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Several identical rods, each of thermal conductance K and cross-sectional area A, form a symmetric network in which the rods AB, AO and AD branch out from corner A and recombine toward corner C. The ends A and C are held at temperatures 2*T0 and T0 respectively. By the symmetry of the network, which of the following statements is correct?

1. The rate of heat flow through AB, AO and AD is the same
2. The rate of heat flow through BO and OD is different
3. The temperature at junction B differs from that at junction D
4. No heat flows from A to C

Correct answer: The rate of heat flow through AB, AO and AD is the same

Solution

Because the three branches from A are symmetric and identical, they each carry an equal share of the total heat current, and the symmetric junctions reach the same temperature. Thus the equal-flow statement is correct, while the statements claiming asymmetry are false, and heat clearly flows since 2*T0 > T0.

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