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The Thermal Boundary Layer
The thermal boundary layer is the thin region of walladjacent viscous
flow in which temperature gradients exist.
Consider T
s
= Constant.
Then, the thickness of the thermal boundary
layer is the normal distance from the surface to the location where
s
s
TT
0.99
∞
⎛⎞
−
θ=
=
⎜⎟
−
⎝⎠
, i.e.,
s
th
th
0.99
s
y0
.
9
9
,
i
.
e
.
,
y
−
−
∞
δ=
=
.
(1)
At the surface, there is no fluid motion.
Therefore, at the surface, energy
transfer occurs due to conduction, so that
0
y
f
'
'
s
y
T
k
q
=
∂
∂
−
=
Fourier’s law of heat conduction
(2)
Then,
)
T
T
(
y
T
k
h
s
0
y
f
∞
=
−
∂
∂
−
=
,
when combined with Newton’s Law of Cooling.
(3)
For 2D, incompressible, constantproperty, nonreacting fluid flow with
negligible body forces and no energy generation, the energy equation is
q
y
T
k
y
x
T
k
x
y
T
v
x
T
u
C
p
±
+
Φ
μ
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
∂
∂
∂
∂
+
⎟
⎠
⎞
⎜
⎝
⎛
∂
∂
∂
∂
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
∂
∂
+
∂
∂
ρ
(4)
Φ
≡
Viscous dissipation
 rate at which mechanical energy is
irreversibly converted to thermal energy; this term is important
only in highviscosity flow and highspeed flow.
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 Winter '06
 Ghia

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