Page 417 - Design and Operation of Heat Exchangers and their Networks

400 Design and operation of heat exchangers and their networks

With known values of k and α o , the heat transfer coefficient at the tube
inside can be evaluated by
1
1 d i d i ln d o =d i Þ
ð
α i ¼ (8.31)
k α o d o 2λ t
Eq. (8.31) is meaningful only when α o ≫ α i . The relative deviation of α i
due to the relative deviation of α o can be expressed as

Δα i Δα o α i d i
(8.32)
α i α o α o d o
That means, if Eq. (8.29) has a maximum deviation of 30% in α o , to limit the
relative deviation of α i less than 3%, we shall ensure that α o 10α i . Under
this condition, Eq. (8.30) reveals t s t w 0.1(t s t). It means that the wall
temperature t w would be close to the saturation temperature t s .

8.2.3 Modified Wilson plot method

In 1915, Wilson (1915) has proposed a graphical technique to determining
heat transfer coefficients from a number of measured overall heat transfer
coefficients without knowing the temperatures of the heat transfer surfaces.
Since then, the so-called Wilson plot method has been widely applied and
further developed into a computational technique. A detailed description of
the use of the Wilson plot method and meaningful discussion can be found
in Shah and Zhou (1997). Roetzel and Na Ranong (2002, 2003) considered
a few simple examples and their evaluation using the Wilson plot technique.
It is shown that, in spite of good results of the data regression, undesirable
systematic errors in the obtained heat transfer coefficients may occur. The
experiments with different thermal conductivities of the fluids would reduce
such an error. An overview of the Wilson plot method was given by Fer-
nandez-Seara et al. (2007), which reveals numerous modifications and
would be useful for experimental investigation of convective heat transfer.

8.2.3.1 Original Wilson plot method
In the original Wilson plot method, the test fluid (fluid 1) flows on the tested
side (side 1) for which the heat transfer coefficient vs flow rate or Nusselt
number vs Reynolds number shall be determined; however, the heat trans-
fer characteristics of the other side (side 2, fluid 2) are unknown or cannot be
exactly evaluated. If the flow in side 1 is in the fully turbulent region, the
Nusselt number can be expressed as

m
n
Nu 1 ¼ C 1 Re Pr μ =μ w,1 0:14 (8.33)
1
1
1