA Review
P. E. Glaser, A. E. Everest, and A. E. Wechsler, "Thermal Conductivity of Non-Metallic
Materials." Summary Report, NASA Contract NAS 8-1567, Arthur D. Little, Inc., Apr. 1962.
P. J. Perkins, Jr., "Experimental Study Under Ground-Hold Conditions of Several Insulation
Systems for Liquid-Hydrogen Fuel Tanks of Launch Vehicles," NASA TN D-2679, 1965.
V. H. Gray, T. F. Gelder, R. P. Cochran, and J. H. Goddykoontz, "Bonded and Sealed External
Insulations for Liquid-Hydrogen-Fueled Rocket Tanks During Atmospheric Flight," NASA TN
D-476, 1960.
Saturn S-II Materials and Processes Development During the First Half of 1964. Contract
NAS 7-200, SID-63-600-2, North American Aviation, Inc., July 30, 1964.
Cryogenic Insulation Materials Development. Topical Report, Task 2.1, NASA Contract
NAS 8-9500, Lockheed Missiles and Space Co., October 29, 1964.
R. L. Middleton, J. M. Stuckey, J. T. Schell, L. B. Mulloy, and V. E. Dumire, "Development of a
Lightweight, External Insulation System for the Liquid Hydrogen States of the Saturn V Vehicle,"
Advanced in Cryogenic Engineering 10. Paper E-3, Plenum Press, New York, NY, 1965.
1975 Rogers Review
J. Dewar, Proceedings of the Royal Institute fLondon"i. 1898, p. 824.
R. B. Scott, Cryogenic Engineering. D. Van Nostrand Company, Inc., Princeton, New Jersey,
1967, p. 202.
A R. Miller, The Adsorption of Gases on Solids. Cambridge University Press, 1949.
R. R. Irani and C. F. Callis, Particle Size: Measurement Interpretation and Application. John
Wiley & Sons, New York, NY, 1963, p. 23.
J. D. Verschoor and P. G. Greebler, "Heat Transfer by Gas Conduction and Radiation in Fibrous
Insulations," Transaction of the ASME. August 1952, pp. 961-968.
M. M. Fulk, "Evacuated Powder Insulation for Low Temperature," Progress in Cryogenics. Vol. 1,
K. Mendelssohn (ed.), Heywood and Company, Ltd., London, 1959, pp. 65-84.
D. Cline and R. H. Kropschot, "The Thermal Properties of Powder Insulators in the Temperature
Range 300° to 4°K." Radiative Transfer From Solid Materials. Macmillian, New York, NY, 1963,
pp. 61-81.
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21
R. Berman, "The Thermal Conductivity of Dielectric Solids at Low Temperatures," Advances in
Physics. Vol. 2, 1953, pp. 103-140.
R. Berman, "The Thermal Conductivities of Some Dielectric Solids at Low Temperatures," Proc.
Rov. Soc. (London'). Series A., Vol. 208, 1951, pp. 90-109.
R. Berman, The Thermal Conductivities of Some Polycrystalline Solids at Low Temperatures,"
Proceedings of the Physical Society. Vol. 65, 1952, pp. 67-76.
R. Gardon, "The Emission of Radiation by Transparent Materials," Radiative Transfer From Solid
Materials. Macmillian, New York, NY, 1963, pp. 8-23.
R. Gardon, "The Emissivity of Transparent Materials," Journal of the American Ceramic Society.
Vol. 39, No. 8, 1956, p. 278.
H. O. McMahon, "Thermal Radiation From Partially Transparent Reflecting Bodies," Journal of
the Optical Society of America. Vol. 40, No. 6, 1960, pp. 376-380.
C. L. Johnson and D. J. Hollwcger, "Some Heat Transfer Considerations in Nonevacuated
Cryogenic Powder Insulation," Advances in Cryogenic Engineering. Vol. 2, 1966, pp. 77-88.
W. H. Power, "Improvement of Evacuated Aerogel Powder Insulation," Advances in Cryogenic
Engineering. Vol. 6, 1961, pp. 42-49.
B. J. Hunter, R. H. Kropschot, J. E. Schrodt, and M. M. Fulk, "Metal Powder Additives in
Evacuated-Powder Insulation," Advances in Cryogenic Engineering. Vol. 5, 1960, pp. 146-156.
