Natural convection cooled enclosure

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CruiserFJ62
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I have a transformer in a box that is cooled using natural convection. There are louvered openings on the box to pull cool air in the bottom and let heated air out of the top. How do I determine how much heat is actually leaving the enclosure? Info that I have is the area of the enclosure, the amount of heat that the transformer is putting out, ambient outside air temp. Any suggestions or websites that would get me going?
 
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At steady state the amount of heat going out is the amount of heat generated by the transformer. This is fundamental. Are you perhaps more interested in the actual inside temperatures?
 
Yes, what is the temp inside the enclosure? I am trying to determine if the natural convection through the louvers can pull enough heat out to keep the transformer below its rated operating temp. Any ideas?
 
Is this something you could model using FEA? It seems to me the problem would be a little too complex for an analytical approach.
 
That would be tough to do without some kind of numerical analysis. You could maybe ballpark it with Archimedes' principle and Newton's law of heating but that would be based on some big assumptions.