• id: JME-10-N12
• title: Finding Interface Temperatures
• tags: composite, interface, series

For two slabs in series with outer temperatures $T_1$ and $T_2$: the interface temperature $T_i$ is found from equal heat flow rates through both slabs:

$\frac{k_1 A(T_1 - T_i)}{L_1} = \frac{k_2 A(T_i - T_2)}{L_2}$

Using thermal resistance: $T_i = T_1 - (dQ/dt) \times R_1$, where $dQ/dt = (T_1 - T_2)/(R_1 + R_2)$. For $n$ slabs in series: $R_{\text{total}} = \sum R_i$. The temperature at any interface is found by subtracting the appropriate resistance fraction times the total temperature drop.