1. INTRODUCTION TO CONVECTION
Convection Heat Transfer Coefficient
Conservation Equations
Boundary Layer Approximation
Reynolds Analogy
Turbulent Flow

2. Forced Convection
Free Convection
Boiling and Condensation
External flows
Internal flows
Laminar flows
Turbulent flows

3. Convection Heat Transfer Coefficienty
T(x,y) y x Ts

4. y
T(x,y) y x Ts
total heat transfer rate over As
If Ts = constant,
average heat transfer coefficient:

5. Convection Boundary Layer
Velocity (or momentum) boundary layer
wall shear stress:
m: dynamic viscosity
friction coefficient:

6. Temperature (or thermal) boundary layer
local heat flux:
local heat transfer coefficient:

7. Laminar and Turbulent Flows
Viscous sublayer

8. laminar: molecular diffusion
turbulent: eddy motion (fluctuation)
Critical Reynolds number
external flow:
internal flow:

9. Comparison of laminar and turbulent velocity profile in the boundary layer

10. Variation of heat transfer coefficient

11. Conservation Equations Continuity Equation: Mass Conservation
incompressible flow
2-dimensional flow

12. Newton’s 2nd law of motion
Momentum Equations
Newton’s 2nd law of motion
f : force per unit volume
force:
body force, surface force
body force: gravitational force, centrifugal force, electromagnetic force
surface force: viscous force, pressure force

13. incompressible flow with constant viscosity
2-dimensional steady flow

14. 1st law of thermodynamics
Energy Equation
1st law of thermodynamics
rate change of internal energy
= heat transferred in the system
+ work done on the system by forces
+ internal heat generation
internal energy:
thermal energy,
kinetic energy
heat transfer:
conduction, radiation
work:
work done by body force
and surface force

15. energy per unit mass of fluid
thermal energy: e
kinetic energy:
total energy:
Total energy equation

16. Mechanical energy equation
Thermal energy equation
: viscous dissipation

17. Thermal Energy Equation
thermal energy equation for enthalpy
When it is assumed that (ideal gas)
and

18. When pressure work and viscous dissipation are negligible, and internal heat generation is not present,
When the fluid is transparent to radiation and its thermal conductivity is constant,
steady-state:

19. For a 2-dimensional flow

20. Summary
2-dimensional, steady, incompressible, constant property, transparent to radiation, no internal heat generation

21. Boundary Layer Approximation
2-D Boundary Layer Flow
dt(x)
T(x,y) y
d(x)
u(x,y) x Ts L
d(x): thickness of velocity boundary layer
dt(x): thickness of temperature boundary
layer

22. dt(x) y
d(x) x
u(x,y) Ts
T(x,y) L
scaling
from continuity
pressure
temperature

23. dimensionless variables
continuity

24. momentum equation in the streamwise direction
for a high Reynolds number flow:

25. momentum equation in the wall-normal direction
→ p = p(x) in the boundary layer

26. flow over a flat plate:

27. energy equation
Pr: Prandtl number

28. Summary: 2-D Boundary layer equations
continuity:
momentum:
energy:
Boundary layer approximation
Parabolic in the streamwise direction
Pressure is constant across the
boundary layer.

29. Fundamental Form of Solutions

30. Friction coefficient

31. Convection heat transfer coefficient
Nusselt number
local Nusselt number
average Nusselt number

32. Reynolds Analogy
When
and Pr = 1, that is, n = a

33. Let
boundary conditions
Thus,

36. Stanton number
When Pr = 1,
Modified Reynolds analogy or Chilton-Colburn analogy

37. Example 6.5
air
coolant channel
original conditions
Find:
1) heat flux to the blade if the surface temperature is reduced to 700°C
2) heat flux at the same dimensionless location for a similar blade having a chord length of L = 80 mm when T∞ = 1150°C, V = 80 m/s, and Ts = 800°C

38. 1)
air
x*, ReL, Pr are independent
on Ts.
L and k are also unchanged.
Thus, h = h1
original conditions
air
Case 1

39. 2)
air
x*, Pr are also unchanged.
Local Nusselt number remains the same.
original conditions
air
Case 2