Posted by admin on Saturday, January 15, 2011 · Leave a Comment
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 (the bottom of the Y-shape)is maintained at T1 and the free ends of rods 2 and 3 (the upper rods of the Y-shape)are maintained at a lower temperature T0. You may assume that there is no heat loss from the surfaces of the rods.
What is , the temperature of the junction point Tj?( T0 < Tj < T1)
-> I tried to use the equation of heat current. the heat current of the bottom rod and one of the upper rods must be the same. Thus, i set up an equation : K*A*(T1 -Tj)/L (heat current for the bottom rod)= K*A*(Tj-T0)/L (heat current for the upper rods) then I erased the variables K, A, and L and led to T1-Tj = Tj-T0. I solved for Tj, getting Tj = (T1 + T0)/2. But, the homework programm says it is not a right answer. How do you do it?
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.
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