ME421
Heat Exchanger and
Steam Generator Design
Lecture Notes 7 Part 2
Shell-and-Tube Heat Exchangers
Basic Design Procedure
Flow rates & compositions,
temperatures, pressures.
Process Eng  Design Eng
Shell and head types, baffles,
tube passes, etc.
Preliminary design/analysis
Use heat transfer and
pressure drop correlations
Preliminary Design
• Estimate heat transfer coefficients and fouling resistances.
– Tables 8.4 and 8.5 give h and U values for various cases
– Estimating h is preferred (Table 8.4)
• With h, Rf’s, Rw, and overall surface efficiencies (in case
of fins on either side) estimated, evaluate the overall heat
transfer coefficient
1
Uf 
At
A t Rf i
Rf o
1

 A tR w 

A iihi A i i
o oho
• This is the most general expression, also estimate Uc.
• Take F = 1.0 for counterflow HEX (single tube pass), or
F = 0.9 for any even number of tube passes.
Preliminary Design (continued)
• Estimate heat load
 cp  Tc 2  Tc1   m
 cp  Th1  Th2 
Q  m
c
h
• Calculate Tlm,cf
• Estimate the size of the HEX
Q
Q
Ao 

Uo Tm UoFTm,cf
• This area is also related to tube diameter do and number of
tubes Nt
A o  doNtL
• The objective is to find the number of tubes with diameter
do, and shell diameter Ds to accommodate the number of
tubes, with the given tube length.
Preliminary Design (continued)
• Shell diameter, Ds is
CL  A o (PR) do 
Ds  0.637


CTP 
L

CL is the tube layout constant
2
1/ 2
– CL = 1.0 for 90o and 45o, CL = 0.87 for 30o and 60o
CTP is the tube count calculation constant
– CTP = 0.93 for one tube pass
– CTP = 0.90 for two tube passes
– CTP = 0.85 for three tube passes
PR is the tube pitch ratio, PT/do
• Number of tubes, Nt is
2
 CTP  Ds
Nt  0.785

2 2
CL
(
PR
)
do


See Example 8.1
Rating of the Preliminary Design
• If HEX is available, skip preliminary design and proceed with
rating only. If rating shows that Q and/or pressure drop
requirements are not satisfied, select a different HEX and
iterate.
• If not, preliminary design output is the rating input. Calculate
the heat transfer coefficients and pressure drops.
• If length is fixed, rating output is outlet temperatures; if heat
load is fixed, rating output is HEX length.
Rating of the Preliminary Design (continued)
• Tube side: Chapters 3 & 4 for heat transfer coefficient and
pressure drop calculations (two-phase flow later)
• Shell side: more complicated
• If rating output is not acceptable, modify
– HEX cannot deliver the heat required: increase h or area
• To increase hi, increase um in tubes, thus number of passes
• To increase ho, decrease baffle spacing or decrease baffle cut
• To increase area, increase length or shell diameter, or use shells in series
– ptube > pall: decrease number of tube passes or increase tube
diameter (thus decrease tube length, increase shell diameter and
number of tubes)
– pshell > pall: increase baffle spacing, tube pitch and baffle cut, or
change type of baffles
Shell Side Analysis
Kern Method (simple method)
Shell Side Heat Transfer Coefficient
• Baffles increase heat transfer coefficient due to increased
turbulence, tube correlations are not applicable
• Without baffles, h can be based on De, similar to double-pipe
HEX, and Chapter 3 correlations can be used
• On the shell side, McAdams correlation for Nu
D G 
hD
Nu  o e  0.36 e s 
k
  
