Oneeq14

Name: Oneeq14 - Heat duty of a countercurrent flow heat exchanger
Source:      
       
Reference/s Shacham, M. 1989, Chem. Engng. Sci., 44(7), 1495
       
Model: 1 implicit equation, indep. variable name: Q
  Moderate difficulty level
  Constraints: V>0
  Discontinuities: function undefined for DT1<=0 or DT2<0
  Initial range: Qmin=1E6, Qmax=7.0E6
       
Solved by Shacham, M., POLYMATH 5.1, build 19, Dec. 12, 2000
       
Model Eqs. Heat duty of a shell and tube heat exchanger|POLVER05_1

EXCEL FILE 

f(Q)=U*A*(DT2-DT1)/ln(DT2/DT1)-Q #

TEXT FILE  

DT1=T1-t1-Q/(M*Cp) #

POLYMATH FILE 

DT2 = T1-t1-Q/(m*cp) #
  M=43800.0 #
  m=149000.0 #
  Cp=0.605 #
  U=55.0 #
  A=662.0 #
  T1=390.0 #
  t1=100.0 #
  cp=0.49 #
  Q(min)=1000000, Q(max)=7000000
       
       
Variable/function values Variable Value f(x)
  Q

4000000

2.6608E+06
  DT1

139.05
 
  DT2

235.21
 
  t1

100
 
  cp

0.49
 
  M

43800
 
  m

149000
 
  Cp

0.605
 
  U

55
 
  A

662
 
  T1

390
 
       
       
Root Variable Value f(x)
  Q

5281024.23857737

9.3132E-10
  DT1

90.7085460365702
 
  DT2

217.6671108262300
 
       
Additional information Function value obtained by substraction of 2 numbers
  of the order of 5E6 in the vicinity of the root. Care should be
  given to specifying achievable error tolerance.
       
Function plot