1. Heat transfer in boilers
Heat Engines & Boilers

2. Combustion chamber calculation
Radiation heat transfer
Adiabatic flame temperature
Heat transfer in combustion chamber
Retention time in fire chamber
Flame size variation

3. Heat transfer forms from gas to solid surface
Convection
Radiation
By means of
Fluid flow and conduction through boundary layer
Electromagnetic radiation
Contact in between gas and solid surface
Necessary
Not necessary
(even in vacuum)
Depends mainly on
Fluid flow type
and velocity
Temperature difference
raising to the 4th power
Equilibrium state
Q = 0
In case of equal temperature
T1 = T2
Even in case of different temperatures
T1  T2

4. Incident radiation
Absorption a = Ia/ Itotal - absorption coefficient a = black body
Reflection r = Ir/ Itotal - reflection coefficient r = absolute mirror body
Transmission d = Id/ Itotal - transmission coefficient (diffraction) d = transparent body
a + r + d = 1 - in each case

5. Radiation emission of black body
The Planck law with Wien type simplification
Where:
c - velocity of light in vacuum c =  3*108 [m/s]
h - Planck constant h = 6.625* [Js]
k – Boltzmann constant k = 1,38* [J/K]

6. Radiation emission of black body

7. Radiation energy density of black-body - - Stefan-Boltzman law
where: - Stefan-Boltzman constant

8. Flame and fire chamber connection Heat transfer by means of radiation in between two bodies are in totally enveloping surface position

9. Heat transfer by radiation
where: Emissivity factor
A - effective water wall surfaces subject to radiation; [m2]
Tf - average flame temperatur [K]
Tw - average wall temperature [K]

10. Emissivity factor variation in real
Black body - theoretical maximum
Grey body - solid body radiation emissivity is constant
Color body - gas radiation
emissivity is not constant

11. Combustion process in real
Parallel procedures running at the same time
having dependence on one another:
Chemical reaction
Fluid flow
Heat transfer
Simplification model:
Chemical reaction happens first
Hot flue-gas radiates heat

12. Adiabatic flame temperature
Maximal theoretical temperature of flue-gas without any heat transfer

13. Calculation of adiabatic flame temperature
Heat flow into the combustion chamber:
adiabatic flame temperature
where: - B: mass flow rate of fuel [ kg/s]
- v: specific flue gas amount, [kgfluegas/kgfuel] considering excess air and flue-gas recirculation
- cpfg: mean specific heat of flue gas [kJ\kg K]

14. Heat balance in combustion chamber
Qr = Qin - Qfgout
Outlet flugas heat capacity
where:

15. Emissivity variation in case of different fuels

16. Flame size variation

17. Flame size variation

18. Retention time in fire chamber needed for 99.99% oxidization
Needed temperature [°C]
Material
0,5 sec
1 sec
2,0 sec
At retention time
Benzene
880
830
790
Butane
930
900
870
Ethane
1090
990
910
Methane
950
920
Tetrachloromethane
Toluene
1260
1220
1180
Vinyl chloride
770
740
720

19. Retention time calculation

20. Summary of combustion chamber calculation
You are already familiar with:
Radiation heat transfer
Adiabatic flame temperature
Heat transfer in combustion chamber
Flame size variation
Retention time in fire chamber

21. Convective heat transfer calculation
Definition of convective surfaces
Types and arrangements of convective heating surfaces
Calculation method
Heat balance
Radiation / Convective heat transfer variation

22. Definition
We call “Convective Heating Surfaces” surfaces which are built in the boiler after the combustion chamber until the boiler exhaust. Where heat transfer happens mainly by combustion:
These can be:
- superheater
- evaporator
- water heater (economizer)
- combustion air heater
Each heating surface can not be found in every boiler.

23. Flue-gas flow can be inside tubes

24. Convective heating surface construction Fluegas is streaming around water tubes

25. Convective heating surface construction

26. Typical superheater arrangements

27. Tube arrangement examples

28. Finned watertube type heating surface constructions

29. Heat transfer calculation
Input data:
sizes of the heating surface
construction of the heating surface
built in materials
flue gas - inlet temperature
- inlet pressure
- mass flow rate
heat absorp.fluid - inlet temperature
(water/steam/air) - inlet pressure

30. Iteration process
Outlet temperature of the flue gas and the heat absorption fluid has to be estimated. Then average temperatures can be calculated
flue gas:
heat abs.fluid:

31. Characteristic features
Knowing the average temperatures you can determine the characteristic features belonging to the temperature and pressure both of the flue gas and the heat abs. fluid, which is needed to the calculation.
These can be:
density 
thermal conductivity 
Prandtl number Pr
specific heat cp
kinematic viscosity 
etc.

32. Heat transfer coefficient calculation

33. Explanation of different quantities

34. Turbulent fluid flow inside tubes

35. Fluid flow around (between) tubes

36. Heat transfer coefficient in case of water boiling

37. Ranges of heat transfer coefficients
These are only examples.
According to the surface arrangement you can find several cases in the literature.
Heat transfer coefficient has different value range at different types of fluid:
In case of: water boiling: <  < W/m2K
In case of water flow: <  < W/m2K
In case of steam flow: <  < W/m2K
In case of air or flue gas: <  < W/m2K

38. Heat transmission coefficient

39. Convective heat transfer

40. Convective heat transfer modification in case of deposit formation flue gas side medium side

41. Transferred heat

42. Simple heat balance

43. Radiation / Convective heat transfer variation
Radiation and convective heat transfer has different principal
Radiation heat transfer is proportional with ~T4
Convective heat transfer is proportional with velocity
In case of part load operation less fuel is burnt - less fuel produce less fluegas on same cross section gives less velocity - combustion reaction temperature remains nearly the same
Consequently radiation/convection heat transfer ratio increases with power load decrease

44. Summary of convective heat transfer calculation
You are already familiar with
Definition of convective surfaces
Types and arrangements of convective heating surfaces
Calculation method
Heat balance
Radiation / Convective heat transfer variation
(see calculation example)

45. Thank You for Your Attention !

46. ZH eredmények