Page 345 - Fluid mechanics, heat transfer, and mass transfer

SHELL AND TUBE HEAT EXCHANGERS
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L pp ¼ 0.866L tp for a 30 layout, L tp ¼ L tp for a 90 & J m is viscosity correction factor. For heating and
layout, and L pp ¼ 0.707L tp for a 45 layout. cooling of liquids, the effect of variation of the fluid

➢ There is a maximum limit of J b ¼ 1, at r ss 1/2. properties between bulk fluid temperature and the
0.14
wall temperature is corrected by J m ¼ (m/m w ) .
➢ For relatively small clearance between the outer-
most tubes and the shell for fixed tube sheet ➢ For gases and low-viscosity liquids, no such cor-
construction, J b ¼ 0.90. rection is required as temperature variation be-
tween the bulk fluid and thewall will be negligible.
➢ For a pull-through floating head, requiring larger
clearance, J b ¼ 0.7. ➢ For heating of gases, correction based on temper-
ature rather than viscosity is applied.
& J s : Correction factor for variable baffle spacing at the
inlet and outlet. Because of the nozzle spacing at the 0:25
J m ¼ðT=T w Þ ; ð10:82Þ
inlet and outlet and the changes (decrease) in local
velocities, the average heat transfer coefficient on the where T is in K.
shell side will be adversely influenced. & A s cross-flow area at the centerline of shell for one
1 n 1 n cross flow between two baffles.
J s ¼½ðN b 1ÞþðL bi =L bc Þ þðL bo =L bc Þ Š=
& Subscripts s and w stand for shell and wall temper-
½ðN b 1ÞþðL bi =L bc ÞþðL bo =L bc ފ: ð10:77Þ ature, respectively.
& The combined effects of all these correction factors
for a reasonably well-designed shell and tube heat
n ¼ 0.6 for turbulent flow and 1/3 for laminar flow. L bi
and L bo are inlet and/or outlet baffle spacings, larger
exchanger are of the order of 0.60.
than the central baffle spacing L bc . J s < 1, for larger
& Taborek gave the following equation for the estima-
inlet and outlet baffle spacings than the central baffle
tion of h ideal :
spacing and for inlet and outlet equal to the central
baffle spacing, J s ¼ 1, that is, no correction is required. 2=3
h ideal ¼ J i C P _ m ðN Pr Þ ; ð10:83Þ
J s value will usually be between 0.85 and 1.00. N b is
the number of baffle compartments, determined from where _ m is the mass velocity of the fluid based on the
the effective tube length and baffle spacings. total flow through the minimum flow area normal to
2
& J r : Laminar flow correction factor. In laminar flows, the flow, kg/m s ¼ M/S m .
heat transfer is reduced by the adverse temperature & M is shell side flow rate (kg/s) and S m is as defined
gradient formed in the boundary layer as the flow earlier.
thermally develops along the flow channel. J r ac- a
J i ¼ a 1 ½1:33=ðL tp =D t Þ ðN Re Þ : ð10:84Þ
a 2
counts for this effect.
➢ J r < 1 for laminar flow, that is, 100 N Re .
a ¼ a 3 =ð1 þ 0:14ðN Re Þ : ð10:85Þ
a 4
➢ J r ¼ 1, for N Re > 100.
➢ For N Res < 20, & The values of the empirical constants a 1 , a 2 , a 3 , and
a 4 are given by Taborek in tabular form.
0:18
J r ¼ðJ r Þ ¼ð10=N c Þ : ð10:78Þ
20 & Values of a 1 and a 2 are functions of N Re and tube

➢ N c is the total number of tube rows crossed by the layout angles, that is, whether 30 ,45 ,or90 .
flow over the entire heat exchanger and is given by & Values of a 3 and a 4 are dependant on the tube layout
angles.
N c ¼ðN tcc þ N tcw ÞðN b þ 1Þ: ð10:79Þ
& Equations for DP are given by empirical equations by
➢ N tcc is the number of tube rows crossed between Taborek.
baffle tips and is given under J b . & Solutions for Bell Delaware equations with
➢ N tcw is the number of tube rows crossed in the Taborek’s empirical equations are best handled by
window area and is given by available software.
. Compare Kern and Bell Delaware methods for the
N tcw ¼ð0:8=L pp Þ½D s ðB c =100Þ ðD s D ctl Þ=2Š:
design of shell and tube heat exchangers.
ð10:80Þ & Kern method is commonly used giving satisfactory
results. Its main advantage is that it requires little
➢ For 20 > N Re < 100, the value of J r is prorated as
knowledge of the geometrical parameters of the
J r ¼ðJ r Þ þ½ð20 N Re Þ=80Š½ðJ r Þ 1Š: ð10:81Þ exchanger. It only requires tube diameter and pitch,
20 20
physical properties of the fluid entering shell side,
➢ The minimum value of J r in all cases is 0.4.
and assumes a 25% baffle cut in all cases.