Introduction to Convection:
Introduction to Convection:
Flow and Thermal Considerations
Flow and Thermal Considerations
Chapter Six and Appendix E
Chapter Six and Appendix E
Sections 6.1 to 6.9 and E.1 to E.3
Sections 6.1 to 6.9 and E.1 to E.3

Boundary
Layer Features
Boundary Layers: Physical Features
•
Velocity Boundary Layer
–
A consequence of viscous effects
associated with relative motion
between a fluid and a surface.
–
A region of the flow characterized by
shear stresses and velocity gradients.
–
A region between the surface
and the free stream whose
thickness
increases in
the flow direction.
δ
–
Why does
increase in the flow direction?
δ
(
)
0.99
u y
u
δ
∞
→
=
0
s
y
u
y
τ
µ
=
∂
=
∂
–
Manifested by a
surface shear
stress
that provides a drag
force,
.
s
τ
D
F
s
D
s
s
A
F
dA
τ
=
∫
–
How does
vary in the flow
direction?
Why?
s
τ

Boundary Layer Features (cont.)
•
Thermal Boundary Layer
–
A consequence of heat transfer
between the surface and fluid.
–
A region of the flow characterized
by temperature gradients and heat
fluxes.
(
)
0.99
s
t
s
T
T
y
T
T
δ
∞
−
→
=
−
–
A region between the surface and
the free stream whose
thickness
increases in the flow direction.
t
δ
0
s
f
y
T
q
k
y
=
∂
′′
= −
∂
–
Why does
increase in the
flow direction?
t
δ
–
Manifested by a
surface heat
flux
and a
convection heat
transfer coefficient
h
.
s
q
′′
0
/
f
y
s
k
T
y
h
T
T
=
∞
−
∂
∂
≡
−
–
If
is constant, how do
and
h
vary in the flow direction?
(
)
s
T
T
∞
−
s
q
′′

Local and Average Coefficients
Distinction between
Local
and
Average Heat Transfer Coefficients
•
Local Heat Flux and Coefficient
:
(
)
s
q
h T
T
∞
′′
=
−
•
Average Heat Flux and Coefficient for a Uniform Surface Temperature
:
(
)
s
s
q
hA
T
T
∞
=
−
s
s
A
q
q dA
′′
=
∫
(
)
s
s
s
A
T
T
hdA
∞
=
−
∫
1
s
s
A
s
h
hdA
A
=
∫
•
For a
flat plate in parallel flow
:
1
L
o
h
hdx
L
=
∫

Boundary Layer Equations
The Boundary Layer Equations
•
Consider concurrent velocity and thermal boundary layer development for
steady,
two-dimensional, incompressible flow
with
constant fluid properties
and
negligible body forces
.
(
)
,
,
p
c
k
µ
•
Apply
conservation of mass
,
Newton’s 2
nd
Law of Motion
and
conservation of energy
to a differential control volume and invoke the
boundary layer approximations
.
Velocity Boundary Layer
:
,
,
u
v
u
u
v
v
y
x
y
x
∂
∂
∂
∂
∂
∂
∂
∂
±
±
Thermal Boundary Layer
:
T
T
y
x
∂
∂
∂
∂
±