Three identical rods are welded together to form a Y-shaped figure. The cross-se
ID: 2206676 • Letter: T
Question
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. (Figure 1) The free end of rod 1 is maintained at T1 and the free ends of rods 2 and 3 are maintained at T0 a lower temperature . You may assume that there is no heat loss from the surfaces of the rods. _________________________________________________________________________________What is Tj, the temperature of the junction point? Express your answer is T1 and T0 _________________________________________________________________________________ What is the heat current in rod 1? Express the heat current in terms of any or all of K ,L ,A , and the temperatures T1 and T0 _________________
_______________________________________________________________ .
Explanation / Answer
Q/t = K*A*(T1 -Tj)/L This looks good since it is just the standard formula However you have the Y shape so that half the heat transfer goes into each part of the Y. So you need a factor of 2 when you add in the Y parts. (Q/t)bottom = 2x(Q/t)top (T1 - Tj) = 2(Tj - T0) T1 + 2T0 = 3Tj Tj = (T1 + 2T0)/3
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