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So I am an Aero-Thermo Intern at Pratt and Whitney, and my supervisor gave me the following problem to set up a mathematical Excel model for the temperature gradient inside an enclosed box with a heat source underneath it to be used in thermal analysis of an engine component. He detailed the problem exactly as follows:

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Problem Statement:

To calculate the temperature profile of an enclosure wall with a fire (heat flux) input at the bottom.

Assume:

• The box is 10” by 8” by 21”, made of cres 345

• The fire is at the bottom of 10” by 8” floor.

• The outside temperature is 59ºF

• The heat flux is 4,500 BTU/min

• The temperature is uniform in the horizontal plane ( 1D problem in Z direction)

Physics:

• The primary form of heat transfer is to the outside environment.

• Use natural convection for a flat plate on the outside.

• The primary driver is buoyancy force for the velocity to calculate the heat transfer coefficient. (Can assume flat plate to start with)

• The heat balance enables to calculate

o We can calculate the wall temperature

o The temperature of the air inside the box

Method:

• Initially cut the box into variable # of horizontal slices

• Calculate the wall area and volumes

• Calculate inside vertical velocity of air due to buyoncy.

• Calculate the internal and external heat transfer coefficients

• Assume an initial internal air temperature.

• Calculate the heat flux.

• Calculate the wall temperature and new air temperature for the next slice

• Continue till the last slice.

• Sum the heat flux and iterate the initial temperature to get the right total heat flux.

Results:

• Plot the temperature profile of the wall temperature and air temperature.

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I'm only just now taking my first thermodynamics class, and the conditions and method of solving this problem are foreign to me. My supervisor is very old school and could not explain how to do this very well, and if there is an easier method of obtaining the temperature profile of the walls and air then by all means inform me :). I'm familiar with the physics and equations for conduction and convection, but am not sure how to solve this problem. Thanks for your help!

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# Thermodynamics - Free Convection and Temperature Gradient Problem

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