Correction Factor for Shell and Tube Heat Exchanger

cold fluid temperature (°C)

inlet (

T

1

)

35

outlet (

T

2

)

54

hot fluid temperature (°C)

inlet (

t

1

)

130

outlet (

t

2

)

80

Consider a shell and tube heat exchanger (1 shell 2 tube Tubular Exchanger Manufacturers Association TEMA E). For this flow arrangement, a correction factor

F

must be used with the equation

q=UALMTD

,

where

U

and

A

are the overall heat transfer coefficient and the area of the heat exchanger, respectively, and

LMTD

is the logarithmic mean temperature difference defined by:

LMTD=

Δ

T

2

-Δ

T

1

ln

Δ

T

2

Δ

T

1

,

where

Δ

T

1

=

t

2

-

T

1

and

Δ

T

2

=

t

1

-

T

2

.

Use the sliders to set the inlet and outlet temperatures of the hot fluid (

t

1

and

t

2

) and cold fluid (

T

1

and

T

2

). The corrected logarithmic mean temperature difference is

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

F

, which is given by:

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

(

2

R

+1)

R-1

.

Here, take

N

s

=1

(1 shell pass). If

R=1

, use this equation:

F=

2

1-W'

W'

ln

W'

1-W'

+

1

2



W'

1-W'

-

1

2

,

with

W'=

N

s

-

N

s

P

N

s

-

N

s

P+P

.

The green dot in the graph indicates the position in the

P

-

F

plane corresponding to your choice of the hot fluid (

t

1

and

t

2

) and cold fluid (

T

1

and

T

2

) temperatures. The red curves correspond to the values of

R

(between 0.2 and 4.0) commonly reported in the LMTD correction factor charts.