u
f ′ = U ∞
1
0.5
Universal
velocity profile
Experimental data
5
y
η =
Re x
x
�
�
From η, obtain or derive f " and u(x, y).
The similarity function for temperature is shown in Figure 7.3.
Let
T − T w
u − 0
∼
θ =
=
= f
"
(7.21)
T ∞ − T w
U ∞ − 0
The energy equation becomes
∂Ψ ∂θ ∂Ψ ∂θ
∂ 2 θ
−
= α
(7.22)
∂y ∂x
∂x ∂y
∂y 2
146
Analytical Heat Transfer
FIGURE 7.2
raphical sketch of velocity profile from similarity.
G
U ∞ ,T ∞
x
y
T ∞
T w
FIGURE 7.3
Concept of thermal boundary layer.
f ′ = U ∞
1
0.5
Universal
velocity profile
Experimental data
5
y
η =
Re x
x
�
�
From η, obtain or derive f " and u(x, y).
The similarity function for temperature is shown in Figure 7.3.
Let
T − T w
u − 0
∼
θ =
=
= f
"
(7.21)
T ∞ − T w
U ∞ − 0
The energy equation becomes
∂Ψ ∂θ ∂Ψ ∂θ
∂ 2 θ
−
= α
(7.22)
∂y ∂x
∂x ∂y
∂y 2
146
Analytical Heat Transfer
FIGURE 7.2
raphical sketch of velocity profile from similarity.
G
U ∞ ,T ∞
x
y
T ∞
T w
FIGURE 7.3
Concept of thermal boundary layer.