P. E. Glaser, A- E. Wechsler, I. Simon, and J. Berkowitz, "Investigation of Materials for Vacuum
Insulation up to 4000° F," ASD-TRD-62-88, Directorate of Materials and Processes, Aeronautical
Systems Division, Wright-Patterson AFB, Ohio. Prepared by Arthur D. Little, Inc., under
Contract AF 33 (6160-6816), January 1962.
A L. Waddams, "The Flow of Heat Through Granular Material," Journal of the Society of
Chemical Industry Transactions. Vol. 63, November 1944, p. 339.
B. L. Knight, "Thermal Properties of Selected Evacuated Insulations at Cryogenic Temperature,"
Ph.D. Thesis, University of Colorado, 1969.
M. G. Langseth, F. E. Ruccia, A. E. Wechsler, "Thermal Conductivity of Evacuated Glass Beads:
Line Source Measurements in a Large Volume Bead Bed Between 225-300° K," Heat
Transmission Measurements in Thermal Insulations. ASTM STP 544, American Society for
Testing and Materials, 1974.
M. Smolochowski, Proc. 2nd Refrigeration Congress. 1910, pp. 187-195.
W. R. Smith and G. B. Wilkes, "Thermal Conductivity of Carbon Blacks," Industrial and
Engineering Chemistry. Vol. 36, No. 12, 1944, pp. 1111-1112.
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22
S. S. Kistler, The Relation Between Heat Conductivity and Structure in Silica Aerogel," Journal
of Physical Chemistry. Vol. 39, 1935, pp. 658-662.
S. S. Kistler and A G. Caldwell, "Thermal Conductivity of Silica Aerogel," Industrial and
Engineering Chemistry. Vol. 26, No. 6, 1934, pp. 658-662.
F. B. Rowley, R. C. Jordan, C. E. Lund, and R. M. Landen, "Gas Is An Important Factor in the
Thermal Conductivity of Most Insulating Materials," ASHVE Trans.. Vol. 58, 1952, p. 155.
J. Aberdeen and T. H. Laby, "Conduction of Heat Through Powder and Its Dependence on the
Pressure and Conductivity of the Gaseous Phase," Proc. Roval Soc. CLondonV VoL 13, 1927,
pp. 459-477.
W. G. Kannuluik, F. K. Scholar, and J. H. Martin, "Conduction of Heat in Powders," Proc. Roval
Soc. f London 1. Vol. A141, 1933, pp. 144-158.
J. E. W. Schumann and V. Voss, "Heat Flow Through Granulated Material," Fuel in Science and
Practice. Vol. 13, No. 8, 1934, pp. 249-256.
H. W. Russell, "Principles of Heat Flow in Porous Insulators," Journal of the American Ceramic
Society. Vol. 18, 1935.
R. G. Deissler and C. S. Eian, "Investigation of Effective Thermal Conductivities of Powders,"
National Advisory Committee for Aeronautics, NACA RM E52C05, June 24, 1952.
L. Topper, "Analysis of Porous Thermal Insulating Materials," Industrial and Engineering
Chemistry. Vol. 47, 1955, pp. 1377-1379.
S. Yagi and D. Kunii, "Studies on Effective Thermal Conductivities in Packed Beds," A.I. Ch. E.
X, Vol. 3, 1957, pp. 373-381.
W. Woodside, "Calculation of the Thermal Conductivity of Porous Media," Canadian J. of Phvsics.
Vol. 36, 1958, pp. 813-823.
M. J. Laubitz, "Thermal Conductivity of Powders," Canadian Journal of Phvsics. Vol. 37, 1959,
pp. 798-808.
G. T-N Tsao, "Thermal Conductivity of Two-Phase Materials," Industrial and Engineering
Chemistry. Vol. 53, 1961, pp. 395-397.
W. Woodside and J. H. Messmer, "Thermal Conductivity of Porous Media I, Unconsolidated
Sands," J. of Applied Phvsics. Vol. 32, 1961, pp. 1688-1690.
R. L. Gorring and S. W. Churchill, "Thermal Conductivity of Heterogeneous Materials," Chemical
Engineering Progress. Vol. 57, 1961, pp. 53-59.
G. P. Willhite, D. Kunii, and J. M. Smith, "Heat Transfer in Beds of Fine Particles (Heat Transfer
Perpendicular to Flow)," A.I.Ch.E. J.. Vol. 8, 1962, pp. 340-345.
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R. L. Hamilton and O. K. Crosser, "Thermal Conductivity of Heterogeneous Two-Component
Systems," Industrial and Engineering Chemistry Fundamentals. Vol. 1, 1962, pp. 187-191.
