1. Date of download: 12/31/2017
Copyright © ASME. All rights reserved.
From: A Simplified Model for Effective Thermal Conductivity of Highly Porous Ceramic Fiber Insulation
J. Thermal Sci. Eng. Appl. 2015;7(4): doi: /
Figure Legend:
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.

2. Date of download: 12/31/2017
Copyright © ASME. All rights reserved.
From: A Simplified Model for Effective Thermal Conductivity of Highly Porous Ceramic Fiber Insulation
J. Thermal Sci. Eng. Appl. 2015;7(4): doi: /
Figure Legend:
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.

3. Date of download: 12/31/2017
Copyright © ASME. All rights reserved.
From: A Simplified Model for Effective Thermal Conductivity of Highly Porous Ceramic Fiber Insulation
J. Thermal Sci. Eng. Appl. 2015;7(4): doi: /
Figure Legend:
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].

4. Date of download: 12/31/2017
Copyright © ASME. All rights reserved.
From: A Simplified Model for Effective Thermal Conductivity of Highly Porous Ceramic Fiber Insulation
J. Thermal Sci. Eng. Appl. 2015;7(4): doi: /
Figure Legend:
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.

5. Date of download: 12/31/2017
Copyright © ASME. All rights reserved.
From: A Simplified Model for Effective Thermal Conductivity of Highly Porous Ceramic Fiber Insulation
J. Thermal Sci. Eng. Appl. 2015;7(4): doi: /
Figure Legend:
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.

6. Date of download: 12/31/2017
Copyright © ASME. All rights reserved.
From: A Simplified Model for Effective Thermal Conductivity of Highly Porous Ceramic Fiber Insulation
J. Thermal Sci. Eng. Appl. 2015;7(4): doi: /
Figure Legend:
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.

7. Date of download: 12/31/2017
Copyright © ASME. All rights reserved.
From: A Simplified Model for Effective Thermal Conductivity of Highly Porous Ceramic Fiber Insulation
J. Thermal Sci. Eng. Appl. 2015;7(4): doi: /
Figure Legend:
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.

8. Date of download: 12/31/2017
Copyright © ASME. All rights reserved.
From: A Simplified Model for Effective Thermal Conductivity of Highly Porous Ceramic Fiber Insulation
J. Thermal Sci. Eng. Appl. 2015;7(4): doi: /
Figure Legend:
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.

9. Date of download: 12/31/2017
Copyright © ASME. All rights reserved.
From: A Simplified Model for Effective Thermal Conductivity of Highly Porous Ceramic Fiber Insulation
J. Thermal Sci. Eng. Appl. 2015;7(4): doi: /
Figure Legend:
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.

10. Date of download: 12/31/2017
Copyright © ASME. All rights reserved.
From: A Simplified Model for Effective Thermal Conductivity of Highly Porous Ceramic Fiber Insulation
J. Thermal Sci. Eng. Appl. 2015;7(4): doi: /
Figure Legend:
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.

11. Date of download: 12/31/2017
Copyright © ASME. All rights reserved.
From: A Simplified Model for Effective Thermal Conductivity of Highly Porous Ceramic Fiber Insulation
J. Thermal Sci. Eng. Appl. 2015;7(4): doi: /
Figure Legend:
Conduction contribution to keff in N2 at 1 atm

12. Date of download: 12/31/2017
Copyright © ASME. All rights reserved.
From: A Simplified Model for Effective Thermal Conductivity of Highly Porous Ceramic Fiber Insulation
J. Thermal Sci. Eng. Appl. 2015;7(4): doi: /
Figure Legend:
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.

13. Date of download: 12/31/2017
Copyright © ASME. All rights reserved.
From: A Simplified Model for Effective Thermal Conductivity of Highly Porous Ceramic Fiber Insulation
J. Thermal Sci. Eng. Appl. 2015;7(4): doi: /
Figure Legend:
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.

14. Date of download: 12/31/2017
Copyright © ASME. All rights reserved.
From: A Simplified Model for Effective Thermal Conductivity of Highly Porous Ceramic Fiber Insulation
J. Thermal Sci. Eng. Appl. 2015;7(4): doi: /
Figure Legend:
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.

15. Date of download: 12/31/2017
Copyright © ASME. All rights reserved.
From: A Simplified Model for Effective Thermal Conductivity of Highly Porous Ceramic Fiber Insulation
J. Thermal Sci. Eng. Appl. 2015;7(4): doi: /
Figure Legend:
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.

16. Date of download: 12/31/2017
Copyright © ASME. All rights reserved.
From: A Simplified Model for Effective Thermal Conductivity of Highly Porous Ceramic Fiber Insulation
J. Thermal Sci. Eng. Appl. 2015;7(4): doi: /
Figure Legend:
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.

17. Date of download: 12/31/2017
Copyright © ASME. All rights reserved.
From: A Simplified Model for Effective Thermal Conductivity of Highly Porous Ceramic Fiber Insulation
J. Thermal Sci. Eng. Appl. 2015;7(4): doi: /
Figure Legend:
keff of materials A, B, and C in N2 at 1, 20, and 40 atm