Heat Shield temperature question

[Cosmin M.]

Hi all, new to this forum.

I'm a member of University of Illinois at Chicago's Formula SAE team. I'm making the heat shield for our formula car and I was wondering if you guys and gals could help me with a heat transfer problem.

We want to figure out what the temperature will be on the other side of a heat shield over our exhaust header. We have:

header temperature (600 deg. F)
header size (roughly a .25m^2 box)
distance from the header to the heat shield (30 cm)
size and thickness of the heat shield (1m^2, 1mm thick)
and the thermal conductivity (167 w/m-k) of the heat shield material (Al 6061).

How can I go about finding what the temperature would be on the surface of the other side of the heat shield?Apologies if this is in the wrong forum. Thanks for any help!

 

[Doug Huffman]

Empirically, to include the cooling air temperature and mass flux.

I raced SCCA F-Vee and B Sedan for SWAG Engineering. Measure once, cut twice, trim to fit and paint to suit.

 

[Baluncore]

Outer surface temperature will depend on the cooling by airflow on both sides of the heat shield.

 

[jh0]

I work for a company that makes automotive heat shields. You state the distance between heat source and the heat shield as 30 cm, this is a lot! I'm assuming you meant 30 mm, which is a quite standard gap between the heat source and the heat shield in automobiles.
According the data we have I'd say the cold side will be around 105°C or 221°F, supposing there is some air flow between the heat source and the heat shield.
I don't know the actual calculations, but if I recall correctly you have to know the emissivity of the heat source and the heat shield, calculate the configuration factor, assume some convection parameters on both sides of the heat shield and they involve some iterations, pretty cumbersome.
I don't know about racing cars, but in automotive applications heat shields are usually made from thinner aluminium, around 0.5mm, we use mainly 1050 and 3004.
Anyways, in my opinion 600°F/316°C is too cold for an exhaust header. These applications call for aluminised steel or stainless steel: I’d say the heat source could be as high as 700°C, and the heat shield then will surpass 200°C, aluminium’s mechanical properties drop considerably at these temperatures.

 

[Cosmin M.]

Thanks everyone for their replies! I did miscalculate the exhaust distance from the heat shield, it is much closer to 30 mm like jho said. Today I will be doing a test on our current exhaust so we can get a solid temperature reading on our header temperatures and get a baseline off of our old car to see how hot our current set up gets.

If you don't mind jho, would you be able to tell me the equations used to get the numbers you got? I would love to be able to understand it and alter variables by myself as we get more accurate numbers. Thanks for the help everyone!

 

[jh0]

I'm sorry, the temperatures I gave come from a database that I cannot share outside the company. It was made by a colleague some years ago, all I know is that he had to do some programming to run iterations for each combination of parameters (temperatures, distances, materials...) and all the results were put in Excel tables. This of course was done for a very simplified geometry, heat source is a cylinder and heat shield is just a flat surface at the specified distance.
I'd have to look at some heat transfer book, heat transfer is not my area of expertise in the company! What I know is that the day-to-day work regarding heat transfer at my company is made with the 3D CAD design and with a commercial software that simulates the heat exchange and predicts (quite accurately) the temperatures.