Page 341 - Fluid mechanics, heat transfer, and mass transfer

SHELL AND TUBE HEAT EXCHANGERS
322
& Equations for Shell Diameter and Shell Equivalent & Equations for the Estimation of Shell Side and Over-
Diameter: all Heat Transfer Coefficients, Heat Transfer Area,
and Exchanger Tube Length and Shell Diameter:
2
2
2
N ¼ pðCTPÞ D =4ðCLÞðPRÞ ðd Þ; ð10:37Þ
s o ➢ Shell side
where N is the total number of tubes. CTP is the tube
N Nu ¼ h o D e =k s
count calculation constant that accounts for the in-
0:55 1=3 0:14
complete coverage of the shell by the tubes due to ¼ 0:36ðN Re s Þ ðN Pr s Þ ðm =m Þ ð10:44Þ
w
b
necessary clearances between the shell and the outer
tube circle and tube omissions due to tube pass lanes 2 10 < N Re s ¼ðG s D e =mÞ < 1 10 :
6
3
for multitude pass design. CTP values for different
ð10:45Þ
tube passes are 0.93 for one tube pass, 0.90 for two
➢ Overall coefficient for clean surfaces, U c :
tube passes, and 0.85 for three tube passes. D s is the
shell inside diameter and CL is the tube layout
1=U c ¼ 1=h o þ 1=h i ðd o =d i Þþ r o lnðr o =r i Þ=k;
constant (1.0 for 90 and 45 layouts and 0.87 for

30 and 60 layouts). PR ¼ P T /d o , where P T is the ð10:46Þ

tube pitch and d o is the outside tube diameter. where r refers to radius and the subscripts c, o, and
& Equation for Shell Inside Diameter, D s : i refer to clean, outside, and inside, respectively.
➢ Considering fouling resistances, overall coeffi-
1=2 2 1=2
D s ¼ 0:637ðCL=CTPÞ ½A o ðPRÞ d o =LŠ ; cient for fouled surface is
ð10:38Þ
1=U f ¼ 1=U c þ R ft ; ð10:47Þ
where A o is outside heat transfer surface area based
where R ft is total fouling resistance.
on tube outside diameter ¼ pd o NL, L being tube
➢ Heat transfer area A f , for fouled exchanger, is
length.
given by
& Shell Equivalent Diameter, D e : The equivalent di-
ameter is calculated along (instead of across) the long A f ¼ Q=U f ðFÞðLMTDÞ: ð10:48Þ
axes of the shell and therefore is taken as four times
➢ Exchanger length is given by
the net flow area as layout on the tube sheet (for any
pitch layout) divided by the wetted perimeter. L ¼ A f =N t pd o : ð10:49Þ
& D e ¼ 4 (free flow area/wetted perimeter).
➢ Shell diameter, D s , is calculated by the equation
& For square pitch,
given earlier.
2 2 & Method for finding LMTD is given earlier along with
D e ¼ 4ðP pd =4Þ=pd o ð10:39Þ
T o
sample plots for finding LMTD correction factor, F.
& For triangular pitch, & Kern method involves estimation of LMTD, which
assumes that both inlet and outlet temperatures are
p 2
2
D e ¼ 4f½ðP T 3Þ=4Š ðpd =8Þg=pd o =2 ð10:40Þ known. When this is not the case, the solution to a
o
heat exchanger problem becomes somewhat tedious.
& Equation for the Number of Tubes at the Centerline
of the Shell:
10.2.2 «-NTU Method
Number of tubes; N t ¼ D s =P T : ð10:41Þ
. Define effectiveness of a heat exchanger.
& Equation for Shell Side N Re : & Effectiveness is the ratio of actual heat transfer rate
from hot to cold fluid in a given exchanger of any
N Re s ¼ðm s =A s ÞðD e =m Þ: ð10:42Þ flow arrangement to the thermodynamically limited
s
maximum possible heat transfer rate.
where m s is shell side fluid flow rate and A s is the
cross-flow area at the shell diameter. « ¼ Q=Q max ¼ actual heat transfer rate=
maximum possible heat transfer
A s ¼ðD s =P T ÞCB; ð10:43Þ rate from one stream to the other:
where A s is the bundle cross-flow area, C is the ð10:50Þ
clearance between adjacent tubes, (P T d o ), and B & Equations for effectiveness for parallel and counter-
is the baffle spacing. current flows are given below: