How Hot Should the Radiant Heat Lamp Be to Maintain Pizza at 250 F?

[gfd43tg]

Homework Statement

Cheese Board Pizza just hired me to design a radiant pizza warming system. The pizza must be maintained at 250 F until the order is picked up by the delivery driver. The one square foot pizza sits on a ½ inch thick ceramic pan (k = 0.50 BTU /hr ft F) on a counter that is at 85 F. A fan blows air at 70 F over the top of the pizza (the convective film coefficient is estimated to be 2.0 BTU / hr ft2 F). the emissivity (ε) of the pizza is 0.60.

How hot must the radiant heat lamp be to keep the pizza at the desired temperature ?

Homework Equations

The Attempt at a Solution

Hello, I am having some confusion over if the blackbody radiates energy, as well as the pizza radiating energy back at the lamp, which can be approximated as a blackbody.

I originally had 4 terms, a convection and conduction term leaving the pizza, a radiation term leaving the pizza, and a radiation term from the blackbody going to the pizza. However, if I consider the blackbody radiation, I have no equation to find the Q because I don't know the view factor F12 since I don't have a ratio of the smaller side/distance between planes.

 

[gfd43tg]

Solved disregard

 

[berkeman]

Yeah, but now I'm hungry...

 

[collinsmark]

I like pizza.