
292 Heat Transfer: Thermal Management of Electronics
. (12.12)
This equation states that the pressure gradient along the length of a vertical plate is
the same inside and outside the boundary layer, and is equal to the pressure gradient
in the still uid outside the boundary layer.
Using Equation 12.12 and setting
in the steady-state forms of
Equations 9.13 through 9.16 in Chapter 9 results in the boundary layer equations for
steady-state natural convection ows with no heat generation:
(12.13)
U
U
x
V
U
y
gU
y
∂
∂
+
∂
∂
=
−
+
∂
∂
∞
()
,
ρρ
ρ
ν
2
2
(12.14)
(12.15)
The rst term on the right side