cool down time calculation

[kprook]

I'm looking for a simple calculation to help me figure out the time it takes to cool a solution in a tank to a certain temperature.

For example, I have a 100 gallon tank of 125 deg F USP water and want to cool it to 70 deg using 15 GPM water at 60 deg F and 15 GPM. How long would this take?

 

[vpl]

First: Is this homework?

Patricia Lougheed

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

 

[kprook]

no, it's not homework, and I did search the website as best as possible to find a solution. This website was recommended several times. If you have a simple calculation, I would appreciate it.

 

[dvd]

Is the tank full to begin with? Are you adding water only, or are you adding and draining simultaneously?

This amounts to blending masses of water until the desired temperature is achieved. For no mass leaving the system then:

m1*T1 + m2*T2 = (m1+m2)*T3,

since the specific heat of the water is fairly constant. From the mass required to balance the equation you can calculate the time required based on your GPM.

 

[Latexman]

Is this direct or indirect contact heat transfer? If indirect, I'd recommend you refer to Perry's Chemical Engineers' Handbook or Donald Q. Kern's "Process Heat Transfer" for the solved integration of the unsteady-state energy balance that pertains to your application. If direct, see dvd's post.

Good luck,
Latexman

 

[kprook]

Thanks DVD and Latexman,

It's more of an indirect heat transfer problem. It's a jacket type tank with USP water inside (stationary)at 125 deg and 15 GPM water at 60 deg circulating thru the jacket, I'm assuming 3/4" tubing thru the jacket since that's the connection size on the outside of the tank. After the USP water is cooled to 70 deg, circulation is turned off.

Thanks for the suggestions, I'll refer to these references.

 

[Latexman]

In my 6th Ed. of Perry's it's in the Heat Transmission Chapter under the section on Batch Operations: Heating and Cooling of Vessels, pages 10-38 to 10-39.

Good luck,
Latexman