De 
0.55
1/ 3
 c p 


 k 


 b

 w



0.14
for
4  free  flow area
wetted perimeter

4 PT2  do2 / 4
De 
do


square
4 PT2 3 / 4  do2 / 8
De 
do / 2

triangular
2  10 3  Res 
GsDe
 1 10 6

Kern Method (simple method)
Shell Side Heat Transfer Coefficient (continued)
Gs (shell side mass velocity) can be evaluated from

m
Gs 
As
D sCB
where A s 
is the bundle crossflow area at the center
PT
of the shell
Ds: shell diameter
C: clearance between adjacent tubes
B: baffle spacing
PT: pitch size
• Gs evaluated here is a fictional value because there is actually
no free-flow area on the shell side. This value is based on the
bundle crossflow area at the hypothetical tube row
possessing the maximum flow area corresponding to the
center of the shell
Kern Method (simple method)
Shell Side Pressure Drop
• Depends on the number of tubes the fluid passes through in
the bundle between baffles and the length of each crossing.
• The following correlation uses the product of distance across
the bundle, taken as Ds, and the number of times the bundle
is crossed.
fG 2s Nb  1Ds
ps 
2De s
s = (b/w)0.14
Nb = L/B – 1 is the number of baffles
(Nb + 1) is the number of times the shell fluid passes the tube
bundle
f takes into account entrance and exit losses
f  exp 0.576  0.19 ln Re s 
Gs D e
where 400  Re s 
 1 106

Kern Method (simple method)
Tube Side Pressure Drop
• Total pressure drop including sudden expansions and
contractions during a return (for multiple tube passes)
 LNp
 um2
ptube,total   4f
 4Np 
di

 2
• Ignore second term if single tube pass
• See Example 8.2 for the application of Kern method on
Example 8.1
Bell-Delaware Method (complex method)
• Shell side flow is complex, combines crossflow and baffle
window flow, as well as baffle-shell and bundle-shell
bypass streams and other complex flow patterns
• Five different streams are identified; A, B, C, E, and F
• Bell-Delaware method takes into account the leakage and
bypass streams, most reliable method for shell side
• B-stream is the main stream, others reduce it and change
shell side temperature profile, thus decrease h
• A: leakage through tube/baffle clearance, C: bundle bypass
stream, E: baffle bypass stream, F: multi tube pass
Bell-Delaware Method
Shell Side Heat Transfer Coefficient
ho  hideal Jc JlJbJsJr
hideal
 s  k s 
m


 jic p,s 0.36


 A s  c p,s s 
2/3
 s


 s,w




0.14
hideal is the ideal heat transfer coefficient for pure crossflow in
an ideal tube bank
J’s are correction factors
ji is the Colburn j-factor for an ideal tube bank (Figures 8.15 s /  s A s , tube layout,
8.17, depend on shell side Re,Re s  dom
and pitch size; or correlation 8.25)
As is the crossflow area at the centerline of the shell for one
crossflow between baffles, As = Ds CB/PT
Note that Res is different for this method (based on do)
Bell-Delaware Method
Shell Side Heat Transfer Coefficient (continued)
• Correlation for the Colburn j-factor for an ideal tube bank
a
 1.33 
a3
a2


Re s  where a 
ji  a1
a4

P
/
d


1

0
.
14
Re
 T o
s
a1 – a4 from Table 8.6 in book
• Correlation for ideal friction factor
b
 1.33 
b3
b2


