Shell and tube HX – Taborek-method
 See course thermal installations + Wolverine engineering data book III
Taborek-method
Valid for single-phase shell-side flows of S&T HXs with single segmental baffles (TEMA E-shell)
Bundle and shell geometries



Lbi: inlet baffle spacing
Lbo: outlet baffle spacing
Lbc: central baffle spacing



Dotl: outer tube limit diameter
Dctl: centreline tube limit diameter
Dt: outside diameter of tubes
o Dctl = Dotl – Dt
Ds: shell internal diameter






Lbch: baffle cut height
Bc: baffle cut = (Lbch/Ds)*100%
Lbb: diametral clearance between shell internal diameter and tube limit diameter
o If Dotl is not known:
 Lbb assumed = 9.525 mm (3/8 inch) for Ds < 300 mm
 Lbb assumed = 12.7 mm (1/2 inch) for 300 < Ds < 1000 mm
 Lbb assumed = 15.875 mm (5/8 inch) for Ds > 1000 mm
Lsb: diametral clearance between shell internal diameter and the diameter of the baffle Db
o If Lsb is not known:
 Lsb = 2.0 mm for Ds < 400 mm (15.75 inch)
 Lsb = 1.6 + 0.004*Ds for Ds > 400 mm (15.75 inch)
Ltb: If the diametral clearance between the baffle holes and the outside of the tube is not
known, the maximum TEMA value can be assumed 0.794 mm (1/32 inch) or a smaller value
in the range from 0.397 mm (1/64 inch) to 0.794 mm.
Configuration
The pitch between the pipes is minimum 1.25*Dt.
The type of configuration depends on the fluid on the shell side:
Pitch configuration
Triangular
Triangular
Square
Square




Angle
30°
60°
90°
45°
Shell fluid
Clean
Clean
Fouled
Fouled
Flow regime
All
Not often used
Turbulent
Laminar
Ltp: tube pitch (= distance centre-to-centre between tubes in the bundle)
Lpp: pitch parallel to the flow direction
Lpn: pitch normal to the flow direction
The simple estimation for fixed tubesheets for single tubepass units without any tubes
removed in the nozzle entrance and exit areas:
2
0.7854 𝐷𝑐𝑡𝑙
2
𝐶𝑙 𝐿𝑡𝑝
o
Number of tubes 𝑁𝑡𝑡 =
o
Constant Cl = 1.0 for square (90°) and rotated square tube (45°) layouts and Cl =
0.866 for triangular (30°) tube layouts
For multiple tubepasses  fewer tubes will be used than this expression
o


Compactness  triangular
Square 90°  best heat transfer for turbulent flow + maintenance
Convection coefficient shell side - hs
hs = hid Jc Jl Jb Jr Js J
 Jc Jl Jb Jr Js J≈ 0.6 for a classical S&T HX
with:

hid = convection coefficient for ideal case of complete cross flow over the tube stack
o
𝑚̇
𝑚
o
2⁄3
𝜆𝑠
)
𝑝,𝑠 𝜇𝑠
ℎ𝑖𝑑 = 𝑗𝑖 𝑐𝑝,𝑠 (𝑆 𝑠) (𝑐
𝑗𝑖 = Colburn j-factor for an ideal tube stack
𝑎

1.33
𝐷𝑡

o
𝑎
𝑗𝑖 = 𝑎1 ( 𝐿𝑡𝑝 ) 𝑅𝑒𝑠 2
𝑎=
𝑎3
𝑎
1+0.14𝑅𝑒𝑠 4
𝐷 𝑚̇
𝑅𝑒𝑠 = 𝜇𝑡 𝑆 𝑠
𝑠 𝑚
o
o
𝑚̇𝑠 = mass flow shell side
𝑆𝑚 = cross section in the centre of the shell for cross flow between two baffles.
𝐷𝑐𝑡𝑙

𝑆𝑚 = 𝐿𝑏𝑐 [𝐿𝑏𝑏 + 𝐿

𝐿𝑡𝑝,𝑒𝑓𝑓 = 𝐿𝑡𝑝 for 30° and 90° tube layouts and 𝐿𝑡𝑝,𝑒𝑓𝑓 = 0.707𝐿𝑡𝑝 for 45°
staggered layouts
𝑡𝑝,𝑒𝑓𝑓
(𝐿𝑡𝑝 − 𝐷𝑡 )]
𝐿𝑡𝑝
𝐿𝑡𝑝 − 𝐷𝑡
Lbc

o 𝑐𝑝,𝑠 = specific heat at shell side at MEAN bulk fluid temperature
o 𝜇𝑠 = the dynamic viscosity at MEAN bulk fluid temperature
o 𝜆𝑠 = thermal conductivity fluid at MEAN bulk fluid temperature
Baffle cut correction factor Jc (typical 0.65 – 1.175)
o Jc = 0.55 + 0.72*Fc
o Fc = 1 – 2*Fw

𝜃
𝑐𝑡𝑙
𝐹𝑤 = 360
−
𝑠𝑖𝑛𝜃𝑐𝑡𝑙
2𝜋
(fraction of the cross sectional area occupied by the
window)


𝐷
𝐵
𝑐
𝜃𝑐𝑡𝑙 = 2𝑐𝑜𝑠 −1 {𝐷 𝑠 [1 − 2 (100
)]} (angle of the baffle cut relative to the
𝑐𝑡𝑙
centreline of the HX [°]) (valid for Bc of 15% to 45%)
Baffle leakage correction factor Jl (typical 0.7 – 1)
o 𝐽𝑙 = 0.44(1 − 𝑟𝑠 ) + [1 − 0.44(1 − 𝑟𝑠 )]𝑒 −2.2𝑟𝑙𝑚


