Heat transfer

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Question

12 rods of same length are connected to form a cube. Junction ‘A’ is maintained at 0ºC and B at 100ºC. Rods connected to A and B have conductivity k and all other rods have conductivity 2k. Find the temperature of Junction D in ºC.

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Solution

$H e a t c u r r e n t = i = \frac{△ T}{R_{t h}} = \frac{100}{\frac{9 R}{12}}$
$N o w, T_{D} - T_{A} = i \times R_{A D} = \frac{100}{\frac{9 R}{12}} \times \frac{5 R}{12}$
$\Rightarrow T_{D} = \frac{500}{9} = 55.56$

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