Thermal conductivity of solids with gas pockets
Input(s)
\(k_{o}\): Thermal Conductivity of Solid Phase \((\mathrm{W} / \mathrm{m} \mathrm{K})\)
\(k_{1}\): Thermal Conductivity of the Gas (W/m K)
Ø: Porosity (fraction)
\(\mathrm{T}\): Temperature \((\mathrm{K})\)
L: Length \((\mathrm{m})\)
\(\sigma\): Stefan-Boltzmann Constant \(\left(\mathrm{kg} / \mathrm{s}^{3} \mathrm{~K}^{4}\right)\)
Output(s)
\(k_{\text {eff: }} \quad\) Effective Thermal Conductivity (W/m K)
Formula(s)
\[
\frac{\mathrm{k}_{\mathrm{eff}}}{\mathrm{k}_{\mathrm{o}}}=\frac{1}{1-\emptyset+\left(\left(\frac{\mathrm{k}_{1}}{\mathrm{k}_{\mathrm{o}} * \varnothing}\right)+\left(\frac{4 * \sigma * \mathrm{~T}^{3} * \mathrm{~L}}{\mathrm{k}_{\mathrm{o}}}\right)\right)^{-1}}
\]
Reference(s)
Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 9, Page: 282.