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WOLFRAM NOTEBOOK
Correction Factor for Shell and Tube Heat Exchanger
Correction Factor for Shell and Tube Heat Exchanger
Consider a shell and tube heat exchanger (1 shell 2 tube Tubular Exchanger Manufacturers Association TEMA E). For this flow arrangement, a correction factor must be used with the equation
F
q=UALMTD
where and are the overall heat transfer coefficient and the area of the heat exchanger, respectively, and is the logarithmic mean temperature difference defined by:
U
A
LMTD
LMTD=
Δ-Δ
T
2
T
1
ln
Δ
T
2
Δ
T
1
where and .
Δ=-
T
1
t
2
T
1
Δ=-
T
2
t
1
T
2
Use the sliders to set the inlet and outlet temperatures of the hot fluid ( and ) and cold fluid ( and ). The corrected logarithmic mean temperature difference is .
t
1
t
2
T
1
T
2
FLMTD
This Demonstration computes the following ratios:
R=--
t
1
t
2
T
2
T
1
P=--
T
2
T
1
t
1
T
1
and the corresponding correction factor , which is given by:
F
F=Sln(W)ln
1+W-S+SW
1+W+S-SW
where
W=
1
N
s
1-PR
1-P
and
S=
0.5
(+1)
2
R
R-1
Here, take =1 (1 shell pass). If , use this equation:
N
s
R=1
F=ln+-
2
1-W'
W'
W'
1-W'
1
2
W'
1-W'
1
2
with
W'=-P-P+P
N
s
N
s
N
s
N
s
The green dot in the graph indicates the position in the - plane corresponding to your choice of the hot fluid ( and ) and cold fluid ( and ) temperatures. The red curves correspond to the values of (between 0.2 and 4.0) commonly reported in the LMTD correction factor charts.
P
F
t
1
t
2
T
1
T
2
R