Time to Equilibrium 2

[SirMarek]

Its been a long time since my last thermo class, and I am trying to brush up on my basics.

If I had a steel plate(7°C) that is A x B x C in a room of air (20°C), how would I go about calculating the time for the steel plate to reach equilibrium with the air (within say 1°C)? Assuming the plate is mounted in such a way to simulate floating and the air temp is constant.

 

[EdStainless]

This is what you use Heisler charts for.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, Plymouth Tube

 

[ione]

You could evaluate whether a lump system analysis can fit your specific problem. Look for "transient heat conduction Cengel" on the web.

 

[chicopee]

This is a heat transfer problem and not an easy one to solve. Best bet, get a good textbook on heat transfer. What has to be considered are plate thickness to determine if edges add significant heat loss and if a temperature gradient exist between top and bottom of plate; Boit modulus can help determining if there is thermal resistance leading to that temperature gradient. Heat transfer coefficients above and below the "floating" plate have to also be estimated. Then in your heat transfer textbook, you'll need the topics on free convection, steady and unsteady conduction and convection. No easy task, so the charts mentioned by EdStainless should help.

 

[racookpe1978]

You cannot solve it by algebra and simple formulas because the formulas change with each orientation.

Assume all of the following are placed in simple room of uniform still air = T_air_initial.

Now, assume you have flat thin plate: 100x100x1.0 = 10,000 units volume & 10,000 mass but surface area = 20,400 sq units. That horizontal plate will cool (literally) with different film coefficients and radiation losses than a equal volume cube of 21.54 units per side. A horizontal plate will require different equations and approximations than a vertical thin plate. The relative plate, air and room wall temperatures will directly control the thermal equations as well: Hot plate, cool air; colder plate and hotter air.
A vertical box 10x10x100 will have 4x sides cooling as vertical walls, and two as small (near negible) horizontal plates. Turn that box horizontal, and you have two vertical walls, and two horizontal sides, but the four act more like a horizontal cylinder. Rotate the horizontal long box by 45 degrees, and it begins acting like a fin with low flow resistance.
A horizontal sheet 400x400x0.625 will act exactly opposite the vertical box.


[pre]
Width Length Height Vol Surface Surface/Vol
100 100 1 10000 20400 2.04
1000 10 1 10000 22020 2.20
100 10 10 10000 4200 0.42
10 10 100 10000 4200 0.42
1 1 10000 10000 40002 4.00
3.16 3.16 1000 10000 12669 1.27
21.54 21.54 21.54 10000 2785 0.28
200 200 0.25 10000 80200 8.02
400 400 0.0625 10000 320100 32.01[/pre]