Heat Flow through Three Rods problem

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Homework Help Overview

The problem involves three identical rods welded together in a Y-shape, with specific temperatures maintained at their ends. The context is thermal conductivity and heat flow, focusing on determining the temperature at the junction and the heat current in one of the rods.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need to apply thermodynamic principles and the law of thermal equilibrium. Some express uncertainty about how to begin solving the problem, while others suggest considering the relationship between heat flow in the rods.

Discussion Status

There is an ongoing exploration of the problem, with some participants attempting to clarify concepts related to thermal conductivity and heat flow. Guidance has been offered regarding the application of thermal equilibrium, but no consensus has been reached on the specific approach to take.

Contextual Notes

Participants note a lack of understanding of thermal conductivity and its implications for the problem, indicating that foundational knowledge may be necessary for progress.

kenau_reveas
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Homework Statement


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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Please post your attempt to solve this problem.
 
I don't even know how to start.
 
Use thermodynamic equation and apply law of thermal equilibrium at center.
 
kenau_reveas said:
I don't even know how to start.

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?
 
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