Research Papers

A Simplified Model for Effective Thermal Conductivity of Highly Porous Ceramic Fiber Insulation

[+] Author and Article Information
Nicholas P. G. Lumley

Colorado School of Mines,
Golden, CO 80401
e-mail: nlumley@burnsmcd.com

Emory Ford

Materials Technology Institute,
St. Louis, MO 63141
e-mail: eford@mti-global.org

Eric Minford

Air Products and Chemicals, Inc.,
Allentown, PA 18195
e-mail: minfore@airproducts.com

Jason M. Porter

Colorado School of Mines,
Golden, CO 80401
e-mail: jporter@mines.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received October 16, 2014; final manuscript received July 13, 2015; published online October 6, 2015. Assoc. Editor: Srinath V. Ekkad.

J. Thermal Sci. Eng. Appl 7(4), 041022 (Oct 06, 2015) (11 pages) Paper No: TSEA-14-1247; doi: 10.1115/1.4031540 History: Received October 16, 2014; Revised July 13, 2015

Highly porous ceramic fiber insulations are beginning to be considered as a replacement for firebrick insulations in high temperature, high pressure applications by the chemical process industry. However, the implementation of such materials has been impeded by a lack of experimental data and predictive models, especially at high gas pressure. The goal of this work was to develop a general, applied thermophysical model to predict effective thermal conductivity, keff, of porous ceramic fiber insulation materials and to determine the temperature, pressure, and gas conditions under which natural convection is a possible mode of heat transfer. A model was developed which calculates keff as the sum of conduction, convection, and radiation partial conductivities. The model was validated using available experimental data, including laboratory measurements made by this research effort. Overall, it was concluded that natural convection is indeed possible for the most porous insulations at pressures exceeding 10 atm. Furthermore, keff for some example insulations was determined as a function of temperature, pressure, and gas environment.

