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Journal of Thermal Analysis and Calorimetry

, Volume 135, Issue 3, pp 1713–1721 | Cite as

Theoretical investigation of heat transfer in structurally graded silica aerogels with pores diameter changing

  • Mina Noroozi
  • Mahyar Panahi-Sarmad
  • Ahmad Reza BahramianEmail author
  • Alireza Sharif
Article
First Online:

Abstract

In graded structure aerogels, change of pores diameter through the thickness affects the effective thermal conductivity as the most important parameter. As the diameter of the pores is reversely correlated to the density, the effective thermal conductivity (\(\lambda_{\text{eff}}\)) of aerogel is often normalized to the apparent density (\(\rho\)) and it is expressed as the B (\(\frac{{\lambda_{\text{eff}} }}{\rho }\)) parameter. Lower values of B would be the optimum conditions for the insulation performance of resulting aerogel. The objective of this work is to simulate the heat transfer of the optimum structure and to compare it with functionally graded structures that pore diameter varies through the thickness. For this purpose, the structural characteristics and properties of silica aerogel along with the effect of coupling thermal conductivity have to be taken into consideration. The heat transfer and time–temperature history diagram were modeled for an optimum structure (OPT) having a minimum value of the B parameter. The results were compared to the structurally graded aerogels in which the density was varied in two fashions, from higher to lower values (HtL) density and from lower to higher values (LtH) density. The change of temperature with time was tracked for all the cases. Results indicated that the minimum value of heat transfer was obtained for the structurally graded aerogel of the type of LtH (2% increase in efficiency for LtH compared to OPT). Therefore, this structure introduces as the best candidate for producing a thermal insulator.

Keywords

Silica aerogel Gradient structure Heat transfer Simulation 

List of symbols

Cp

Specific heat capacity, J kg−1 K−1

dp

Aerogel particle diameter, m

D

Mean pore size of aerogel, m

Es/ρs

Specific extinction coefficient of aerogel, m2 kg−1

Kn

Kundsen number

l

Height of sample, m

n

Refractive index

Qn

Normal heat flux, W m−2

R

Radius of sample, m

Sext

Specific surface area, m2 kg−1

t

Time, s

T

Temperature, K

TH

Temperature in hot surface, K

Vpore

Pore volume, m3 kg−1

Greek symbols

β

Coefficient in Eq. 3

λ

Thermal conductivity, W m−1 K−1

ρ

Density of aerogel, kg m−3

ρs

Density of aerogel solid backbone, kg m−3

σB

Stefan–Boltzmann constant in Eq. 4

\(\upsilon\)

Sound velocity in aerogel, m s−1

\(\upsilon_{\text{s}}\)

