Page 59 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

3.2 Design 55

3.2.6 Thermal design
The following outlines the steps of calculation for a tube-in-tube double-pipe exchanger utilising the
applicable equations outlined in Chapter 2.
For a double-pipe exchanger, the heat transfer area A in Eq. 2.3 is the outer surface area of the inner
conduit. The size designation for heat exchanger tubes is different from
pipes. The nominal outside diameter of a heat exchanger tube is its actual
(outside) diameter and the wall thickness is specified by Birmingham Wire
Heat transfer area
Gage (BWG) instead of Schedule number.
Thus Eq. 2.3 reduces to
Q
(3.1)
A ¼ A o ¼ pD o L ¼
U o DT LMTD
U in Eq. 3.1 is obtained from Eq. 2.13 based on the outer diameter of the inner pipe, viz.

1 1 D o lnðD o =D i Þ D o
(3.2)
¼ þ þ
U o h o 2k w h i D i
Overall Heat Transfer Coefficient
Subscripts o and i denote conditions at the tube outside and
inside, respectively. Thus, (1/U o ) is the overall thermal resis-
tance based on the tube outside area, h i and h o are the heat transfer coefficient for the inner and annular
fluids and D i , D o are the inner and outer diameter of the tube. Incorporating the dirt factors R Di and R Do
for the inner and outer wall of the tube respectively, the design overall heat transfer coefficient for a
finned multi-tube double-pipe exchanger can be expressed as
1 1 A total lnðD o =D i Þ A total R Do R Di A total
(3.3)
¼ þ þ þ þ
U D h o E f ;effective 2pk w L h i A i E f;effective A i
One may note that U D is defined with respect to the total area A total . Although fins can be attached
to both internal and external pipe surface, external fins are most frequently used. Accordingly,
E f,effective the weighted fin efficiency for the entire finned surface, is associated with the pipe outer wall
only in Eq. 3.3 where E f,effective is given as
A prime þ E f A f
(3.4)
E f;effective ¼
A total
The area of the prime surface (A prime ), longitudinal fin surface (A f ) and total cross-sectional area
(A total )is e
A prime ¼ðpD o N f t f ÞnL (3.5a)

t f
L (3.5b)
A f ¼ 2nN f h f þ
2
(3.5c)
A total ¼ A prime þ A f