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Pauken, M. , Li, L. , Almasco, D. , Del Castillo, L. , Van Luvender, M. , Beatty, J. , Knopp, M. , and Polk, J. , 2011, “ Insulation Materials Development for Potential Venus Surface Missions,” AIAA Paper No. 2011-256.
Daryabeigi, K. , 2003, “ Heat Transfer in High-Temperature Fibrous Insulation,” J. Thermophys. Heat Transfer, 17(1), pp. 10–20. [CrossRef]
Nield, D. , and Bejan, A. , 2006, Convection in Porous Media, 3rd ed., Springer, New York.
Bejan, A. , and Kraus, A. D. , 2003, “ Porous Media,” Heat Transfer Handbook, Wiley, Hoboken, NJ.
Bejan, A. , and Khair, K. R. , 1985, “ Heat and Mass Transfer by Natural Convection in a Porous Medium,” Int. J. Heat Mass Transfer, 28(5), pp. 909–918. [CrossRef]
Bejan, A. , Dincer, I. , Lorente, S. , Miguel, A. F. , and Reis, A. H. , 2004, Porous and Complex Flow Structures in Modern Technologies, Springer-Verlag, New York.
Kaviany, M. , 1995, Principles of Heat Transfer in Porous Media, 2nd ed., Springer, New York.
Bhattacharya, R. , 1980, “ Heat Transfer Model for Fibrous Insulations,” Thermal Insulation Performance, D. McElroy and R. Tye , eds., American Society for Testing and Materials, Philadelphia, PA, pp. 272–286.
Ferkl, P. , Pokorný, R. , Bobák, M. , and Kosek, J. , 2013, “ Heat Transfer in One-Dimensional Micro- and Nano-Cellular Foams,” Chem. Eng. Sci., 97, pp. 50–58. [CrossRef]
Prasad, V. , and Kulacki, F. , 1985, “ Natural Convection in Porous Media Bounded by Short Concentric Vertical Cylinders,” ASME J. Heat Transfer, 107(1), pp. 147–154. [CrossRef]
Stark, C. , and Fricke, J. , 1993, “ Improved Heat-Transfer Models for Fibrous Insulations,” Int. J. Heat Mass Transfer, 36(3), pp. 617–625. [CrossRef]
Litovsky, E. , Shapiro, M. , and Shavit, A. , 1996, “ Gas Pressure and Temperature Dependences of Thermal Conductivity of Porous Ceramic Materials: Part 2, Refractories and Ceramics With Porosity Exceeding 30%,” J. Am. Ceram. Soc., 79(5), pp. 1366–1376. [CrossRef]
Daryabeigi, K. , Cunnington, G. R. , and Knutson, J. R. , 2011, “ Combined Heat Transfer in High-Porosity High-Temperature Fibrous Insulation: Theory and Experimental Validation,” J. Thermophys. Heat Transfer, 25(4), pp. 536–546. [CrossRef]
Zhao, S. , Zhang, B. , and He, X. , 2009, “ Temperature and Pressure Dependent Effective Thermal Conductivity of Fibrous Insulation,” Int. J. Therm. Sci., 48(2), pp. 440–448. [CrossRef]
Kamiuto, K. , Kinoshita, I. , Miyoshi, Y. , and Hasegawa, S. , 1982, “ Experimental Study of Simultaneous Conductive and Radiative Heat Transfer in Ceramic Fiber Insulation,” J. Nucl. Sci. Technol., 19(6), pp. 460–468. [CrossRef]
Hayashi, K. , 1984, “ Thermal Conductivity of Ceramic Fibrous Insulators at High Temperatures,” Int. J. Thermophys., 5(2), pp. 229–238. [CrossRef]
Zheng, G. , Verret, A. , Burke, N. , Prescott, N. , Cai, D. , and Perera, R. , 2001, “ An Update on Heat Transfer in a Porous Insulation Medium in a Subsea Bundled Pipeline,” ASME J. Energy Res. Technol., 123(4), pp. 285–290. [CrossRef]
Kurtbas, I. , and Celik, N. , 2009, “ Experimental Investigation of Forced and Mixed Convection Heat Transfer in a Foam-Filled Horizontal Rectangular Channel,” Int. J. Heat Mass Transfer, 52(5–6), pp. 1313–1325. [CrossRef]
Bhattacharya, A. , and Mahajan, R. L. , 2006, “ Metal Foam and Finned Metal Foam Heat Sinks for Electronics Cooling in Buoyancy-Induced Convection,” ASME J. Electron. Packag., 128(3), pp. 259–266. [CrossRef]
Bejan, A. , and Kraus, A. D. , 2003, Heat Transfer Handbook, Wiley, New York.
Otero, J. , Dontcheva, L. A. , Johnston, H. , Worthing, R. A. , Kurganov, A. , Petrova, G. , and Doering, C. R. , 2004, “ High-Rayleigh-Number Convection in a Fluid-Saturated Porous Layer,” J. Fluid Mech., 500, pp. 263–281. [CrossRef]
Kamiuto, K. , 1991, “ Analytical Expression for Total Effective Thermal Conductivities of Packed Beds,” J. Nucl. Sci. Technol., 28(12), pp. 1153–1156. [CrossRef]
Siegel, R. , and Howell, J. R. , 2002, Thermal Radiation Heat Transfer, 4th ed., Taylor and Francis, New York.
Van de Hulst, H. C. , 1957, Light Scattering by Small Particles, Dover, New York.
Kerker, M. , 1969, The Scattering of Light, and Other Electromagnetic Radiation, Academic, New York.
Leachman, J. , Jacobsen, R. , Penoncello, S. , and Lemmon, E. , 2009, “ Fundamental Equations of State for Parahydrogen, Normal Hydrogen, and Orthohydrogen,” J. Phys. Chem. Ref. Data, 38(3), pp. 721–748. [CrossRef]
McCarty, R. , and Arp, V. , 1990, “ A New Wide Range Equation of State for Helium,” Adv. Cryog. Eng., 35, pp. 1465–1475.
Arp, V. , McCarty, R. , and Friend, D. , 1989, “ Thermophysical Properties of Helium-4 From 0.8 to 1500 K With Pressures to 2000 MPa,” National Institute of Standards and Technology, Boulder, CO, Technical Report No. N-90-28681.
Hands, B. , and Arp, V. , 1981, “ A Correlation of Thermal Conductivity Data for Helium,” Cryogenics, 21(12), pp. 697–703. [CrossRef]
Span, R. , Lemmon, E. , Jacobsen, R. , Wagner, W. , and Yokoezki, A. , 2000, “ A Reference Equation of State for the Thermodynamic Properties of Nitrogen for Temperatures From 63.151 to 1000 K and Pressures to 2200 MPa,” J. Phys. Chem. Ref. Data, 29(6), pp. 1361–1433. [CrossRef]
Lemmon, E. , and Jacobsen, R. , 2004, “ Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air,” Int. J. Thermophys., 25(1), pp. 21–69. [CrossRef]
Tegler, R. , Span, R. , and Wagner, W. , 1997, “ Eine neue fundamental-gleichung für das fluide zustandsgebiet von argon für temperaturen von der schmelzlinie bis 700 K und drücke bis 1000 MPa,” Fortschr.-Ber. Verfahrenstech., 3(480).
Lemmon, E. , Jacobsen, R. , Penoncello, S. , and Friend, D. , 2000, “ Thermodynamic Properties of Air and Mixtures of Nitrogen, Argon, and Oxygen From 60 to 2000 K at Pressures to 2000 MPa,” J. Phys. Chem. Ref. Data, 29(3), pp. 331–385. [CrossRef]
Span, R. , and Wagner, W. , 1996, “ A New Equation of State for Carbon Dioxide Covering the Fluid Region From the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa,” J. Phys. Chem. Ref. Data, 25(6), pp. 1509–1596. [CrossRef]
Vesovic, V. , Wakeham, W. , Olchowy, G. , Sengers, J. , Watson, J. , and Millat, J. , 1990, “ The Transport Properties of Carbon Dioxide,” J. Phys. Chem. Ref. Data, 19(3), pp. 763–808. [CrossRef]
Fenghour, A. , Wakeham, W. , and Vesovic, V. , 1998, “ The Viscosity of Carbon Dioxide,” J. Phys. Chem. Ref. Data, 27(1), pp. 31–44. [CrossRef]
Gembarovic, J. , and Taylor, R. , 2007, “ A Method for Thermal Diffusivity Determination of Thermal Insulators,” Int. J. Thermophys., 28(6), pp. 2164–2175. [CrossRef]


