# Thermal conduction between 3 rods

• j3dwards
In summary: Your equation doesn't seem to account for the 24cm length of the steel rod.But, maybe your idea is that you could ignore the steel rod because the heat flow thru it is negligible compared to the heat flow thru the copper and brass rods. If that's the case, then you need to show that the heat flow thru the steel rod is negligible.In summary, rods of copper, brass, and steel with different lengths and thermal conductivities are welded together to form a Y-shaped figure. The free end of the copper rod is maintained at 100◦C while the free ends of the brass and steel rods are at 0◦C. The temperature at the junction point is calculated to be 83.
j3dwards

## Homework Statement

Rods of copper, brass and steel are welded together to form a Y-shaped figure. The cross-sectional area of each rod is 2.0 cm2 . The free end of the copper rod is maintained at 100C, and the free ends of the brass and steel rods at 0 C. Assume there is no heat loss from the surface of the rods. The lengths of the rods are: copper, 13 cm; brass, 18 cm; steel, 24 cm. The thermal conductivities are: copper, 385 W m−1 K −1 ; brass, 109 W m−1 K −1 ; steel, 50.2 W m−1 K −1
(a)What is the temperature of the junction point?
(b)What is the heat current in each of the three rods?

## Homework Equations

H = kA (TH - TC)/L

## The Attempt at a Solution

(a) I assumed that the heat flow through all 3 rods was the same:

kc (100 - T)/Lc = kb (T - 0.0)/Lb = ks (T - 0.0)/Ls

Lb kc (100 - T) = Lc kb]T

And with rearranging:

T = (100Lbkc)/(Lckb + Lbkc) = 83.0C

Is this correct? Can I just assume that heat flow is the same and ignore the steel rod?

(b) Do i just used: H = kA (TH - TC)/L again but for each metal? Because H = dQ/dt?

Copper: dQ/dt = (385)(2 x 10-4)(100-83)/0.13 = 10.1

Last edited:
j3dwards said:
(a) I assumed that the heat flow through all 3 rods was the same:
I don't think that's a good assumption.

I'd switch the thermal circuit to an electric circuit ( temperatures = voltages, thermal conductivity = resistors, heat flow = current ).

Use Kirchhoffs current law ( KCL ) to calculate voltage and currents. ( It's only one equation needed ).

j3dwards said:
Is this correct? Can I just assume that heat flow is the same and ignore the steel rod?
Presumably, the junction temperature will be somewhere between 0 and 100C. Does it then make sense that, the ends of the steel rod being at different temperatures, that there be no heat flow thru the steel rod?

## 1. What is thermal conduction?

Thermal conduction is the transfer of heat from one object to another through direct contact, without the movement of the material itself.

## 2. How does thermal conduction occur between 3 rods?

In the context of thermal conduction between 3 rods, heat is transferred from one rod to another through direct contact, and eventually to the third rod. This process continues until thermal equilibrium is reached, where the temperatures of all three rods are equal.

## 3. What factors affect the rate of thermal conduction between 3 rods?

The rate of thermal conduction between 3 rods is affected by the thermal conductivity of the materials the rods are made of, the surface area of the rods in contact, and the temperature difference between the rods.

## 4. How is thermal conduction between 3 rods calculated?

The rate of thermal conduction between 3 rods can be calculated using the thermal conductivity of the materials, the surface area of the rods in contact, and the temperature difference between the rods. The formula for calculating heat transfer is Q = kA(T2-T1)/L, where Q is the amount of heat transferred, k is the thermal conductivity, A is the surface area, T2 and T1 are the temperatures of the two rods in contact, and L is the length of the rods.

## 5. What are some real-life examples of thermal conduction between 3 rods?

Examples of thermal conduction between 3 rods include the transfer of heat between metal rods in a car engine, the transfer of heat between the metal rods in a stove or grill, and the transfer of heat between rods in a heating system. It is also a common phenomenon in everyday objects, such as when a spoon placed in a hot cup of coffee becomes warm due to thermal conduction.

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