Re s  where b 
fi  b1
b4

P
/
d


1

0
.
14
Re
 T o
s
b1 – b4 from Table 8.6 in book as well
Bell-Delaware Method
Shell Side Heat Transfer Coefficient (continued)
Correction factors (J’s)
• Jc is the correction for baffle cut and spacing. For a large baffle
cut, 0.53; for no tubes in window, 1.0; and for small windows
with a high window velocity, 1.15.
• Jl is the correction factor for baffle leakage effects (A- and Estreams). Putting baffles too close increases leakage. Typical
value 0.7 - 0.8.
• Jb is the correction factor for bundle bypassing effects and shell
and pass dividers (C- and F- streams). For small clearance
between outermost tubes and shell for fixed tube sheet
construction, ~0.9. For a pull-through rotating head, ~0.7.
• Js is the correction factor for variable baffle spacing at the inlet
and outlet. Usually between 0.85 and 1.0.
• Jr applies if Res < 100. If Res > 100, Jr = 1.0.
• The combined effects of all J’s is ~0.6.
Example 8.3
• Given specifications for a HEX, first perform preliminary design,
then detailed thermal analysis
• Compares the heat transfer coefficient on the shell side,
evaluated using three methods:
– Kern Method (note the different equation for As, but gives the same
result as As = DsCB/PT)
– Taborek Method (just a different Nu correlation than McAdams, other
procedures same as Kern Method, but Res is based on do, not De)
– Bell-Delaware Method (Res is again based on do not De)
• All three methods give comparable ho as a result
• Then, hi, Uc, Uf (Rft given in the problem), Af, Ac are calculated
• OS is evaluated as 43%, but it should not exceed 30% in
design specifications. Therefore, a new OS is assumed (20%)
and Rft is recalculated, which will help determine a suitable
cleaning schedule. With this OS, the new Af and Ds are found.
• With these new constructional parameters, the design must be
re-rated (you can do this as an exercise)
Bell-Delaware Method
Shell Side Heat Pressure Drop
The total nozzle-to-nozzle pressure
drop has 3 components
• Entrance and exit
• Internal
• Window
each is one central
baffle spacing
entrance and exit
internal
window
Bell-Delaware Method
Shell Side Heat Pressure Drop (continued)
Entrance and Exit
• Affected by bypass but not by leakage
• Effect due to variable baffle spacing
Nc  Ncw
RbR s
Nc
where pbi is the pressure drop in an equivalent ideal tube bank
in one baffle compartment of central baffle spacing
Rb is the correction factor for bypass flow (C- and F-streams),
0.5-0.8 depending on the construction type
Nc is the number of tubes crossed during flow through one
crossflow in HEX
Ncw is the number of tube rows crossed in each baffle window
Rs is the correction factor for the entrance and exit section
having different baffle spacing (see literature for tabulated
correction factors)
p e  2pbi
Bell-Delaware Method
Shell Side Heat Pressure Drop (continued)
Internal
• Interior crossflow section (baffle tip to baffle tip)
pc  pbi (Nb  1)RlRb
where Rl is the correction factor for baffle leakage effects (Aand E-streams), 0.4-0.5
Nb is the number of baffles
Bell-Delaware Method
Shell Side Heat Pressure Drop (continued)
Window
• Affected by leakage but not by bypass
• Combined pressure drop in all windows
p w  p wiNbRl
where pwi is the pressure drop in an equivalent ideal tube bank
in the window section
Bell-Delaware Method
Shell Side Heat Pressure Drop (continued)
• The total pressure drop over the shell side is then
ps  pe  pc  p w
p s  Nb  1pbiRb  Nb p w iRl  2pbi 1  Ncw / Nc RbR s
• The pressure drop in nozzles must be calculated separately
• pbi is calculated from
G2s  s,w 


pbi  4fi
2s  s 
• fi from Figs. 8.15 – 8.17 or correlation 8.26
• For an ideal baffle window section, pwi is calculated from
 2s 2  0.6Ncw 
m
p wi 
for Re s  100
2s A s A w
 s  Ncw
s
 sm
m
B 

p wi  26
 2  
for Re s  100
s A s A w    do Dw  s A s A w
Bell-Delaware Method
Shell Side Heat Pressure Drop (continued)
• See literature for Dw, Aw, and correction factors.
• Number of tube rows crossed in one crossflow section, Nc
di 1  2Lc / Ds 
Pp
• Lc is the baffle cut distance from
baffle tip to inside of shell
Nc 
Bell-Delaware Method
Shell Side Heat Pressure Drop (continued)
• Number of tube rows crossed in each window, Ncw
Ncw
0.8L c

Pp
• Number of baffles, Nb
L  Bi  B o
Nb 
1
B
• If Bi = B = Bo, then Nb = L/B – 1
• The total shell side pressure drop of a typical shell-and-tube
HEX is about 20-30% of the pressure drop that would be
calculated without taking into account baffle leakages and tube
bundle bypass effects.
• Read the Chapter on Shell-and-Tube HEX from D.
Biniciogullari’s M.S. Thesis, PDF document on web.
Example 8.4
• Given the HEX designed in Example 8.3, and other
specifications, calculate the shell-side pressure drop using BellDelaware method to see if HEX is suitable.
• Takes into consideration all factors mentioned in the previous 7
slides.
• Compares the result with that obtained through Kern method.
• pBD < pK, about 48%.
Example 8.5
• Complete design of a HEX for given process specifications with
the Kern method.
• The example can be repeated with the Bell-Delaware method
as an execise.