Effective thermal conductivity of composite solids

Input(s)

$k_{o}$: Thermal Conductivity of Continuous Phase (W/m K)

$k_{1}$: Thermal Conductivity of Embedded Phase (W/m K)

$\emptyset$: Porosity (fraction)

Output(s)

$k_{\text {eff: }} \quad$ Effective Thermal Conductivity $(\mathrm{W} / \mathrm{m} \mathrm{K})$

Formula(s)

$$ \frac{\mathrm{k}_{\mathrm{eff}}}{\mathrm{k}_{\mathrm{o}}}=1+\left(\frac{3 * \varnothing}{\left(\frac{\mathrm{k}_{1}+2 * \mathrm{k}_{\mathrm{o}}}{\mathrm{k}_{1}-\mathrm{k}_{\mathrm{o}}}\right)-\varnothing}\right) $$

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley \& Sons, Chapter: 9, Page: 281.