�
�
��
�
�
�
where
(T w − T c ) = (T w − T 5 ) + (T 5 − T 30 ) + (T 30 − T c )
""
R +
q
=
5Pr + 5 ln(5Pr + 1) + 2.5 ln
ρC p u ∗
30
Therefore,
""
""
q
q
h =
w
=
w
T w − T b
0.833(q "" /ρC p u ∗ )[5Pr + 5 ln(5Pr + 1) + 2.5 ln(Ru ∗ /v30)]
The final heat transfer coefficient and the Nusselt number are expressed as
√
hD
Re · Pr C f /2
Nu D ≡
=
[
(
√
)] (10.49)
k
0.833 5Pr + 5 ln(5Pr + 1) + 2.5 ln (Re D C f /2)/60
where
0.046
0.079
C f =
or C f =
Re 0.2
Re 0.25
D
D
For given Re D , and Pr, the above prediction is fairly close to the following
experimental correlation:
D Pr
0.3
D Pr
0.4
Nu D ≡
hD ≈ 0.023 Re
0.8
or ≈ 0.023 Re
0.8
k
Consider a fully turbulent boundary-layer flow over a flat plate with
uniform wall temperature as the thermal BC (T w = C) [4–6]. From energy
equation,
∂T
∂T
∂
∂T
u
+ v
=
(α + ε H )
(10.50)
∂x
∂y
∂y
∂y
For a fully turbulent boundary-layer flow (v = 0) and assume
∂T
∂T w
∼
≈ 0
∂x
∂x
One can obtain the law of wall for temperature profile as
y +
1
T
+
+
=
dy
(1/Pr) + (ε H /ν)
0
213
Turbulent Flow Heat Transfer