Convection
Chapters 6, 7, 8, 9, 10, and 11
Chapter 6 Introduction
Chapter 8 Internal Flows
Chapter 7 External Flows
9 Free Convection
Chapter 10 Condensation
Chapter 11 Heat Exchangers

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Introduction to Convection:
Flow and Thermal Considerations
Chapter Six

Chapter 1 Review: Newton’s Cooling Law
- Definition of
convective heat transfer coefficient, h

Boundary
Layer Features
Boundary Layers:
•
Velocity Boundary Layer
What is the boundary layer?
What is the shear stress at wall?

Boundary Layer Features (cont.)
•
Thermal Boundary Layer
(
)
0.99
s
t
s
T
T
y
T
T
δ
∞
−
→
=
What is the thermal boundary layer?

Velocity profiles in Laminar and Turbulent Flows

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

Transition
Transition from Laminar to Turbulent Flow (Chapter 7)
•
Transition criterion
for a flat plate in parallel flow:
,
critical Rey
nolds number
c
x c
u x
Re
ρ
μ
∞
≡
→
location at which transition to turbulence begins
c
x
→
10
5
<
Re
x
,
c
<
3
×
10
6

Q:
Does heat transfer increase or decrease with x?

Transition (cont.)
Effect of transition on boundary layer thickness and local convection coefficient: Why does transition increase the boundary layer thickness? Why? Why?

Boundary Layer Equations
How to Characterize the Boundary Layer Flows?
Velocity Boundary Layer:
2
2
2
2
,
u
u
p
dp
x
dx
x
y
∞
∂
∂
∂
<<
≈
∂
∂
∂
Thermal Boundary Layer:
2
2
2
2
T
T
x
y
∂
∂
<<
∂
∂

Example 6.5
Objectives:
Determine h, the convective heat transfer coefficient
on the outer wall of the blade.
Given: Local heat flux = 95 kW/m
2
.
T
s
= 800
o
C through internal cooling.