Tank recircualtion heatup calc... 1

[gacollier]

I'm looking for a means to roughly estimate the following:

I have a 300 gallon vessel filled with 110 deg F milk. I'd like to pull off milk from the bottom of the tank, heat to 180 deg F and blend back into top of vessel. What would my flow rate need to be in order to accomplish this task in 10-12 minutes?

Any calculations would be appreciated.

 

[gacollier]

Sorry, I meant to add that the entire tank needs to end up at roughly 180 deg F.

 

[sailoday28]

If one assumes the heated milk is returned at 180F and negligible heat transfer from the system AND a well miked tank (taking no credit for work of a paddle)
The approximate flow rate, w, #/sec

w=(mc/t)*(ln[110-180)/Tfinal-180)]
where t is time in seconds,
m, mass of milk in tank
c, specific heat of milk
Tfinal is the final temp of milk
The above analysis also neglects time to heat up milk in external piping

 

[sailoday28]

Correction
w=(mc/t)*(ln[110-180)/(Tfinal-180)]

 

[vpl]

sailoday28

Being somewhat persnickity (ok, maybe a whole bunch), it looks like the formula is going to result in division by 0, because T_finalis 180°.

gacollier

More information is needed. Is there mixing in the tank? How is the milk being heated and what time does it take for that to occur? How long is the piping loop? What size pipe is being used?

And, most important, this isn't a homework problem, is it?

Patricia Lougheed

Please see FAQ731-376 for tips on how to make the best use of the Eng-Tips Forums.

 

[sailoday28]

vpl(nuclear)
Typically one uses this lumped mode approximation to see how long it would take to get to Tfinal with a given flow.
This mode of lumped paramenters is quite often used in modeling. In reality it states that to reach 180F, the time is infinite.

To use it as an approximation, one makes a judgement-base on the selected time what flow is need to get to 175, 176 and so on.

 

[gacollier]

Patricia,

No, though it might look as if it is, it's not homework. I'm trying to compare heat up time for an application that requires milk to move from one batch tank (at 110 deg F) to another for final heat up of up to 180 deg F. My thought is to use an inline plate and frame between the two tanks such that the product enters the second tank at the desired temp. Another option would be to transfer the milk at 110 def F, and use a recirc. pump through a plate and frame to heat the contents of the tank after it's been transferred. I'm looking to calc the actual time it would take to heat up the contents of the tank by continuing to "turn over" the contents of the tanks in this fashion. I don't want to scorch the milk, so the plate will only allow the milk to heat up to approx. 185 deg F.

The tank is well agitated.

I have a PHE package that can increase the milks temp +70 deg F per pass at 40 GPM max, keeping in mind that the PHE will only allow the milk to heat up to 185 deg F max temp.

The piping loop is roughly 15 feet from beginning to end.

Line size is 2" OD tube.

I'll review the other posts as well.

Thanks.

 

[Latexman]

gacollier,

The equations you need can be found in Chapter 18 of Process Heat Transfer by Donald Q. Kern. They are also in Perry's Chemical Engineer's Handbook. In my 6th Ed. it starts on page 10-38. It's called Batch Operations: Heating and Cooling of Vessels.


Good luck,
Latexman

 

[gacollier]

Latexman,

Perry's was on the money.

Thanks!