1. Andreas Gubner University of Applied Science Munich
Joint European Summer School for Fuel Cell and Hydrogen Technology Heat Exchangers
Andreas Gubner
University of Applied Science Munich

2. Outline Heat transfer fundamentals
Modes of Heat Transfer
Heat transfer by forced convection
Mean heat transfer coefficient in and around circular tubes and fuel cell gas channels, respectively
Fluid properties
Fundamentals of heat exchanger design
Co-, Counter- and Cross-Flow
Introduction to special heat exchangers:
Plate- and Compact Heat Exchangers
Outlook & Further Reading

3. Introduction: Scope
Introduction to an engineering approach to heat exchanger design and performance calculations
Introduction to common heat exchanger types
Introduction to compact heat exchangers
Literature used for most of the fundamentals and further reading tip:
F. P. Incropera, D. P. de Witt, Fundamentals of Heat and Mass Transfer, 4th edition, John Wiley & Sons [InWitt]

4. Introduction: What is Heat?
A temperature difference (always) causes an energy flux.
That energy flux called Heat. It is directed toward decreasing temperature.
Alternative definition by M. Planck: Heat is the difference between the internal energy change and work.
Since thermodynamics does not deliver information how the heat transfer rate is related to the driving temperature difference, additional transport laws must be established.
That is the subject of Heat Transfer

5. Introduction: What is a Heat Exchanger?

6. Tube and Shell Heat Exchanger

7. Modes Of Heat Transfer Heat Conduction in a
resting (not moving, stationary) body
Heat Conduction from a surface into a flowing (moving): Convection
Heat Transfer due to electromagnetic radiation between two surfaces

8. Forced Convection
Heat Transfer between a moving fluid and its containing wall
A velocity boundary layer and a thermal boundary layer is formed next to the wall
There is a constant bulk temperature outside the thermal boundary layer.
Turbulent Flow = Bulk Flow
Laminar Flow = Boundary Layer
Wall

9. Forced Convection TF x TW Wall Turbulent Flow = Bulk Flow
Laminar Flow = Boundary Layer x TW

10. Thermal Boundary Layer
Friction forces keep fluid at the wall stagnant so the standard model is a steady velocity increase toward the pipe center called the velocity boundary layer.
This model also knows a velocity boundary layer that corresponds to the velocity boundary layer (not equal)

11. Heat Transfer Model Theory
Newton‘s law of cooling
Task: How to determine the heat transfer coefficient h?
Modern CFD can be used, however experimental validation still needed.
Too complicated and expensive for everyday engineering jobs, a model für the thermal boundary layer t is used
Determining h is equivalent to the determination of the thermal boundary layer thickness.

12. Heat transfer coefficients for inner flow
Typical Values für h in W/m²K:
Transport-mechanism
Medium
h in
W/m²K
free convection
in gas:
in liquids:
2 – 25
50 – 1000
forces convection
10 – 250
100 – 15000
boiling (evaporation)
2000 – 25000
condensation
5000 –

13. The average (mean) heat transfer coefficient
Newton‘s Law of Cooling:
Local hear transfer coefficient:
Local heat transfer rate (per unit area):
The total heat transfer rate (by the heat exchanger) must be „added up“:
This leads to the concept of averaged heat transfer coefficients
with:

14. The normalized convection transfer equations
A mathematical analysis of the fluid mechanical phenomena delivers a set of normalized equations how the heat transfer rate depends on the flow conditions.
Physical phenomena are assigned to dimensionless groups that allow its characterization.
Most important examples:
Reynolds Number Re
Prandtl Number Pr
Re and Pr are used to calculate another dimensionless number quantity called the Nusselt Number Nu.
The heat transfer coefficient is then calculated using the Nusselt Number.

15. Formal structure and Fluid Properties
The most important dimensionless groups (numbers) for heat transfer due to forced convection are displayed in the box on the left.
There are many others.
They are used for forced convection in pipes, ducts (channels), across cylinders (tubes) or tube banks etc.
Each geometry has its own equation which must be determined experimentally.
The Fluid Properties must be taken from the literature or calculated by using suitable databanks/software.
[InWitt]
Unfortunately all fluid properties are temperature dependent. Finding suitable simplifications / average temperatures or taking the temperature dependance into account fully can be challenging.

16. External Flow Spatially and temporally constant surface temperature
Semi empirical models by curve fitting to free parameters
Measurements can be reproduced well by relationships of the form:
Fluid properties for calculating Re and Pr have to be evaluated using an average temperature given by

17. The cylinder in cross flow
laminar boundary layer facing upstream
flow separation and turbulences downstream
Hilpert Equation:
Re and Nu are calulated using the cylinder diameter D.
The constants depend on the Reynolds Number
ReD C m
0,4 to 4
0,989
0,330
4 to 40
0,911
0,385
40 to 4000
0,683
0,466
4000 to 40000
0,193
0,618
40000 bis 106
0,027
0,805
The equation is experimentally verified for:

18. Flow across tube banks In-line (aligned): Staggered:
In-line (aligned):
Staggered:
If Amin found in alternate location:
If Amin same as aligned:

19. Calculation of the Nusselt Number
Equation proposed by Zhukauskas
[InWitt]
Fluid Properties evaluated at

20. Correction Factor for Few Tubes
If NL < 20 a correction factor should be applied
[InWitt] 13 16
0.98
0.99

21. Flow Through Tubes and Ducts

22. Thermal Entry Length Flow in circular tubes
Development of the thermal boundary layer
Flow in circular tubes
Corresponding local heat transfer coefficient hx

