SI units for Heat transfer equation

  1. 1. The problem statement, all variables and given/known data
    I am trying to get the units to match up on both sides. [tex]\frac{\partial T}{\partial t} = \frac{\nabla ^{2} T}{k} = \frac{1}{K}(\frac{\partial ^2 T}{\partial x^2} + \frac{\partial ^2 T}{\partial y^2} + \frac{\partial ^2 T}{\partial z^2}})[/tex], where k is the thermal resistivity.

    3. The attempt at a solution
    By searching all over the web, I've found that thermal resistivity "k" has units of [tex]\frac{Kelvins}{W}[/tex].

    Therefore,

    [tex]\frac{\partial T}{\partial t} = \frac{Kelvins}{s} \neq (\frac{W}{Kelvins})*(\frac{Kelvins}{m^2})[/tex]. Could someone help me correct the units.


    Thanks,


    JL
     
  2. jcsd
  3. LowlyPion

    LowlyPion 5,332
    Homework Helper

  4. Oh I see it now, but what about the unit for seconds "s"?
     
    Last edited: Jul 9, 2009
  5. Mapes

    Mapes 2,532
    Science Advisor
    Homework Helper
    Gold Member

  6. Are you sure? I mean the units do infact check out if you are correct- but according to my class notes they've referred it to thermal resistivity.

    Thanks a lot.

    JL
     
  7. Mapes

    Mapes 2,532
    Science Advisor
    Homework Helper
    Gold Member

    It doesn't matter if I'm sure. :smile: Check the literature; ask your teacher for a reference.
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?