S. Masamune and J. M. Smith, "Thermal Conductivity of Beds of Spherical Particles," Industrial
and Engineering Chemistry Fundamentals. Vol. 2, 1963, pp. 136-143.
H. W. Godbee, "Thermal Conductivities of MgO, A02O3, and Zr02 Powders to 850° C," Ph.D.
Thesis, Georgia Institute of Technology, 1963.
A. E. Wechsler, P. E. Glaser, and J. A. Fountain, "Thermal Properties of Granulated Materials,"
Progress of Astronautics and Aeronautics. Vol. 8, The MIT Press, 1972, pp. 215-241.
J. D. Verschoor and P. Greebler, "Heat Transfer by Gas Conduction and Radiation in Fibrous
Insulations," Trans. AS ME. 1952, pp. 961-968.
N. C. Hamaker, "Radiation and Heat Conduction in Light-Scattering Material," Phillips Research
Reports. Vol. 2, 1947, pp. 103-111.
B. K. Larkin and S. W. Churchill, "Heat Transfer by Radiation Through Porous Insulations,"
AI.Ch.E. J.. VoL 5, 1969, pp. 467-474.
J. Chen and S. W. Churchill, "Radiation Heat Transfer Through Powders," A.I.Ch.E- J.. Vol. 7,
1961, pp. 332-339.
T. N. Vezirovlu and S. Chandra, "Thermal Conductance of Two-Dimensional Constrictions,"
Paper No. 68-761, AIAA Third Thermophysics Conference, 1968.
A. F. Devonshire, "The Interaction of Atoms and Molecules with Solid Surfaces, VIII - The
Exchange of Energy Between a Gas and a Solid," Proc. Rov. Soc. ("London). A-158, 1937, p. 269.
F. O. Goodman, "On the Theory of Accommodation Coefficients - III, Classical Perturbation
Theory for the Thermal Accommodation of Light Gases," J. Phvs. Chem. Solids. VoL 24, 1963,
pp. 1451-1466.
J. P. Hartnett, "A Survey of Thermal Accommodation Coefficients," Proceedings of the Second
International Symposium on Rarefied Gas Dynamics. University of California, Berkeley,
California, 1960, Academic Press, 1961.
H. Weiss, "Energy Exchange Between Gases and Solids," J. Phvs. Chem. Solids. Vol. 24, 1963,
pp. 1291-1296.
D. E. Klett and R. K. Irey, "Experimental Determination of Thermal Accommodation
Coefficients," Advances in Cryogenic Engineering. Vol. 14, 1969, pp. 217-223.
C. Bankvall, "Heat Transfer in Fibrous Materials," Journal of Testing and Evaluation. Vol. 1,
1973, pp. 235-243.
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C. S. Chow, The Thermal Conductivity of Some Insulating Materials at Low Temperatures,"
Proc. Phvs. Soc. (London-). Vol. 61,1948, pp. 206-216.
M. M. Reynolds, J. D. Brown, M. M. Fulk, O. E. Park, and C W. Curtis, "Vacuum Powder
Insulation," Advances in Cryogenic Engineering. Vol. 1, 1960, pp. 216-223.
R. M. Christiansen, M. Hollingsworth, Jr., and H. N. Marsh, Jr., "Low Temperature Insulation
Systems," Advances in Cryogenic Engineering. Vol. 5, 1960, pp. 171-178.
M. M. Fulk, R. J. Deveraux, and J. E. Schrodt, "Heat Transport through Powders," Advances in
Cryogenic Engineering. Vol. 2, 1960, pp. 163-165.
S. T. Stoy, "Cryogenic Insulation Development," Advances in Cryogenic Engineering. Vol. 5, 1960,
pp. 216-223.
I. A Black, A A Fowre, and P. E. Glaser, "Development of High-Efficiency Insulation,"
Advances in Cryogenic Engineering. Vol. 5, 1960, pp. 181-188.
H. L. Johnston, C. B. Hood, Jr., J. Bieleisen, R. W. Powers, and J. B. Ziegler, "Performance of
Heat Insulating Materials Down to 20° K," Advances in Cryogenic Engineering. Vol. 1,1960,
pp. 212-215.
P. M. Riede and D. K-J. Wang, "Characteristics and Applications of Some Superinsulations,"
Advances in Cryogenic Engineering. Vol. 5, 1960, pp. 209-215.
I. A Black and P. E. Glaser, "Progress Report on Development of High-Efficiency Insulation,"
Advances in Cryogenic Engineering. Vol. 6, 1961, pp. 32-41.
