natural convection question

bill nye scienceguy!

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?

Mapes

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]?