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Heat and mass transfer analogy to find average Nusselt no.

  1. May 22, 2016 #1
    I am trying to find an expression for the average Nusselt number corresponding to heat transfer from an isothermal disk.

    Given:

    ShD≡hm(r)D/DAB=Sho[1 + a (r/ro)n] (1)

    Sho=hm(r=0)D/DAB=0.814ReD1/2Sc0.36 (2)

    Relevant equations:
    Average nusselt number is defined as Nuav=havD/k
    where k is thermal conductivity, D is diameter of disk and hav is average convection coefficient.

    The heat and mass transfer analogy states that
    Nuav/Prn=Shav/Scn (3)

    Sh is Sherwood number, Nu is Nusselt number, Pr is Prandtl and Sc is Schmidt. In this case n=0.36, from given data.

    hav is defined as: hav=(1/As)∫ h dAs (4)

    where you integrate h, the convection coefficient, over the surface area, As.

    Solution??
    If I solve for hm(r) in (1), and integrate over the surface area, I am still stuck with the constant (DAB/D), but this should NOT be in the final answer. This is obviously the wrong approach, but the rest of the answer is correct, so I am on to something, I am just not sure how to use the analogy correctly.

    Somehow I need to use the analogy and combine it with the formula for hav to obtain the average Nusselt number. Apparently the solution is to integrate Sho[1 + a (r/ro)n] over the area As, and just replace Sho with 0.814ReD1/2Pr0.36. But why can I do this? I understand that it has something to do with the analogy, but I don't understand how or why. Can someone help me out here?
     
  2. jcsd
  3. May 27, 2016 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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