R. H. Kropschot and R. W. Burgess, "Perlite for Cryogenic Insulation," Advances in Cryogenic
Engineering. Vol. 8, 1963, p. 425-436.
R. H. Kropschot, "Advances in Thermal Insulation," Advances in Cryogenic Engineering, Vol. 16,
1971, pp. 104-108.
R. G. Deissle: and J. S. Boegli, "An Investigation of Effective Thermal Conductivities of Powders
in Various Gases," Trans. ASME 1958, pp. 1417-1425.
1977 Review bv Crane. Vachon. and Khader
D. P. Haughey and G.S.G. Beveridge, "Local Voidage Variation in a Randomly Packed Bed of
Equal Sized Spheres," Journal of Engineering Science. Vol. 21,1966, p. 905.
A Waddams, "The Flow of Heat Through Granular Materials," Journal of the Society of
Chemical Industry. VoL 63, 1944, p. 337.
G. T. Tsao, "Thermal Conductivity of Two-Phase Materials," Industrial and Engineering
Chemistry. Vol. 53, 1961, p. 395.
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25
J. C. Maxwell, A Treatise on Electricity and Magnetism. Vol. 1, 3rd ed., Oxford University Press,
London, 1892, p. 440.
H. Fricke, "The Electrical Conductivity of a Suspension of Homogeneous Spheroids," Physical
Review. Vol. 24, 1924, p. 515.
R. L. Hamilton and O. K. Crosser, "Thermal Conductivity of Heterogeneous Two-Component
Systems," Industrial and Engineering Chemistry Fundamentals. Vol. 2, 1962, p. 187.
Lord Rayleigh, "On the Influence of Obstacles Arranged in Rectangular Order Upon the
Properties of a Medium," Philosophical Magazine and Journal of Science. Vol. 34, 1892, p. 481.
R. E. Meredith and C. W. Tobias, "Resistance to Potential Flow Through a Cubical Array of
Spheres," Journal of Applied Phvsics. Vol. 31, 1960, p. 1270.
D.A.G. Bruggeman, "Dielectric Constant and Conductivity of Mixtures of Isotropic Materials,"
Annalen Phvsik. Vol. 24, 1935, p. 636.
R. G. Deissler and J. S. Boegli, "An Investigation of Effective Thermal Conductivities of Powders
in Various Gases," Transactions of the ASME. Vol. 80, 1958, p. 1417.
K. Lichteneker, "The Electrical Conductivity of Periodic and Random Aggregates," Physikalische
Zeitschrift. Vol. 27, 1926, p. 115.
W. Woodside and J. H. Messmer, "Thermal Conductivity of Porous Media in Unconsolidated
Sands," Journal of Applied Phvsics. Vol. 32, 1961, p. 1688.
K. Lichteneker, "The Electrical Conductivity of Periodic and Random Aggregates," Physikalische
Zeitschrift. Vol 25, 1924, p. 169.
W. Schott, "Thermal Conductivity of Packed Beds," American Institute of Chemical Engineers
Journal. Vol. 6, 1960, p. 63.
S. Yagi and D. Kunii, "Studies on Effective Thermal Conductivities in Packed Beds," American
Institute of Chemical Engineers Journal. Vol. 3, 1957, p. 373.
G. P. Willhite, D. Kunii, and J. M. Smith, "Heat Transfer in Beds of Fine Particles," American
Institute of Chemical Engineers Journal. Vol. 8, 1962, p. 340.
S. Masamune and J. M. Smith, Thermal Conductivity of Beds of Spherical Particles, Industrial and
Engineering Chemistry. Vol. 2, 1963, p. 136.
G. N. Dullney, "Heat Transfer Through Solid Disperse Systems," Journal of Engineering Phvsics.
Vol. 9, 1965, p. 399.
A. V. Luikov, A. G. Shashkov, L. L. Vasiliev, and Yu.E., Fraiman, Thermal Conductivity of
Porous Systems," International Journal of Heat and Mass Transfer. Vol. 11, 1968, p. 117.
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26
T.E.W. Schumann, and V. Voss, "Heat Flow Through Granulated Material," Fuel in Science and
Practice, Vol. 13, 1934, p. 249.
M. G. Kaganer, "Thermal Insulation in Low Temperature Engineering," Izd. Mashinostronenie.
1966.
R. Krupiczka, "Analysis of Thermal Conductivity in Granular Materials," Chemia Stosowana.
Vol. 2B, 1966, p. 183.
