Online proceedings - EDA Publishing Association

7-9 October 2009, Leuven, Belgium
10 2 (L/D h /(ReP r)) 1/2
20
15
Shah & London 1978 (Nu q )
Shah & London 1978 (Nu T )
Stephan 1959 (Nu T )
Edwards et al. 1979 (Nu T )
fitted correlation (R 2 = 0.995)
Nu
10
Shah & London 1978 (Nu q )
5
Shah & London 1978 (Nu T )
Stephan 1959 (Nu T )
Edwards et al. 1979 (Nu T )
fitted correlation (R 2 = 0.995)
0
0 100 200 300 400 500
Re
Fig. 4. Heat transfer results for steady flow through the heat sink, compared
to existing heat transfer correlations for developing thermal and hydraulic
boundary layers between parallel plates. Circular markers are experimental
results, fitted with correlation described in Eq. (2).
This conjugate heat transfer problem is too complex to
compare quantitatively to the simple cases of the established
correlations [18-20]. Nevertheless, the same functional form
of the correlation established by Edwards et al. [20] is used
in Fig. 4 to fit the experimental data:
−1 −2 3
⎛LD
⎞ ⎛ ⎛ ⎞ ⎞
h
LDh
Nu = a+ b⎜ ⎟ 1+
c
⎜ ⎜ ⎟
⎝Re Pr ⎠ ⎝ ⎠
⎟
(2)
⎝ Re Pr
⎠
where a = 7.5, b = 0.265, c = 0.0661 (R 2 = 0.995).
Figure 5 shows the same data presented differently, as a
function of the dimensionless entrance length L/D h /(Re.Pr)
as is typical of correlations for thermally developing flow.
Pulsating flow
The results for pulsating flow have been analysed as
dimensionless heat transfer enhancement factors, i.e. the
ratio of the increase of the averaged heat transfer coefficient
in pulsating flow with respect to the steady flow case at the
same steady Reynolds number Re s , or
Nu
p
− Nus
δ Nu =
(3)
Nus
where the subscripts s and p denote steady and pulsating
flow respectively. The steady heat transfer coefficient Nu s is
evaluated from Re s using the correlation given in Eq. (2).
Figure 6 shows the enhancement factors for a range of 50
< Re (= Re s ) < 400 and 35 < Re p < 225. The results show a
higher enhancement for higher pulsation amplitude, and a
tendency to peak at a low steady flow rate. This is not
unexpected, given the definition of the enhancement factor
in Eq. (3), comparing the increase in heat transfer coefficient
to the heat transfer coefficient in steady flow Nu s .
Nu
10 1
Fig 5. Identical to Fig. 4, yet plotted as a function of dimensionless thermal
entrance length.
Figures 7 and 8 present the same data in a different form,
as a function of the ratio of pulsating to steady flow
component Re p /Re. This was found to be the best form to
collapse the heat transfer enhancement factor results. For all
practical purposes, the remaining scatter in the data points in
Figs. 7 and 8 is considered within the uncertainty margins.
For now, the main contribution to the uncertainty is in the
pulsating flow magnitude, thus the value of Re p .
δNu
10 2 10 1 10 0
0.5
0.4
0.3
0.2
0.1
Re p =35
Re p =60
Re p =75
Re p = 115
Re p = 150
Re p = 225
0
0 100 200 300 400 500
Re
Fig. 6. Dimensionless heat transfer enhancement for pulsating flow through
the heat sink as a function of the steady flow Reynolds number Re (=Re s ).
Markers indicate different values of the pulsating Reynolds number Re p .
©EDA Publishing/THERMINIC 2009 165
ISBN: 978-2-35500-010-2