Thermal conduction between 3 rods

  • #1
32
0

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:

Answers and Replies

  • #2
Hesch
Gold Member
922
153
(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 ).
 
  • #3
rude man
Homework Helper
Insights Author
Gold Member
7,945
827
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?
 

Related Threads on Thermal conduction between 3 rods

  • Last Post
Replies
8
Views
966
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
4
Views
5K
  • Last Post
Replies
0
Views
3K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
3
Views
1K
Top