Heat Transfer Coefficient for 304 Stainless Steel 1

[scottwins]

I am trying to calculate what the final temperature would be of a stainless steel block heated to 500°F then sit in ambient air temp of 131 °F for 300 seconds. The variables are listed below:
density (p):0.290 lb/in^3
thermal conductivity (k):0.0312 Btu*in/s*ft^2*°F
Surface area (A): 995.47 in^2
Volume(V):34.839 in^3
thickness (L): .511 in
Specific heat capacity (c):0.12 Btu/lb/°F
Final Temperature (T):?°F
Initial Temperature (Ti): 500 °F
Ambient air temperature (Ta): 131 °F
Cooling time (t): 300 seconds

It has been an extremely long time that I have had to perform a thermodynamic problem and looking through my old textbook from college, I can't find how to calculate the heat transfer coefficient that I need to enter in the equation. Any help would greatly be appreciated. Thanks in advance.

 

[IRstuff]

heat transfer coefficient for a horizontal plate:

https://www.engineersedge.com/heat_transfer/horizontal_plate_natural_convection_13968.htm

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[racookpe1978]

There a few things not defined (yet) that (might) make a significant (or not) difference in your results. Also, thermodynamics is going to require some assumptions and approximations, so the results are going to be "close" - but we don't know how accurate you feel you need to be.

Geometry: (most important)
0.511 is defined as thickness, but listed as L (length)
Volume is defined, as is surface area - but
Exactly what is the width (x) and length and height (Z) of the plate/block/box?

Reason is: The same size plate with thin side vertically (plate "sideways") will cool very differently than with the thin side "sideways" (plate vertical")
Support:
Is the plate freely supported in mid-air as if for painting or powder coating, or is it on a table?
If the plate is vertical, is it supported with the back side on a wall (good contact) or on an easel or frame (nearly free space)?
If flat on a table, is the table insulated from the hot plate?
If flat on a table, is the table "preheated" to the plate temperature, or will the plate be heating the table and the air?
If flat or vertical on a table or heavy frame, will many plates be processed in a row, so the thermal mass of the table heats up over time?
Ambient air at t=0 is 131F:
Still air, or fan-driven? Irregular like in a windy area?
If many plates are being cooled in a row, is the ambient air replaced each time with new air at 131 deg F?

 

[scottwins]

thanks for replying...

racookpe1978,
an approximation is good enough for the result of this calculation and doesn't need to be totally accurate.

You bring up many good questions and I can elaborate further. The plates are within a spring set brake I am designing that requires an emergency stop and manual lowering during a power outage. During the emergency stop, the inner rotating discs absorb the energy dump of the system inertia. I understand that there are other parts of the brake ie. housing, endplate, and other parts where there will be heat dissipation but I am only concerned with the inner discs. The ambient air temp. is 131 °F. The customer wants to be able to lower the load for 1 min then rest for 5 min thus the 300 second time variable. The 497.4°F is what the inner disc heat up to in that 1 minute. So what I need to determine is what does the temperature drop to in the 5 min(300s) wait timeframe? If it does not cool enough, I need to specify a longer wait time. Again, I am only concerned with the inner discs and not other components as the inner disc take the brunt of the energy dump and if they can handle the temp then there is not a concern for the other components as they will aid in the heat dissipation. The final temperature will also aid me in how much I need to add mass(make them thicker) to absorb more heat. I hope that doesn't go too much into detail but answers your questions. The inner discs measure Ø11"O.D. X Ø8.165"I.D. X 0.073" thick X qty.7. Total thickness=0.511" Brake is mounted horizontally. This is shipboard but in an enclosed area that I would have no idea what the volume of air is. The max. ambient air temp is 131°F Thanks.

 

[georgeverghese]

This is an usteady state cooling operation for each of these 7 thin slabs. Though I havent worked these problems myself, the answers to this are most likely found in any heat transfer text that deals with unsteady state cooling in thin slabs. For example, solution methods with the Gurney and Lurie cooling curves for thin metal slabs may be found on page 5-11 / fig 5-4 of Perry Chem Engg Handbook (7th edn) in the chapter on heat transfer.

 

[racookpe1978]

It's 1:45 am, so I'll be brief, then look up actual coefficients later.

The surface-to-air coef will be dynamic (almost like forced convection when braking and rotating) then appears to be stagnant air when cooling because the brakes absorbed the kinetic energy of the shaft, right? That would make stagnant air between the 7x horizontal round plates as worst case, but all seven plates are on a (very hot) central axis which would be the heat source.

If a ship, then air can be exchanged out of the room, and worst case would be "near constant" air temperature of 131 deg F, right? Not 131, 135, 145, 155, 165 etc on subsequent cycles.

Wait. "Brake is mounted horizontally" So the shaft axis is horizontal, and the plates vertical? Is there air exchange between the inside of the brake housing and room?

 

[chicopee]

Few questions come to mind: 1. size of the lock 2. position of the block exposed to air 3. Is the block resting on a bench which may or may not have high thermal conductivity or is it dangling from a string in forced air or in natural air current 4 is forced air sideways or from other direction.

 

[scottwins]

racookpe1978,
Yes, you are correct. It is like forced convection while rotating as there is a slight amount of air that moves over plates while spinning but that would be incidental as I need to know what temperature the discs are roughly at the end of 5 min cool down. There is only the stagnant air in the room at 131°F (near constant). The discs are not on a very hot central axis as there is very little heat transfer down into the shaft due to fit of shaft spline and disc splines. The heat is all in the plates that get hot from essentially slipping the brake for 1 min at 100 rpm. That produces 497.4°F of heat into the plates. With the brake mounted horizontal, I guess the plates would be in a vertical orientation meaning the largest surface areas would be pointing left and right. Being on a ship, most likely air can be exchanged out of the room, but at worst it will not be so that is why I need to focus on max. ambient air temp of 131°F. What is the estimated temperature of the discs sitting in ambient air temp of 131°F after 300 seconds (5 min)? Thanks.