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Natural convection question

  1. Mar 31, 2008 #1
    1. The problem statement, all variables and given/known data

    What is the heat transfer from a 60W electric light bulb at 127C to the stagnant air in a room at 27C. Approximate the bulb to a 50mm diameter sphere. What percentage of the power is lost by free convection?


    2. Relevant equations

    Nu=2 + 0.6(Gr^1/4)(Pr^1/3)
    Gr=(g[tex]\beta[/tex][tex]\theta[/tex]d^3)/[tex]\nu[/tex]^2
    Nu=hd/k


    3. The attempt at a solution

    I started by working out the Grasshof no. with [tex]\nu[/tex] at 27C= 1.568x10^-5m^2/s, [tex]\beta[/tex]=1/T = 1/27, [tex]\theta[/tex] = 100 to be Gr = 1.8x10^7.

    Pr = 0.707

    therefore Nu = 21.702, using the relationship above.

    substitute this into Nu = hd/k and h= 1.139x10^-5kW/m^2K

    the area of a sphere = 4(pi)r^2= 7.854x10^-3

    so finally Q=hAdT

    left me with 8.945x10^-3W
    which is 0.014% of the power being lost by free convection.

    this appears to be out by a factor of 100, but that could just be a coincidence, meaning that im totally wrong. Can anyone assist?
     
  2. jcsd
  3. Mar 31, 2008 #2

    Mapes

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    Check your calculation of [itex]\beta[/itex], [itex]T[/itex] should be in Kelvins. And what value of [itex]k[/itex] are you using? Shouldn't you have [itex]h\approx\mathrm{Nu}[/itex]?
     
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