𝑆𝑠𝑏
𝑆𝑠𝑏 +𝑆𝑡𝑏
𝑆 +𝑆
𝑟𝑙𝑚 = 𝑠𝑏𝑆 𝑡𝑏
𝑚
𝑟𝑠 =


Shell-to-baffle leakage area 𝑆𝑠𝑏 = 0.00436𝐷𝑠 𝐿𝑠𝑏 (360 − 𝜃𝑑𝑠 )
Tube-to-baffle hole leakage area for 𝑁𝑡𝑡 (1 − 𝐹𝑤 ) tube holes 𝑆𝑡𝑏 =
𝜋
{ 4 [(𝐷𝑡 + 𝐿𝑡𝑏 )2 − 𝐷𝑡2 ]} 𝑁𝑡𝑡 (1 − 𝐹𝑤 )

Cross-flow
𝐷𝑐𝑡𝑙
(𝐿𝑡𝑝
𝐿𝑡𝑝,𝑒𝑓𝑓

area at
the
bundle
centreline
𝑆𝑚 = 𝐿𝑏𝑐 [𝐿𝑏𝑏 +
− 𝐷𝑡 )]
o
𝐿𝑠𝑏 = diametral shell to baffle clearance
o
𝑐
𝜃𝑑𝑠 = 2𝑐𝑜𝑠 −1 [1 − 2 (100
)]
o
𝐿𝑡𝑝,𝑒𝑓𝑓 = 𝐿𝑡𝑝 for 30° and 90° tube layouts and 𝐿𝑡𝑝,𝑒𝑓𝑓 =
0.707𝐿𝑡𝑝 for 45° staggered layouts
𝐵
Bundle bypass correction factor Jb
3
o
o
𝐽𝑏 = 𝑒 −𝐶𝑏ℎ 𝐹𝑠𝑏𝑝 (1− √2𝑟𝑠𝑠 )
𝐶𝑏ℎ = 1.35 for laminar flow (Re ≤ 100); 𝐶𝑏ℎ = 1.25 for transition and turbulent flows
(Re > 100)
o
𝐹𝑠𝑏𝑝 = 𝑆 𝑏 = ration of bypass to crossflow area
𝑆
𝑚


𝑆𝑏 = 𝐿𝑏𝑐 ⌊(𝐷𝑠 − 𝐷𝑜𝑡𝑙 ) + 𝐿𝑝𝑙 ⌋
𝐿𝑝𝑙 = width of the bypass lane between tubes

for no pass partition lane or for such a lane normal to the flow
direction  𝐿𝑝𝑙 = 0

for a pass transition lane parallel to the flow direction 𝐿𝑝𝑙 =
1
(𝑎𝑐𝑡𝑢𝑎𝑙
2
o
𝑟𝑠𝑠 =
𝑁𝑠𝑠
𝑁𝑡𝑐𝑐
𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑎𝑛𝑒) or assumed 𝐿𝑝𝑙 = 𝐷𝑡
= ration of number of sealing strips passed by the flow to the number of
tube rows crossed between baffle tips in one baffle section.

𝐷
𝐵
𝑐
𝑁𝑡𝑐𝑐 = 𝐿 𝑠 [1 − 2 (100
)]
𝑝𝑝


𝐿𝑝𝑝 = 0.866 𝐿𝑡𝑝 for 30° layout; 𝐿𝑝𝑝 = 𝐿𝑡𝑝 for 90° layout and 𝐿𝑝𝑝 =
0.707 𝐿𝑡𝑝 for 45° layout
o The expression has a maximum of 𝐽𝑏 = 1 at 𝑟𝑠𝑠 ≥ 1⁄2
Unequal baffle spacing correction factor Js
o For Lbi = Lbc = Lbo  Js = 1
o
Else 𝐽𝑠 =
(𝑁𝑏 −1)+(𝐿𝑏𝑖 ⁄𝐿𝑏𝑐)1−𝑛 +(𝐿𝑏𝑜 ⁄𝐿𝑏𝑐 )1−𝑛
(𝑁𝑏 −1)+(𝐿𝑏𝑖 ⁄𝐿𝑏𝑐 )+(𝐿𝑏𝑜 ⁄𝐿𝑏𝑐 )




n = 0.6 for turbulent flow and n = 1/3 for laminar flow
Nb = number of baffle compartments  determined from the effective tube
length and the baffle spacings.
Laminar flow correction factor Jr
o No necessary here (only for Re ≤ 100)  Jr = 1
Wall viscosity correction factor J
𝜇𝑠
)
𝜇𝑠,𝑤
0.14
o
𝐽𝜇 = (
o
For gasses  no correction factor!
o
𝜇𝑠,𝑤 via a first guess value of 𝑇̅𝑤 =
Effective tube length Lta

𝐴0 = 𝜋𝐷𝑡 𝐿𝑡𝑎 𝑁𝑡𝑡
𝑏

𝑓𝑖 = 𝑏1 (
o
1.33
𝑃𝑇
𝑑𝑢
𝑏=
𝑏
) 𝑅𝑒𝑠 2
𝑏3
𝑏
1+0.14𝑅𝑒𝑠 4
𝑇̅𝑐 +𝑇̅ℎ
2