Page 40 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das
P. 40
36 Chapter 2 Heat transfer processes in industrial scale
Table 2.2 F T expressions for specific heat exchanger flow arrangements.
Flow arrangement Formula
Counterflow F T ¼ 1 a
Parallel flow F T ¼ 1 a
Cross-flow (single pass)
Fluid 1 unmixed, fluid 2 mixed ln½ð1 R 1 S 1 Þ=ð1 S 1 Þ
F T ¼
ðR 1 1Þ ln½1 þð1=R 1 Þ lnð1 R 1 S 1 Þ
ln½ð1 R 2 S 2 Þ=ð1 S 2 Þ
¼
ð1 1=R 2 Þ ln½1 þ R 2 lnð1 S 2 Þ
Fluid 1 mixed, fluid 2 unmixed ln½ð1 R 1 S 1 Þ=ð1 S 1 Þ
F T ¼
ð1 1=R 1 Þ ln½1 þ R 1 lnð1 S 1 Þ
ln½ð1 R 2 S 2 Þ=ð1 S 2 Þ
¼
ðR 2 1Þ ln½1 þð1=R 2 Þ lnð1 R 2 S 2 Þ
1-2 TEMA E-shell fluid mixed q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
1 þ R
1 ln½ð1 R 1 S 1 Þ=ð1 S 1 Þ
F T ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
q
2 3
2
1 þ R
2 S 1 1 þ R 1 1
6 7
ð1 R 1 Þ ln4 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 5
q
2
1 þ R
2 S 1 1 R 1 þ 1
q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
1 þ R
2 ln½ð1 R 2 S 2 Þ=ð1 S 2 Þ
¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
q
2 3
2
1 þ R
2 S 2 1 þ R 2 2
6 7
ð1 R 2 Þ ln4
q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 5
2
1 þ R
2 S 2 1 R 2 þ 2
Plate heat exchanger F T ¼ 0:95
Air-cooled exchanger F T ¼ 0:9
All exchangers with R 1 ¼ 0or N F T ¼ 1
a
F T is unity for true counterflow and parallel flow exchangers and is less than 1 for all other flow arrangements. A value of F T
close to unity does not mean a highly efficient heat exchanger. It simply means a closer approach to counterflow behaviour for
comparable operating conditions of flow rates and inlet fluid temperatures.
The effectiveness-NTU method
The LMTD correction can be directly applied when all the terminal temperatures are known for a
particular flow condition. A solution by trial is needed when one of the terminal temperatures is unknown.
In such cases, if the overall coefficient is known or can be estimated a priori, the iterative procedure can
be avoided by resorting to the effectiveness-NTU method. The effectiveness (ε) of a heat exchanger is the
ratio of the actual heat transfer rate to the maximum possible heat transfer rate if there was infinite surface
area. One should carefully distinguish between ε and thermal effectiveness (S) introduced earlier.
Actual Rate of Heat Transfer in the exchanger ðQÞ
ε ¼
Maximum thermodynamically possible rate of heat transfer ðQ maxÞ