H. W. Russell, "Principles of Heat How in Porous Insulators," Journal of the American Ceramic
Society. Vol. 18, 1935, p. 1.
H. W. Godbee and W. T. Ziegler, "Thermal Conductivity of MgO, Al203 and Zr02 Powders to
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27
M. M. Yovanovitch, "Apparent Conductivity of Glass Microspheres from Atmospheric Pressure to
Vacuum," ASME Paper 73-HT-43, August 5-8, 1973.
1988 Review by Rue
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D. L. McElroy, D. W. Yarbrough, G. L. Copeland, F. J. Weaver, R. S. Graves, T. W. Tong, and
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28
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pp. 608-613.
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29
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30
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31
EPA-600/R-92-203
ORNL/M-2426
INTERNAL DISTRIBUTION
1. T.G. Kollie
2. R.L. Beatty
3. A.O. Desjarlais
4. J.E. Christian
5. F.J. Weaver
6. R.E. Pawel
7. R.K. Williams
8. K.E. Wilkes
9. D.W. Yarbrough
10. D.L. McElroy
11. R.S. Graves
12. Lab Records
13. Patent Office
EXTERNAL DISTRIBUTION
14. Bomberg, M. T., National Research Council of Canada, Institute for Research in
Construction, Ottawa, Ontario, Canada K1A OR6
15. Fine, H. A, U.S. EPA Washington, D.C. 20460
16. Hendricks, R.V., EPA Research Triangle Park, NC 27711
17. Lucus, P., PPG Industries, Inc., Tech Center, 440 College Park Drive, Monroeville, PA 95146
18. Lundy, T.S., Center for Manufacturing, TTU, Cookeville, TN 38505
19. Scofield, M.P., U.S. DOE, Washington, D.C. 20585
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO, 2.
EPA-600/R-92-203
3. RFCfPIE
(PREASS
4. TITLE AND SUBTITLE
Literature Review: Heat Transfer Through Two-phase
insulation Systems Consisting of Powders in a
Continuous Gas Phase
5. REPORT DATE
November 1993
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
David W. Yarbrough
8. PERFORMING ORGANIZATION REPORT NO.
ORNL/M-2426
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Oak Ridge National Laboratory
Building Materials Group
Oak Ridge, Tennessee 37831-6092
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
EPA 1AG DW89934975 and
DOE DE- A CO 5~ 840R21400
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Air and Energy Engineering Research Laboratory
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final; 11/91-5/92
14. SPONSORING AGENCY CODE
EPA/600/13
NOTES -AEERL project officer is Robert V. Ffendriks, Mail Drop 62B,
919/541-3928. Related NTIS number is DE 93014387.
16. abstractrpj.ie -pepQpj^ a review of the literature on heat flow through powders, was
motivated by the use of fine powder systems to produce high thermal resistivities
(thermal resistance per unit thickness). The term 'superinsulations" has been used
to describe this type of material, which has thermal resistivities in excess of 20 sq
ft*It °F/Btu (3. 52 K- sq m/W) per in. (2. 54 cm) of insulation thickness. The report
is concerned with superinsulations obtained using evacuated powders. The literature
review shows that the calculation of heat flow through gas-powder systems is highly
developed. One major weakness in the calculated, procedures is the absence of struc-
tural features for the powders, which are invariably characterized as regular arrays
of spheres or cubes, rather than random irregularly shaped particles. The effect of
particle size distribution on the shape and size of void spaces is not modeled, al-
though it affects the thermal conductivity of the. gas. Calculations of thermal perfor-
mance based on simplified descriptions of the porosity distribution can be used to
show the dependence of thermal resistance on interstitial gas pressure. The litera-
ture reviewed in this report provides a basis for predicting the interstitial gas pres-
sure at which thermal conductivity begins to increase., The objective is to design
filler material for powder insulation systems with ultrafine void spaces.
17. KEY WORDS AND DOCUMENT ANALYSIS
2. DESCRIPTORS
b. IDENTIFIERS/OPEN ENDED TERMS
c. cosati Field/Group
Pollution
Powder (Particles)
[nsulation
Thermal Conductivity
Pollution Control
Stationary Sources
Superinsulation
13 B
14G
20M
18. JISTRIBUTION STATEMENT
Release to Public
19. SECURITY CLASS (Thin Report)
Unclassified
21. NO. OF PAGES
36
20. SECURITY CLASS (This page)
Unclassified
22. PRICE
EPA Form 2220-1 <9-73)
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