Heat Tranfser to a Surface 3

[tmoo]

Can any body give me any pointers;

I'm trying to find the heat tranfer of a metal cube (150x150x150) at 90 deg c through a layer of stationary air to the surface of a plastic tube 200mm away from the cube's surface. It is as if the cube is in the centre of a platsic tube and surrounded by air. I need to know what the temperature of the tube wall will be.

I'd be gratefull of any assitance or pointers

Regards

 

[cbiber]

It's likely that the air isn't exactly stationary. There will be natural convection in parallel with radiation. Then the outside of the plastic tube will transfer the heat to the environment by the same two mechanisms.

I would write myself a little spreadsheet to look at this problem. You will have the three temperatures: cube, tube, and ambient. Calculate the heat flowing between cube and tube, and tube and ambient. The heat flows must balance in and out of the tube. You can make the spreadsheet iterate on the tube temperature until it does.

For a rough estimate, use q=hA(Tcube-Ttube) with the heat transfer coefficient h=10 W/m^2K to account for radiation in parallel with natural convection. A should be the surface area of the cube. Then do the same thing for the tube: q=hA(Ttube-Tambient) where A is the surface area of the tube. Maybe you can see how the tube temperature will be a function of the area ratio in this case, with the constant-heat-transfer-coefficient assumption.

Strictly speaking, h will vary with the length scales and temperatures involved; that's something you might look up in a handbook (Nusselt number as a function of Rayleigh number -- "external natural convection" for the tube to ambient, and "natural convection in enclosures" for the cube to tube heat transfer).

Cathy Biber

Biber Thermal Design

http://www.biberthermal.com

 

[tmoo]

Thank you very much

 

[tmoo]

what would be wrong about using fourier's law? assuming their is no air flow?
Q=(KA)/x *(t1-t2)

What do you think?

 

[tmoo]

what would change if the cube was not in the middle of the tube?

 

[cbiber]

Fourier's law will give you a tube temperature result that is too low. Stationary air makes a great insulating layer, but if the space is begin enough, the air will move. That considerably reduces its insulating power.

If the cube was not in the middle, then I would expect more nonuniformity in the tube temperature. As it is, the highest tube temperature will probably be above the cube. Using the analysis I gave earlier, you're ignoring all those variations to get at the general temperature range of the tube.

 

[poetix99]

Does the metal cube start at 90degC and then cool down?
Does the metal cube (somehow) maintain its temperature at 90C?

If it is a transient problem, then "cbiber" has offered some useful first order ideas for your problem.

If the tube is a closed volume, then you will eventually have to consider heat transfer from the tube to the surroundings; Otherwise the cube'n'tube will come to equilibrium as determined from a simple heat balance based on the initial state of your system.

If the cube is maintained at 90C with some sort of external source of energy brought into the cube (electrical heat, hot fluid, etc.), it's a different transient problem - the transient component is the air, not the cube.

If the cube is heated and the air is flowing, simply measure the energy flux into the cube.

If the air is flowing, you might do well to check the limiting h.t. implied by the Biot Number to see if convective h.t. at the air/metal surface or conductive TO the air/metal surface is limiting.

 

[tmoo]

thanks again, for yor responses

 

[tmoo]

"Cbiber" and "poetix99" thanks again for your excellent help, Is the temperture calculated the max? i.e. how would I calculate the tube temp if the cube was nearer the top of the tube, i.e. 50mm from the top surface?

 

[cbiber]

My previous advice is based on the assumption that you have a steady-state problem -- that the cube is maintained at the temperature you stated.

The temperatures you would find are a representative "average". The localized temps are much harder to get. You'd have to use some sort of method that divides up the tube into segments, and analyzes the temperature and heat flux in each. Not sure you want to get into that...

For natural convection (i.e. buoyancy-induced flow) around the cube, the top will be the hottest because that's where the buoyant plume will hit. I think that should be true regardless of the spacing. Radiant heat transfer will give you additional temperature rise on the tube, independent of the gravity direction -- wherever the cube is closest. This will especially be true if your tube is made of low-conductivity material like plastic, and less noticeable if it were made of aluminum or copper, which would spread the heat better.