What is the heat current in rod 1 and how can it be calculated?

jackson1984
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Three identical rods are welded together to form a Y-shaped figure. The cross-sectional area of each rod is A, and they have length L and thermal conductivity k.
The free end of rod 1 is maintained at T_1 and the free ends of rods 2 and 3 are maintained at a lower temperature T_0. You may assume that there is no heat loss from the surfaces of the rods.

What is the heat current H_1 in rod 1?
Express the heat current in terms of any or all of k, L, A, and the temperatures T_1 and T_0.

I guess the ans is (2kA/3L)(T_1+T_2), but it is wrong...
Can anyone teach me...
 

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What is your T2?

Anyway:
label the junction temperature as T2. Then write the heat flow equations for heat from T1 to T2 and T2 to T0. Solve for T2, then dQ/dt is obvious.
 

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