# 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.

## Related

### Thermal conductivity of liquids

An unhandled error has occurred. Reload 🗙