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Thermal conduction between 3 rods

  1. Jun 10, 2015 #1
    1. The problem statement, all variables and given/known data
    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?

    2. Relevant equations

    H = kA (TH - TC)/L

    3. 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: Jun 10, 2015
  2. jcsd
  3. Jun 10, 2015 #2

    Hesch

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    Gold Member

    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 ).
     
  4. Jun 11, 2015 #3

    rude man

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    Homework Helper
    Gold Member

    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?
     
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