Principles of Convection Heat Transfer Method

Principles of Convection Heat Transfer Method

1. Principles of Convection

5. •Basic heat transfer equation
•Primary issue is in getting convective
heat transfer coefficient, h
)(
 TTAhq
ss
h
average heat
transfer coefficient

L
A
s
s
dxh
L
hdAh
A
h
s 0

1
:unit widthfor or,
1

8. Velocity boundary layer

9. Laminar and Turbulent flow

11. Thermal boundary layer

13. Ludwig Prandtl
Nußelt

17. Flow Inside Tube

18. Internal Flow:
Heat Transfer Correlations

19. Fully Developed Flow
• Laminar Flow in a Circular Tube:
The local Nusselt number is a constant throughout the fully developed
region, but its value depends on the surface thermal condition.
– Uniform Surface Heat Flux : ( )
s
q
4.36
D
hD
Nu
k
 
– Uniform Surface Temperature : ( )
s
T
3.66
D
hD
Nu
k
 
• Turbulent Flow in a Circular Tube:
– For a smooth surface and fully turbulent conditions , the
Dittus – Boelter equation may be used as a first approximation:
 Re 10,000
D

4 / 5
0.023Re Pr
n
D D
Nu
 
 
1/ 2 2 / 3
/8 Re 1000 Pr
1 12.7 /8 Pr 1
D
D
f
Nu
f


 
– The effects of wall roughness and transitional flow conditions
may be considered by using the Gnielinski correlation:
 Re 3000
D

 
 
0.3
0.4
s m
s m
n T T
n T T
 
 

20. Smooth surface:
 
2
0.7901nRe 1.64
D
f

 
Surface of roughness : 0e
Figure 8.3f
• Noncircular Tubes:
– Use of hydraulic diameter as characteristic length:
4
c
h
A
D
P

– Since the local convection coefficient varies around the periphery of a tube,
approaching zero at its corners, correlations for the fully developed region
are associated with convection coefficients averaged over the periphery
of the tube.
– Laminar Flow:
The local Nusselt number is a constant whose value (Table 8.1) depends on
the surface thermal condition and the duct aspect ratio. 
s s
T or q
– Turbulent Flow:
As a first approximation, the Dittus-Boelter or Gnielinski correlation may be used
with the hydraulic diameter, irrespective of the surface thermal condition.

21. Effect of the Entry Region
• The manner in which the Nusselt decays from inlet to fully developed conditions
for laminar flow depends on the nature of thermal and velocity boundary layer
development in the entry region, as well as the surface thermal condition.
Laminar flow in a
circular tube.
– Combined Entry Length:
Thermal and velocity boundary layers develop concurrently from uniform
profiles at the inlet.

26. – Thermal Entry Length:
Velocity profile is fully developed at the inlet, and boundary layer development
in the entry region is restricted to thermal effects. Such a condition may also
be assumed to be a good approximation for a uniform inlet velocity profile if
Pr 1.
• Average Nusselt Number for Laminar Flow in a Circular Tube with Uniform
Surface Temperature:
– Combined Entry Length:
 
1/ 3 0.14
Re Pr/ / / 2:
D s
L D    
 
0.14
1/ 3
Re Pr
1.86
/
D
D
s
Nu
L D


  
    
   
 
1/ 3 0.14
Re Pr/ / / 2:
D s
L D    
 
3.66DNu
– Thermal Entry Length:


2 / 3
0.0668 / Re Pr
3.66
1 0.04 / Re Pr
D
D
D
D L
Nu
D L
 
  
 

27. • Average Nusselt Number for Turbulent Flow in a Circular Tube :
– Effects of entry and surface thermal conditions are less pronounced for
turbulent flow and can be neglected.
– For long tubes : / 60L D
,
D
D fd
Nu Nu
– For short tubes :  / 60L D
,
1
/
D
m
D fd
Nu C
Nu L D
 
1
2/3
C
m


• Noncircular Tubes:
– Laminar Flow:
depends strongly on aspect ratio, as well as entry region and surface
thermal conditions.
h
DNu

28. • When determining for any tube geometry or flow condition, all
properties are to be evaluated at
DNu
 
, ,
/2m
m i m o
T T T 
Why do solutions to internal flow problems often require iteration?
– Turbulent Flow:
As a first approximation, correlations for a circular tube may be used
with D replaced by .
h
D

29. Solution steps
1.Determine properties
- External flow: film temperature
- Internal flow: average temperature between inlet and outlet
2.Determine flow conditions
- Laminar or turbulent?  Re
3.Determine heating/cooling condition
- Average heat transfer along tubes  NuL
- Local heat transfer  Nux
- Thermal entry length considered?
- Fully developed length considered?
4.Select appropriate correlation for Nu
5.Solve for h
6.Calculate )(
 TTAhq
ss

30. The Concentric Tube Annulus
• Fluid flow through
region formed by
concentric tubes.
• Convection heat transfer
may be from or to inner
surface of outer tube and
outer surface of inner tube.
• Surface thermal conditions may be characterized by
uniform temperature or uniform heat flux . 
, ,
,
s i s o
T T ,
i o
q q 
• Convection coefficients are associated with each surface, where
 
,i i s i m
q h T T 
 
,o o s o m
q h T T 

31. i h o h
i o
hD h D
Nu Nu
k k
 
• Fully Developed Laminar Flow
Nusselt numbers depend on and surface thermal conditions (Tables 8.2, 8.3)/
i o
D D
• Fully Developed Turbulent Flow
Correlations for a circular tube may be used with replaced by .D
h
D
h o i
D D D 

32. Convection
in
Heat Exchanger

33. Overall Heat Transfer Coefficient
The coefficient was determined by accounting for conduction and
convection resistances between fluids separated by composite plane
and cylindrical walls, respectively. For a wall separating two fluid
streams, the overall heat transfer coefficient may be expressed as

34. Overall Heat Transfer Coefficient
Additional factors can be included: fins and foulings
Fins Fouling Fins Fouling

35. Logarithmic Mean Temperature Difference

36. Correlations
Internal Flow