Page 420 - Design and Operation of Heat Exchangers and their Networks

Experimental methods for thermal performance of heat exchangers 403

" # 1=4
2 3
1 ln d o =d i Þ gρ λ Δh v,o
ð
l,o l,o
Z ¼ A o (8.47)
kA 2πLλ t μ ð t
l,o s,o t w,o Þd o
As has been aforementioned, the wall temperature t w,o in Eqs. (8.46), (8.47)
and t w,i for μ w,i should be determined by iteration.
By means of the Wilson plot method, the condensation heat transfer
coefficients for steam, R12 and R134a, were evaluated. Kumar et al.
(2001) compared these results with the heat transfer coefficients obtained
with the measured wall temperatures and found that the Wilson plot method
underpredicted the condensation heat transfer coefficients of water on the
plain and finned tubes in the range of 7.5%–15%. For R12 and R134a,
the underprediction is 13%–18% for the plain tube and 15%–25% for the
finned tubes.
Since Eq. (8.44) contains unknown temperature difference, Rose (2004)
expressed Eq. (8.34) as follows:

Δt ¼ Δt i + Δt w + Δt o (8.48)
where Δt¼Q/(kA), Δt i ¼Q/(α i A i ), Δt w ¼QR w , and

" # 1=3
4=3
Q Q μ d o
l,o
Δt o ¼ ¼ (8.49)
2 3
α o A o C o A o gρ λ Δh v,o
l,o l,o
The substitution of Eqs. (8.33), (8.44) into Eq. (8.48) yields
Y ∗ 1
∗
Z ¼ + (8.50)
4=3
C i
Co
where
" # 1=3
2 3
gρ λ Δh v,o
l,o l,o
A o
μ d o q o
l,o
∗
Y ¼ 1=3 0:14 (8.51)
Re 0:8 Pr μ
i i λ i i
A i μ
d i
w,i
" # 1=3
2 3
1 ln d o =d i Þ gρ λ Δh v,o
ð
∗ l,o l,o
Z ¼ A o (8.52)
kA 2πLλ t μ d o q o
l,o
The values of C i and C o are obtained with the linear regression, and
the heat transfer coefficients on both sides of the tube can be evaluated.
Rose (2004) compared the evaluated results with the directly measured heat