# Heat Flow through Three Rods problem

1. Dec 9, 2006

### kenau_reveas

1. The problem statement, all variables and given/known data
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.
View Figure
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.

Part A

What is T_j, the temperature of the junction point?
Express your answer in terms of T_1 and T_0.

Part B

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.

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2. Dec 10, 2006

### OlderDan

Please post your attempt to solve this problem.

3. Dec 10, 2006

### kenau_reveas

I dont even know how to start.

4. Dec 10, 2006

### winwizard3k

Use thermodynamic equation and apply law of thermal equilibrium at center.

5. Dec 10, 2006

### OlderDan

For this and for your other problem you need to understand thermal conductivity

http://en.wikipedia.org/wiki/Thermal_conductivity

In this problem, heat flows from the warm end of the single rod to the cooler ends of the dual rods. The temperature in the middle must be such that the heat flowing through the warm rod must be the sum of the heats flowing through the cooler rods. What junction temperature will make that happen?

Last edited: Dec 10, 2006