|Mar31-08, 04:56 PM||#1|
natural convection question
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)
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?
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