
224 Heat Transfer: Thermal Management of Electronics
, (10.21)
U
T
x
V
T
y
T
y
U
y
LL
*
*
*
*
*
*RePr
*
*
Ec
Re
*∂
∂
+
∂
∂
=
∂
∂
+
∂
∂
1
2
2
**
*
+
2
g
, (10.22)
and the expressions for local friction coefcient and Nusselt number,
(10.23)
and
. (10.24)
These equations will be used to understand what ow variables affect friction
coefcient and convection heat transfer coefcient.
The x-momentum equation shows that the normalized x-component of uid
velocity, U*, depends on x*, y*, Re
L
, ∂P*/∂x, and X*. This can be expressed by a
general functional form,
Ufxy
P
x
X
L
**,*,Re,
*
*
,*=
∂
∂
1
. (10.25)
Equation 10.25 shows that