Three identical rods are weldedtogether to form a Y-shaped figure (Below). The c

Question

Three identical rods are weldedtogether to form a Y-shaped figure (Below). The cross-sectionalarea of each rod is A,and they have length L and thermal conductivity k.The free end of rod 1 is maintained at the free end of rod 1is maintained at T1 and the free ends of rods 2 and 3 are maintained at alower temperature T0. You may assume that there is no heat loss from thesurfaces of the rods.

I have found the first two question answer here:

http://www.chegg.com/homework-help/questions-and-answers/hey-guys-just-havinga-fair-bit-of-trouble-thess-questions-if-anyone-could-give-me-somehint-q297928

But the third one I do not know:

By symmetry, the heat current in rods 2 and 3 will be the same. Find this heat current.

Express your answer in terms of k, L, A and the temperatures T1 and T0.

Explanation / Answer

dQ/dt=(kA/L)(dT/dx). Current in BC and BD are equal because they are of same material and equal temperature gradient. Current in AB=BC+BD=2BC=2BD. Which gives (kA(T1-Tj))/L=2(kA(Tj-T0))/L. Which implies Tj=(2T0+T1)/3. So, Tj-T0=(T1-T0)/3. Current=kA(T1-T0)/3L

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