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Fig. 1

SEM images at 500× magnification of Danser Vacuduct 2300 (a), Zircar AL30 (b), and Unifrax Durablanket S #6 (c). Materials A and B are composed of a heterogeneous matrix of fibers, sheets, spheroidal particles, and other irregular geometries. Material C is composed of smooth cylindrical fibers with nonuniform orientation.

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Fig. 2

Illustration of heat transport pathways in porous ceramic insulation. (a) Convective cells can form in highly porous insulations. (b) and (c) Heat transfer at the microscale is a combination of several mechanisms including fluid conduction, kfluid, solid conduction, ksolid, radiation, krad, and convection, kconv.

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Fig. 3

Fibrous (C-like) material validation, plotted as Tmean. A strong agreement between literature data (markers) and the model is seen both at low temperatures, validating the conduction model, and at high temperatures validating the radiation model. All data points at 1 atm air. Data from Refs. [14] and [16].

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Fig. 4

Fibrous (C-like) material validation in vacuum, data from Ref. [2]. Vacuum data validate the conduction model at low temperature and radiation model at high temperature.

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Fig. 5

Fibrous (C-like) material validation in vacuum, experimental data. The model shows excellent agreement at temperatures below 850 K, validating the conduction model. Data from contract laboratory.

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Fig. 6

Validation against data from manufacturer of material B. Comparison was made to manufacturer supplied data in air at 1 atm. A strong agreement is found at temperatures above 500 K.

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Fig. 7

Material A validation in 1 atm N2. Good general agreement between the model and measured data is observed. The model slightly underpredicts keff at low temperatures. Data from contract laboratory.

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Fig. 8

Material A validation in vacuum. The model performs well in the vacuum condition, where fluid conduction and convection are not possible. Data from contract laboratory.

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Fig. 9

Variation of keff with permeability. keff increases with the square root of permeability at temperature and pressure conditions sufficient to drive natural convection. The model is not sensitive to permeability in the absence of natural convection. The variation is relatively strong, especially for geometrically heterogeneous materials. Note that the ordinate scale is small due to the small values of permeability in the SI system.

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Fig. 10

Variation of keff with mean diameter. The variation of keff with mean diameter is almost linear due to a linear increase in radiation transport with larger diameter and reduced number density of fibers. The effect on permeability and convective transport is relatively smaller.

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Fig. 11

Conduction contribution to keff in N2 at 1 atm

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Fig. 12

Pressure dependence of keff at low pressure. Under full vacuum, heat transfer is solely by solid conduction and radiation. As pressure increases the saturating gas assumes a continuum behavior and attains its limiting fluid conductivity value.

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Fig. 13

krad shows the typical power-law response of radiative heat transport. High-density material B shows superior attenuation. The large number of scattering centers in material C results in better performance than the denser material A.

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Fig. 14

Onset of natural convection at 20 atm in N2. The more permeable material C supports natural convection at a lower temperature than the denser, less permeable materials A and B.

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Fig. 15

Onset of natural convection at 800 K in N2. Note that the pressure where Ra > 40 decreases with increasing temperature. The most permeable materials A and C allow natural convection at lower pressures than material B.

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Fig. 16

Sensitivity of keff of material C to porosity, φ. Analysis conducted at 800 K in N2. The inflection point reflects a balance between solid conduction by increased fiber-to-fiber contact versus reduced radiative and convective transport due to increased fiber density.

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Fig. 17

keff of materials A, B, and C in N2 at 1, 20, and 40 atm



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