Laminate conductivity
= Laminate conductivity
{title2=$a^*=a_Hn\otimes n+a_A(I-n\otimes n)$}
For isotropic phases with planar interfaces normal to $n$, normal conductivity is the weighted harmonic mean $a_H=(\sum p_i/a_i)^{-1}$ and tangential conductivity is the weighted arithmetic mean $a_A=\sum p_i a_i$. Continuity of normal flux and tangential temperature gradient gives the two averages directly.