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Homework Help: Heat and Mass Transfer - finding surface temp

  1. Sep 11, 2010 #1
    1. The problem statement, all variables and given/known data
    A wire is conducting electricity, given values of :

    R' = .4 ohms/m D = .002 m Tinf=300k Tsur=300k k=380W/m*C

    emissivity = 1 h=10W/m^2*C Ts = Find this sigma=Stefan boltzmann

    Plot the Temperature of the wire versus the current I for 0<I<10 amps.


    2. Relevant equations

    P = I^2*R' = q'

    Convective heat = h(Ts-Tinf) + sigma(Ts^4-Tsur^4) = I^2*R' / pi*D = q'/pi*D = q''

    3. The attempt at a solution

    Ok So my attempt as essentially to break down the equation I have set to convective heat. After breaking things up and solving for Ts, I found :

    "(I^2*R' / pi*D) + (h*Tinf) + (sigma*(Tsur)^4)" = Ts(h+sigma*(Ts)^3)

    **Ill use " ..... " for the left hand side of the equation

    So my attempt was to break into in to two equations:

    "..." = Ts and Ts = Cubed Root ( ("..." - h)/sigma)

    For some reason whenever I go to solve for Ts, I get pretty absurd numbers.

    Using Kelvin I get 3932 K for I=0
    I dont even think I can use celsius here because of the stefan boltzman constant (My equations are not temperature differences).

    Where am I going wrong and is this approach even possible?
     
  2. jcsd
  3. Sep 11, 2010 #2

    Mapes

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    Science Advisor
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    Gold Member

    Where are you getting the approach of "break[ing it] into...two equations"? Like if A = BC, then A = B and A = C? That doesn't make sense to me.

    How about solving the equation numerically, or calculating the magnitudes of the convective and radiative heat transfer and seeing if one dominates over the other?
     
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