# 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