Cooling time of fluids 2

[1983cj5]

I need to estimate the cooling time of water inside an infinitely long, 4 inch diameter pipe with 2 inch insulation. Outside temperatue is -40F, initial water temperature is 70F.

Does anyone know or can anyone direct me to a calculation methodology.

My research lead me to the calculation methods for homogeneous substances (water, steel, etc.) but not a composite (insulation, pipe, water) assembly. I am looking for a procedure that takes into account the outside film (15mph wind), insulation, pipe, and fluid inside.

Thanks

 

[desertfox]

Hi 1983cj5

Have a look at this site:-

http://www.roymech.co.uk/Related/Thermos/Thermos_insulation.html

regards

desertfox

 

[desertfox]

Hi again

Try this calculator:-

http://www.epcserver.com/Mechanical/heat/conductionc1.asp

its free at present.

If you have to take wind into account on the outside of the
pipe you will have to do an heat transfer by convection using appropriate coefficients. This calculator deals with the heat transfer by conduction across pipe and insulation but its a start.

regards

desertfox

 

[1983cj5]

Thanks desertfox. However I am looking for solutions incorporating duration (time) in the analysis. I believe the formulae from the links you provided are for instantaneous heat transfer. My problem is transient heat tranfer.

How long will it take to cool the water inside the insulated pipe from 70F to 32F when outside temp is -40F?

Thanks again.

 

[25362]

Look for the Gurney-Lurie diagram for heating and cooling of an infinitely long cylinder. One source:
Fluid flow and heat transfer by professor Aksel L. Lydersen. John Wiley and Sons.

 

[magicme]

hi there

i know this topic was discussed before on this forum and had several good answers.

the SEARCH mechanism is apparently down at the moment, but try it later and i think you'll find what you're looking for.

regards

magicme

------------------------------------
there's no place like gnome.

 

[trashcanman]

The biggest problem is heat transfer coefficients for convection and radiation. They change as outside surface temperature changes.

If not for that, it would be a simple diff. equation.

C1(T-To)dt=C2(DT). Where C1 is pipe A*U, and C2=mass of pipe*specific heat+mass of water*specific heat+mass of insulation*specific heat. T=water temp at time t, T0=outside air temp. The hangup is that U. It includes pipe od, insulation thickness, k, and most of all, the surface coefficient, which is temp. dependent.

Any ideas?

 

[Onno]

Dear 1983cj5

In order for you to put things in perspective I would like to suggest you make an estimation of the actual heat transfer through convection with ambient air. My question is: how much does the heat exchange coefficient change? and is it a (straight forward) function of the outside temperature? (linear dependence). Nothing guaranteed but if you want to find a simple set of equations there is in my honest opinion a need to get a feeling for the "order of magnitude".

Best regards Onno

 

[1983cj5]

Thanks, everyone for your input. I did find an excellent resource for this subject: Heat Transfer in Cold Climate by Virgil J. Lunardini, Van Nostrand Reinhold. We estimated it would take about 65 minutes to go from 70°F to 32°F when ambient is -49°F.

Trashcanman's solution makes sense, but more complex and unwieldy.

Thanks, guys.

 

[trashcanman]

Based on data input: 4" (assumed sched 40), 2" insul (assumed fiberglass), 70 DegF water, -40 Deg.F air:


Time to reach 32 = 20290 sec, or 5.36 hrs.

How was this done? Heat transfer through insulation = heat loss by radiation + convection. Rad & convection depend on outside surface temp. When correct outside surface temp (T1) is computed, then the 2 heat transfer rates are =. After calculating the heat transfer rate (BTUH), I determined rate for BTU/sec. Assuming a step of 1 sec., determine heat loss. Heat loss = water mass x heat capacity x change in temp. Knowing change in temp after 1 sec, this gives new internal water temp (TI). With new TI, recalculate T1 and heat transfer rate. With new BTU/sec, for next sec, this gives new change in temp. This gives new water temp. This gives new heat loss. Round and round till water temp = 32. Sort of numerical integration. Much easier than trying to solve a beast of a diff. equation. Really gives my computer a workout. Did it in GWBasic.

Of course, it assumes all water temp in pipe cools at same rate, and neglects internal pipe surface coefficient and heat capacity of pipe+insulation, but those are relatively minor.

Comments?

 

[droctagon]

I have a similar problem to ones that have been posted here. I am close to solving it, but did not use an iterative process which i think must be done. Basically I have a 30,000gal tank filled with 6,000gal amount of anhydrous ammonia. The tank which is 3/8" thick carbon steel, the anhydrous ammonia, and the ambient air around the tank is at room temperature. Now I want to add 6,000gal of the same fluid at -20 F . We can assume perfect mixing. How long will it take for the mixture to get back to room temperature? Thank you everyone very much.

 

[trashcanman]

I have a similar problem to ones that have been posted here. I am close to solving it, but did not use an iterative process which i think must be done. Basically I have a 30,000gal tank filled with 6,000gal amount of anhydrous ammonia. The tank which is 3/8" thick carbon steel, the anhydrous ammonia, and the ambient air around the tank is at room temperature. Now I want to add 6,000gal of the same fluid at -20 F . We can assume perfect mixing. How long will it take for the mixture to get back to room temperature? Thank you everyone very much.

What is the shape of the tank? Cube, cylinder, sphere?
Is the tank insulated?
Is the tank outside exposed to sunlight?
Is the tank inside exposed to any heat source? If so, you will have to consider radiant heat gain.
If there is considerable steel in and about the tank (valves, manholes, ladders, etc), you should take into account the mass of steel and its heat capacity as well.
Is the tank open to atmosphere? If so, moisture in air can affect heat capacity of the NH3, especially when you hit it with -20 NH3.

 

[droctagon]

The tank is 11 feet in diameter, horizontally oriented. The tank is not insulated, just 3/8" thick carbon steel. The tank is set in a warehouse so it is not exposed to sunlight. The tank is also not exposed to any heat source. Any sort of steel attached to the tank is going to be ignored. I am going to ignore all radiation. I just need a simple estimation. Any further tips?