Tube in Tube heat exchanger example problem?

[USAeng]

I havent done calculations for heat transfer in a long time. The heat exchanger we have is a single tube inside another single tube... the inner is sludge with a Cv of .909 BTU/lb*F the outer is 50/50 water/glycol mix with Cv of .832 BTU/lb*F. I've been told we need 1.77MMBTU to keep the temperature up in the sludge tank. I have to figure out the flow rate of each material so I can size the 2 pumps.... does anyone know of a good example of a similar calculation may be that I can look at? or just help me solve this one? I have the old Q=mCv(T1-T2) but I think that mass flowrate will be good for the 2 amounts it would take if you combined the fluids to transfer heat... thanks for any help

 

[USAeng]

I hope I used the right subscript on the C... whatever it is supposed to be specific heat of the fluids

 

[USAeng]

oh and glycol is being used to heat the sludge in cooler months... glycol starts at 121F and ends at around 105F (just for example) and the sludge is starting at lets say 85F and ending at 100F target temp... and the exchanger is 100 feet long. The outer tube with the glycol is 8" and the inner tube with the sludge is 6".

 

[USAeng]

and the fluids are flowing in opposite directions

 

[vpl]

USAEng

The heat transferred (Q) is equal so what you should have is

ṁ_sc_p(s)(T_2(s) - T_1(s)) = ṁ_gc_p(g)(T_1(g) - T_2(g))

where the "s" subscript is sludge and the "g" is glycol. Since you said the fluids are flowing in opposite directions, the temperatures should be reversed (I believe.) Someone will correct me if I'm wrong.



Patricia Lougheed

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[USAeng]

I guess it is polypropelyne glycol so the Cp is about .850 BTU/lb*F... also found out that the glycol goes from 175 to about 140 through the exchanger.... anyhow so if we need 1.77MMBTU heat transfer to the sludge would you then need Q=mCp(T2-T1) --> 1.77x10^6=m(.850)(175-140) = 59,500 lb/hr = 123 gal/min... then setting the equations equal to eachother and solving for Ms would be Ms=Mg(8.18)... so 1006 gal/min sludge? I must be missing something unless we were given a wrong number for the required heat input (1.77MMBTU)... those numbers are larger than I thought they would be... but maybe a correct estimate?

 

[IRstuff]

You seem to be missing the flowrate or mass related to your 1.77MMBTU. That's an energy quantity, which means that corresponds to some sort of mass*temperature product.

I'm not sure how you managed to balance the units, but you shouldn't have been able to.

TTFN
faq731-376

 

[USAeng]

cant I just use Q=mCp(T2-T1) to solve for m since I know Q=1.77MMBTU and know the temp difference from the beginning to end of the fluid? and then that Q can be used to solve the Q for the sludge... Can someone put me back onto the right path? Thanks

 

[IRstuff]

I'm confused. If you already know all the information, someone must have already done the calculation, so what's the purpose of this exercise?

TTFN
faq731-376

 

[25362]

If the external tube is not thermally insulated it may lose some heat to the surroudings depending on the outside atmospheric conditions.

 

[USAeng]

sorry that is confusing... we have an engineering firm that provided us with a heat requirement for the amount of sludge we have of 1.77MBTU. I am just trying to find the mass flow rate so I can help my boss get an estimate size for hp requirements for the pumps

 

[25362]

I'd add some % to the heat duty on account of loses. What do you think ?

 

[IRstuff]

In any case, what you get out of the specific heat equation is a total mass. You need to have the flow rate, which then determines how long it takes to heat up the sludge

1.77MMBTU/C.p*deltaT = 1.77MMBTU/(0.909BTU/lb-°F * 35°F) = 55634 lb

So, if you have a flow rate of 1 lb/min (which implies the whole process taking 55634 min, i.e., ~1000hr, which is silly, but the equation scales)

(1 lb/min)*(0.909BTU/lb-°F * 35°F) = 559 W of net heat transfer required, so all you need to determine is how fast you want this to happen, and how much you're willing to pay for maintaining the required flow rates and size of exchanger.

TTFN
faq731-376

 

[USAeng]

thanks... I can take it from here... no more replies needed