23. Combined Entry Length, FLow regimes
Transition from laminar to turbulent at
Def. of the mean flow velocity
Entry region
Fully developed region
laminar
Fluid dynamical entry length:
turbulent

24. Thermal Entry Length, Mean Fluid Temperature
boundary condition at tube wall to be applied
Def. of mean fluid temperature TF at x:
Mass flux and Enthalpy flux:
Thermal entry length
laminar
turbulent

25. Correlation for Laminar Flow, Combined Entry Length
Constant surface temperature and combined (thermal and velocity) entry length:
Sieder and Tate

26. Correlations for Turbulent Flow Regime
Fairly complicated equation by Gnielinski is today‘s industrial standard.
However for quick estimations much simpler equations may be used at a max. error of approx 25 %
Use Dittus-Boelter if property variations are small
Use Sieder and Tate if property variations are large
Dittus-Boelter:
Sieder and Tate:

27. Mean Fluid Temperature is a Function of Position
Differential energy balance at circumferential area element dA
1. Constant heat flux:
2. Constant wall temperature:
1. Solution/temperature profile for constant heat flux:
2. Solution/temperature profile for constant wall temperature:

28. Calculation of the overall heat transfer rate
Since the temperature difference TW-T(x) changes with position, it is defined:
with the mean logarithmic temperature difference

29. Non-circular channels and ducts
Usage of the hydraulic diameter:
Example: Rectangular Channel with width B and height H:
Fluid properties at:

30. Heat Exchanger Classification
Basic flow types: used to model most design types
Parallel-Flow
Counterflow
Crossflow
Design types
Shell and tubes
Plates
Compact heat exchangers
Hybrid of shell-tubes/plate: Channel structure instead of inner tubes connected by a single fin per plane
Prominent example: car engine radiator

31. Another Shell and Tube Example

32. Plate Heat Exchangers

33. Plate Heat Exchangers

34. Plate Heat Exchangers

35. The Overall Heat Transfer Coefficient
Determines the heat transfer rate from one fluid to another in heat exchangers.
Applicable to all heat exchanger types
U: Overall heat transfer coefficient in W/(m²K)

36. Typical Model for Heat Exchangers
1d heat conduction through a composite cylinder wall

37. Parallel -Flow
[InWitt]

38. Counterflow
[InWitt]

39. Design Equations a) Parallel-Flow Logarithmic mean temp.
b) Counterflow
Fundamental HEX design equation

40. Special Operating Conditions
[InWitt]

41. Cross-Flow and Multipass Heat Exchangers
See next slide for usage of the correction factor F
[InWitt]

42. Design Equations Fundamental HEX design equation
by introducing the modification
And using the logarithmic mean temp. for counterflow

43. Heat Exchanger Analysis
Log mean temperature difference (LMTD) method is fairly easy to use if all temperatures are specified or can be calculated by the overall energy balances.
This is a typical design case for which the overall heat transfer area A is the remaining unknown to be calculated.
However, if the inlet temperatures and the overall heat transfer area are known but no overall heat transfer rate and outlet temperatures, then an iterative procedure is needed.
This is a typical performance calculation of a given heat exchanger as it occurs in system simulations.
There is an alternative that is called “NTU-effectiveness method”. It does not require iterations.

44. The Effectiveness-NTU Method
Definitions:

45. Definition of Heat Exchanger Effectiveness

46. Definition of the Number of Transfer Units - NTU
Performance Calculation
Design Calculation

47. Effectiveness-NTU Relations
Performance
Calculation
[InWitt]

48. Effectiveness-NTU Relations
Design
Calculation
11.31b
11.31c
[InWitt]

49. Compact Heat Exchangers

50. Compact Heat Exchangers

51. Finned Tubes [InWitt] Repeat Element For each fin:
Left boundary condition:
For each fin:
Repeat Element
a. Adibatic tip:
Two simple solutions are sufficient in many cases:
b. Very long fin:
[InWitt]

52. Fin Effectiveness As a rule of thumb, fins make sense if
For fins of infinite length:
Thermal Resistances:

53. Fin Efficiency It is quite straightforward to define a fin efficiency:
For fins with adiabatic tips:
Thermal Resistances:

54. Overall Finned Surface Efficiency
Number of Fins: N
Total heat transfer rate of finned surface (per tube):
with
it follows:
Definition of overall finned surface efficiency:
Thermal Resistance of finned surface:

55. Caution: Contact Resistances may occur
If the finned surface is manufactured be press-fitting sheets of metal to a bunch of tubes, additional contact resistances may apply that diminish fin performance.
Hence care must be taken that

56. UA – Value of a Finned Tube
Tube composed of N-1 layers including contact resistances and fouling resistances

57. Overall Finned Surface Efficiency Alternative Formulation
Thermal Resistance of finned surface including contact resistance:
[InWitt]

58. Outlook / Further Reading
Include pressure drop calculations
Design conflict
Low pressure drop -> large surface area -> big Investment Costs
small surface area -> great pressure drop -> big operating costs
Design is a trade of between cost and space requirements
R&D in heat transfer rates especially for compact heat exchangers with complex geometry still needed
maybe aided by CFD for heat transfer and pressure drop