Calculation of Cooling Time 2

[SAK9]

Guys,

I need to calculate the time taken for cooling of water at 125 C to 80C in an insulated steel tank(50mm rockwool insulation).The volume of water is 3200 kg.The room temperature is 28 C.The surface area of the tank is 19 sq metre.What is the formula to calculate the time taken for cooling ? I am relying on the heat loss through the insulated tank wall for cooling.What are the available methods to accelarate the cooling process?

Many thanks in advance for your help.

 

[235zzzo]

Hello SAK9

Go read a classic heat transfer manual. Transients heat transfer methods. Thermal systems simulations. Lumped systems. And at the end, the problem you have is very simple and interesting. Justt demands your study for a few hours and it is nice to arrive at the solution by yourself.
Cheers
zzzo

 

[samv]

You asked "What are the available methods to accelarate the cooling process? "

Is removing the insulation an option?

 

[pennpoint]

SAK9
Alternate cooling:
1)Precool the water before it arrives at the tank.
2)Add a cooling jacket to the tank wall under the insulation.
3)Cool the water with coiled tubing which is cooled with compressed air.
4)Cool the water with coiled tubing, inject a liquifed gas i.e. LN2 or CO2 to cool the water.
The water is 45 F above the boiling point so I assume the tank is pressurized.

pennpoint

 

[patrickraj]

What is the wind velocity in the area?
This plays a vital role in insulation thickness calculation

 

[corus]

To calculate the time taken to cool you will need to know the thermal conductivity of your insulation and the cooling to the outside if this is not the usual natural convection and radiation. I'd check but you I think your net heat loss coefficient H is 1/(x/k+1/h), where h is about 10 W/m^2 C. Then solve for T in pCVdT/dt=HA(T-28), where p is density, C is specific heat, V volume, A area. The solution is an exponential function, T = exp(HA/pCVt)+28.
To speed the cooling rate up and you can't alter the tank or insulation then increase the convection from the outer surfaces (h) by either spraying water on to it or blowing air. Cooling water would be better as you get a higher convection coefficient.

 

[corus]

I forgot the integration constant, a minus sign and a few other things, besides that it was ok.
Go to

http://www.tufts.edu/as/tampl/en43/lecture_notes/ch4.html

for the solution.

 

[SAK9]

Corus,
Many thanks for a helpful post

 

[25362]

I think there are still undefined items in the presentation of the query, not in order of importance and not all-inclusive:

a) Is the "final" temperature measured at the center of the
water volume ?
b) Are the tank contents stirred ?
c) Is the room kept at a constant temperature ?
d) Does the quoted surface exclude the tank bottom seating
on the floor or is it also exposed ?
e) What is volume of the room compared with that of the
tank?
f) Does the insulation cover all of the tank's surface ?
g) What is the tank geometry ?

Since, as expressed by all experts, we deal with transient heat transfer conditions, and since the parameters are not so clear, I pressume that the best solution would be to carry out temperature measurements at given time intervals, and build cooling curves from experience.

 

[corus]

25362 is quite correct. The solution I provided is for a lumped mass where it is assumed that the temperature of the water remains constant. Another solution provided assumes 1D heat flow and a variable temperature distribution through the water. To be correct you need 2D or 3D heat flow and the relevant heat transfer coefficients from all the vertical and horizontal surfaces, together with all the relevant emissivities from the surfaces and knowledge of the thermal resistance from the insulation contact with the side walls. The lumped mass solution will give a good enough answer if you want an approximate answer.