Time and cfm for cooling aluminum rods

[prichmon]

Good afternoon;

Could someone assist me in verifying my calculation? Or point me in the right direction to a reasonable estimation?

I am attempting to work out a decent mathematical model for cooling round solid rods on a cooling bed. The material needs cooled from a high of 700*F to 150*F with a max summer temp of ~90*F.

Cooling bed 150' x 40'
Aluminum rods in 3,5,8"
Up to 120' length
Delta T 450*F


I have a possible solution available currently.

#1 up to 6 individual fans at 34K cfm 1.75"wg spaced every 20' blowing perpendicular to the rod as a fin.


I performed a mass comparison:

Mass of 20' section in size of 3,5,8"; times specific heat divided by ration of temps.
Mass of fan times specific heat.

I divided the total heat required by the fan total cooling capacity which gave me:

2" 3 min.
5" 16 min.
8" 41 min.

I can't use water per customer requirements. The cooling bed is the most open location which supports our plans. I wish to follow KISS which leads us to forced air cooling.

Thanks

Rich

 

[MintJulep]

No.

Because you have not considered connective heart transfer coefficient aluminum to air.

 

[prichmon]

So can I use the following for the calculation?

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

Thanks

 

[MintJulep]

That calculator requires that you know the value of convective heat transfer coefficient.

You do not yet.

It will likely not be constantly.

 

[IRstuff]

not to mention that your temperature change is 550F, not 450F

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[prichmon]

Hc = 0.27(Delta T/L)^1/4

Could I model a 20' section as representative of the length with 1 fan at the center line?
Then the Hc could be averaged from center of the fan to the end?

Thanks for the replies.

 

[georgeverghese]

This is a transient heat transfer problem - cooling rate of the skin will be faster, while cooling rate at the core of the rod will be slowest -see your heat transfer texts which treat cooling operations - recall this involves looking up the Gurney Lurie curves. See fig 5-2 in the chapter on heat transfer in Perry Chem Engg Handbook, 7th edn. This topic is also discussed in DQ Kern's ever popular text "Process Heat Transfer".

 

[prichmon]

Why doesn't a mass comparison work for the time?

If I have a known fan doing 34K cfm
Use CFM* delta t *1.08 = btu/hr

The aluminum is a set variable.
mass * specific heat * delta T = btu

I understand the temp of the surface will be cooling than the temp of the center.

I am using Bohn and Keith Heat and mass transfer. The example I found uses biot and fourier numbers for graphing.

Thanks

 

[MintJulep]

Because 2 equations and 3 unknowns.

 

[georgeverghese]

The external htc consists of 2 components; a convective coeff which is related to the air mass rate over the rods, and a radiative component due to the skin temp at the skin at any time. ht=hc+hr. Strictly speaking then, the overall htc changes with time as the skin cools (hc approximately constant while hr is changes with skin temp). You could run this transient heat transfer calc into say 10 time intervals, with ht held constant within each interval.

 

[chicopee]

Not only convective heat transfer but at the temperature mentioned do not discount radiation transfer to the surrounding.

 

[racookpe1978]

It is not clear to me how your rods are configured.

Are they uniformly hot (as if coming out of a furnace,) then cooling off in mid-air (whether forced or natural convection)?

Or are they connected at one end to a hot mass, then the heat energy flows down the rods through the open air flowing past the three groups of rods?

No fins on the horizontal solid rods, right?

 

[chicopee]

I don't deal with Metric just English unit. At those temperatures, there are two modes of heat transfer. The first one being mentioned above is convection for which convective heat transfer coefficients have to be determined at several temperature changes of the rods. Typical magnitude of convective heat transfer coefficients under forced convection for superheated steam or air(btu/(hr sq ft dF))is 5-50. The next mode of heat transfer is radiation heat loss and that subject will require some determination of shape factors and emissivity values of Al at these elevated temperatures. Shape factor values can be in the range from zero(0) to one(1). Research text books and internet for published graphs that suits your situation. Emissivity value of the Al rods range from .04 to 0.18 depending on surface condition and temperatures involved. One more item to consider in the change in internal energy of the rods typically expressed as M*Cp*(Ti- Tf). You may need the assistance of an other engineer competent in heat transfer and spread sheet to program a time step analysis of this heat transfer analysis on a spread sheet and you'll do pretty well is you final solution is within 50% of reality. To ease the programming work check into the subject of combined heat transfer(ie between convection and radiation) mechanism which is discussed in heat transfer text book. I also suggest that you do a sketch of your problem with all variables shown to ensure that nothing has been omitted in your analysis

 

[chicopee]

Oops, forgot to include the rate of change in internal energy of the rods and should typically be expressed as M*Cp*(Ti- Tf)/dt. dt being time interval in all likelihood in seconds for units. Cp specific heat of Al 0.208 btu/lbm-dF @ 32dF which is the only value presently at hand so check the Chemistry HB, ME HB, ChemEng HB and the internet for other Cp's for your temperature range. The rate of chang should only apply to the temperature change expression in your spread sheet. Cp's changes can be directly inserted in the program with IF statements.

 

[prichmon]

Thanks all.

 

[MortenA]

Opening some of my really old text book, i can tell you that these kind of problems also were solved prior to computers. Some folks made some generalised solutions - you could try to look for "gurney-lurie chart for a cylinder" - but the theory of trancient heat transfer coupled with non-forced/forced convection is not that simple (but of great interest in many industries).The Gurney-Lurie method is for semi-infinite rods - just one of many simplifications i guess

Bset regards, Morten

 

[GrouchyStressedTensePoor]

Hi all,

Not a thermal engineer of any kind, just curious. Wouldn't the forced convection heat transfer mode dominate? Then following on from the convective heat transfer wouldn't conductive heat transfer be the next most significant? Or am I misunderstanding what a cooling bed is? (I'm picturing a group of rods sat on a metal tray of some sort). Wouldn't radiative heat transfer be the least significant mode at these temperatures? And wouldn't the magnitude of the convective heat transfer render the other modes insignificant?

I just have this vague recollection from university that the magnitude of heat transfer via forced convection is something like 10⁶ times the magnitude of heat transfer via conduction, which is again something like 10⁴ times the magnitude of the radiative heat transfer (in most everyday engineering situations).

Thanks,

GSTP

Graduate Mechanical Design Engineer
UK

 

[IRstuff]

I think you forget that radiative transfer goes as T^4, so that translates to, for the OP's stated environment, ~490 W/m^2, which is in the regime of liquid cooling.

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