Sound velocity in solid backbone, m s−1

Subscripts

°

Aerogel solid backbone

c

Coupling

eff

Effective

g

Gas

g,°

Gas in free space

g − s

Between solid and gas phase

p

Solid particle

r

Radiation

s

Solid

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References

  1. 1.
    Nojoomizadeh M, D’Orazio A, Karimipour A, Afrand M, Goodarzi M. Investigation of permeability effect on slip velocity and temperature jump boundary conditions for FMWNT/water nanofluid flow and heat transfer inside a microchannel filled by a porous media. Phys E Low Dimens Syst Nanostruct. 2018;97:226–38.CrossRefGoogle Scholar
  2. 2.
    Hooman K, Tamayol A, Dahari M, Safaei MR, Togun H, Sadri R. A theoretical model to predict gas permeability for slip flow through a porous medium. Appl Therm Eng. 2014;70:71–6.CrossRefGoogle Scholar
  3. 3.
    Sadeghi R, Shadloo MS, Hopp-Hirschler M, Hadjadj A, Nieken U. Three-dimensional lattice Boltzmann simulations of high density ratio two-phase flows in porous media. Comput Math Appl. 2018.  https://doi.org/10.1016/j.camwa.2017.12.028.CrossRefGoogle Scholar
  4. 4.
    Nasiri H, Abdollahzadeh Jamalabadi MY, Sadeghi R, Safaei MR, Nguyen TK, Safdari Shadloo M. A smoothed particle hydrodynamics approach for numerical simulation of nano-fluid flows: application to forced convection heat transfer over a horizontal cylinder. J Therm Anal Calorim. 2018;4:1–9.Google Scholar
  5. 5.
    Heydari A, Akbari OA, Safaei MR, Derakhshani M, Alrashed AAAA, Mashayekhi R. The effect of attack angle of triangular ribs on heat transfer of nanofluids in a microchannel. J Therm Anal Calorim. 2018;131:2892–912.CrossRefGoogle Scholar
  6. 6.
    Pierre AC, Pajonk GM. Chemistry of aerogels and their applications. Chem Rev. 2002;102:4243–65.CrossRefGoogle Scholar
  7. 7.
    Pan Y, He S, Gong L, Cheng X, Li C, Li Z. Low thermal-conductivity and high thermal stable silica aerogel based on MTMS/water-glass co-precursor prepared by freeze drying. Mater Des. 2017;113:246–53.CrossRefGoogle Scholar
  8. 8.
    Fang WZ, Zhang H, Chen L, Tao WQ. Numerical predictions of thermal conductivities for the silica aerogel and its composites. Appl Therm Eng. 2017;115:1277–86.CrossRefGoogle Scholar
  9. 9.
    Antonietti M, Fechler N, Fellinger TP. Carbon aerogels and monoliths: control of porosity and nanoarchitecture via sol–gel routes. Chem Mater. 2014;26:196–210.CrossRefGoogle Scholar
  10. 10.
    Aegerter M, Leventis N, Koebel M. In: Aparicio M, Jitianu A, Klein LC, editors. Aerogels handbook. Boston: Springer; 2012.Google Scholar
  11. 11.
    Williams JC, Nguyen BN, McCorkle L, Scheiman D, Griffin JS, Steiner SA. Highly porous, rigid-rod polyamide aerogels with superior mechanical properties and unusually high thermal conductivity. ACS Appl Mater Interfaces. 2017;9:1801–9.CrossRefGoogle Scholar
  12. 12.
    Maleki H, Durães L, Portugal A. An overview on silica aerogels synthesis and different mechanical reinforcing strategies. J Non Cryst Solids. 2014;385:55–74.CrossRefGoogle Scholar
  13. 13.
    Shahistha ACPM, Binol V, Anjali B. A review on functionally graded materials. Int J Aeronaut Mech Eng. 2016;4:8–14.Google Scholar
  14. 14.
    Schachtschneider A, Wessig M, Spitzbarth M, Donner A, Fischer C, Drescher M. Directional materials-nanoporous organosilica monoliths with multiple gradients prepared using click chemistry. Angew Chem Int Ed. 2015;54:10465–9.CrossRefGoogle Scholar
  15. 15.
    Tang GH, Bi C, Zhao Y, Tao WQ. Thermal transport in nano-porous insulation of aerogel: factors, models and outlook. Energy. 2015;90:701–21.CrossRefGoogle Scholar
  16. 16.
    Bi C, Tang GH, Tao WQ. Prediction of the gaseous thermal conductivity in aerogels with non-uniform pore-size distribution. J Non Cryst Solids. 2012;358:3124–8.CrossRefGoogle Scholar
  17. 17.
    Bi C, Tang GH. Effective thermal conductivity of the solid backbone of aerogel. Int J Heat Mass Transf. 2013;64:452–6.CrossRefGoogle Scholar
  18. 18.
    Khodabandeh E, Safaei MR, Akbari S, Akbari OA, Alrashed A. Application of nanofluid to improve the thermal performance of horizontal spiral coil utilized in solar ponds: geometric study. Renew Energy. 2018;122:1–16.CrossRefGoogle Scholar
  19. 19.
    Bi C, Tang GH, Hu ZJ, Yang HL, Li JN. Coupling model for heat transfer between solid and gas phases in aerogel and experimental investigation. Int J Heat Mass Transf. 2014;79:126–36.CrossRefGoogle Scholar
  20. 20.
    Hemberger F, Weis S, Reichenauer G, Ebert H-P. Thermal transport properties of functionally graded carbon aerogels. Int J Thermophys. 2009;30:1357–71.CrossRefGoogle Scholar
  21. 21.
    Wei G, Liu Y, Zhang X, Yu F, Du X. Thermal conductivities study on silica aerogel and its composite insulation materials. Int J Heat Mass Transf. 2011;54:2355–66.CrossRefGoogle Scholar
  22. 22.
    Bi C, Tang GH, Hu ZJ. Heat conduction modeling in 3-D ordered structures for prediction of aerogel thermal conductivity. Int J Heat Mass Transf. 2014;73:103–9.CrossRefGoogle Scholar
  23. 23.
    Lee SC, Cunnington GR. Conduction and radiation heat transfer in high-porosity fiber thermal insulation. J Thermophys Heat Transf. 2000;14:121–36.CrossRefGoogle Scholar
  24. 24.
    Liu H, Xia X, Ai Q, Xie X, Sun C. Experimental investigations on temperature-dependent effective thermal conductivity of nanoporous silica aerogel composite. Exp Therm Fluid Sci. 2017;84:67–77.CrossRefGoogle Scholar
  25. 25.
    Xie T, He YL, Tong ZX, Yan WX, Xie XQ. Transient heat transfer characteristic of silica aerogel insulating material considering its endothermic reaction. Int J Heat Mass Transf. 2014;64:633–40.CrossRefGoogle Scholar
  26. 26.
    Hajizadeh A, Bahramian AR, Seifi A, Naseri I. Effect of initial sol concentration on the microstructure and morphology of carbon aerogels. J Sol–Gel Sci Technol. 2015;73(1):220–6.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Department of Polymer Engineering, Faculty of Chemical EngineeringTarbiat Modares UniversityTehranIran

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