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

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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.

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Abbreviations

C p :

Specific heat capacity, J kg−1 K−1

d p :

Aerogel particle diameter, m

D :

Mean pore size of aerogel, m

E s/ρ s :

Specific extinction coefficient of aerogel, m2 kg−1

K n :

Kundsen number

l :

Height of sample, m

n :

Refractive index

Q n :

Normal heat flux, W m−2

R :

Radius of sample, m

S ext :

Specific surface area, m2 kg−1

t :

Time, s

T :

Temperature, K

T H :

Temperature in hot surface, K

V pore :

Pore volume, m3 kg−1

β :

Coefficient in Eq. 3

λ :

Thermal conductivity, W m−1 K−1

ρ :

Density of aerogel, kg m−3

ρ s :

Density of aerogel solid backbone, kg m−3

σ B :

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

° :

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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Author notes

  1. Mina Noroozi and Mahyar Panahi-Sarmad have equally contributed to this work.

Authors and Affiliations

  1. Department of Polymer Engineering, Faculty of Chemical Engineering, Tarbiat Modares University, P.O.Box 14115-114, Tehran, Iran

    Mina Noroozi, Mahyar Panahi-Sarmad, Ahmad Reza Bahramian & Alireza Sharif

Authors
  1. Mina Noroozi
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  2. Mahyar Panahi-Sarmad
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  3. Ahmad Reza Bahramian
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  4. Alireza Sharif
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Correspondence to Ahmad Reza Bahramian.

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Noroozi, M., Panahi-Sarmad, M., Bahramian, A.R. et al. Theoretical investigation of heat transfer in structurally graded silica aerogels with pores diameter changing. J Therm Anal Calorim 135, 1713–1721 (2019). https://doi.org/10.1007/s10973-018-7315-7

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  • DOI: https://doi.org/10.1007/s10973-018-7315-7

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