BATCH HEATER (PHEX SIZING) 1

[GATE3]

BATCH HEATER
Hi, everybody
I am try to size a plate heat exchanger for a Batch heater. The problem is that I stack to find the final temperatures.
Note: I found a software that calculated the temperature but I don’t understand how.

BATCH DATA
Batch Content=1000 Kg
Heating Milk From tinitial=4DegCtfinal=94DegC In 30min
Specific Heat Of Milk Cpc=3950 J/KgK @49 DegC
Density of Milk ρ=1013 Kg/m3 @49 DegC
Milk Circulated via a pump through the PHEX and back
to the tank with a flow rate mc=2.78 kg/s

Heating Medium DATA
Hot Water @ T1=97DegC
Specific Heat Of Hot Water Cp=4220J/KgK @ 97 DegC
Density of Hot Water ρ=960Kg/m3@ 97 DegC
Hot Water flow rate mh=4 kg/s

Solution
Heat Duty Qduty=MC*ΔT/ Heating time
Qduty=(1000*3950*(94-4)/(30*60))/1000=197.5Kw

Qduty=mh*Cph*(T1-T2)=>T2=T1-Q/mh*Cph
T2=97-((197.5*1000)/(4*4220))=85.29DegC
T2=85.29DegC

Qduty=m *Cpc*(t2-t1)
(t2-t1)=Q/m*Cpc=(197.5*1000)/(2.78*3950)
(t2-t1)=ΔT=17.98DegC

I try many solutions but I stack again and again and as i realized (I’AM NOT SURE) that the program include efficiency and from the Equation n=Qduty/Qmax calculated the Qmax .
Known The Qmax and from the usual equation calculated t1=T1-(Qmax/mc*Cpc)=70.79DegC and with combination of ΔT=17.98DegC=t2-t1 found the t2=17.98DegC+70.79=88.77DegC but again I don’t understand how calculated the efficiency in order to found the Qmax. Or how to find the Qmax to find the efficiency.
I try to calculated the Qmax with Qmax=mc*Cpc*(T1-t1) but is to high.

Software Results
n, efficiency=68%
Product inlet Temp=70.79 DegC
Product Outlet Temp=88.77 DegC

Please Advice how can I calculated the final temperatures .
Note: Area And Overall Heat Transfer Of PHEX are Unknown.

 

[Latexman]

I recommend you get Donald Q. Kern's Process Heat Transfer. Chapter 18 is Batch and Unsteady-state Processes. A good Engineering library should have it.

Good luck,
Latexman

 

[Latexman]

While Kern may not show the full analytical solution derivation to the differential equation for your exact application, he shows them for similar applications, AND he does show the final analytical solution for your application. IIRC, he also cites the literature reference(s) to the original published analytical solution derivation to the differential equation for your exact application.

The final analytical solution for your application is also in the 6th Edition of Perry's Chemical Engineers' Handbook. I think they go by "Batch Operations" in the heat transfer section. It may be in more recent editions too.

If you do not have access to a copy of Kern or Perry's, you may be able to search and find the original published analytical solution derivation to the differential equation for your exact application.


Good luck,
Latexman