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Thermal conduction – rods in parallel
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Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are $K_1$ and $K_2$. The thermal conductivity of the composite rod will be
Rods side by side (equal area) give the average conductivity.
Thermal current $H = H_1 + H_2 = \frac{K_1A(T_1 - T_2)}{d} + \frac{K_2A(T_1 - T_2)}{d}$ $\frac{K_{EQ}\,2A(T_1 - T_2)}{d} = \frac{A(T_1 - T_2)}{d}(K_1 + K_2)$ $K_{EQ} = \frac{K_1 + K_2}{2}$