Page 62 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

58 Chapter 3 Double pipe heat exchanger

h i T i;avg þ h o ðD o =D i ÞT o;avg
(3.8)
T w ¼
h i þ h o ðD o =D i Þ
Wall Temperature
Eq. 3.8 is obtained by assuming that the entire heat transfer occurs be-
tween the fluids at their average temperature through the wall of the inner
pipe. For hot fluid flowing through the inner pipe, this gives

h i A i T i;avg T w ¼ h o A o T w T o;avg (3.9)
where T i,avg and T o,avg are the average temperature for the inner and outer fluids, respectively.
Use of Eq. 3.8 involves an iterative procedure since T w is required to calculate (h i ) and (h o ) and vice
versa. Initially, the values of (h i ) and (h o ) are calculated by assuming ðm=m Þ¼ 1. The calculated
w
values of (h) are used to calculate T w and obtain m w . The viscosity correction factor for each fluid is
then multiplied to the preliminary values of (h i ) and (h o ) to obtain the final value of the film co-
efficients. A single iteration usually suffices.
For finned tubes, the viscosity correction factor for the fluid in the inner pipe ðm=m Þ is calculated
w i
at T prime , the temperature of the prime surface and for the outer fluid ðm=m Þ is calculated at T wf , the
w o
weighted average temperature of the extended and prime surfaces. The derivation for the two wall
temperatures is based on the assumption that all the heat is transferred between the streams at their
average temperatures, T i,avg and T o,avg or

Q ¼ h i A i T i;avg T prime ¼ h o E f A Total T prime T o;avg (3.10)
Where T wf is defined by

(3.11)
Q ¼ h o A total T wf T o;avg
This gives the expressions of the wall temperatures as

h i T i;avg þ h o E f;effective ðA total =A i ÞT o;avg
(3.12a)
T prime ¼
h i þ h o E f ;effective ðA total =A i Þ

h i E f;effective T i;avg þ h i 1 E f ;effective þ h o E f;effective ðA total =A i Þ T o;avg
(3.12b)
T wf ¼
h i þ h o E f;effective ðA total =A i Þ
The equivalent diameter (D e ) is the inside diameter (D i ) for the inner pipe.
Equivalent diameter (D e ) for the annulus is four times the mean hydraulic radius r H that is defined
as the ratio of flow area and wetted perimeter.
(3.13a)
D e ¼ D io D o
where D io is the inner diameter of the outer pipe.
Equivalent diameter, D e
According to Kern (1950) the wetted perimeter for heat transfer
calculations is the outer circumference of the inner tube (pD o ).
Therefore, the equivalent diameter (D ) for thermal calculations as defined by Kern (1950) is
0
e
2
D D 2
0 io o (3.13b)
e
D ¼
D o