Heat transfer in boilers
Heat Engines & Boilers
Combustion chamber calculation
•
•
•
•
•
Radiation heat transfer
Adiabatic flame temperature
Heat transfer in combustion chamber
Retention time in fire chamber
Flame size variation
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
Incident radiation
• Absorption
• Reflection
• Transmission
(diffraction)
a = Ia/ Itotal - absorption coefficient
a=1
- black body
r = Ir/ Itotal - reflection coefficient
r=1
- absolute mirror body
d = Id/ Itotal - transmission coefficient
d=1
- transparent body
a+r+d=1
- in each case
Radiation emission of black body
I0 
2hc
2

5
1

e
hc
kT

1
2hc
2

5
e

hc
kT
The Planck law with Wien type simplification
Where:
c - velocity of light in vacuum
c = 299 792 458  3*108 [m/s]
h - Planck constant
h = 6.625*10-34
[Js]
k – Boltzmann constant
k = 1,38*10-23
[J/K]
Radiation
emission
of black
body
Radiation energy density of black-body - Stefan-Boltzman law

Es   I  d    T
4
0
• where:
  5. 6787  10 8 W/ m2  K
- Stefan-Boltzman constant
Flame and fire chamber connection
Heat transfer by means of radiation in between two
bodies are in totally enveloping surface position
Heat transfer by radiation

4
Qr   fw    A  T f  Tw
 fw
• where:
1
f
A
•
•
Tf
Tw
 [kW]
- Emissivity factor
 fw 
•
4

1
1
w
1
- effective water wall surfaces
subject to radiation; [m2]
- average flame temperatur [K]
- average wall temperature [K]
Emissivity factor variation in real
1. Black body
2. Grey body
3. Color body
- theoretical maximum
- solid body radiation
emissivity is constant
- gas radiation
emissivity is not constant
Combustion process in real
Parallel procedures running at the same time
having dependence on one another:
• Chemical reaction
• Fluid flow
• Heat transfer
Simplification model:
1. Chemical reaction happens first
2. Hot flue-gas radiates heat
Adiabatic flame temperature
• Maximal
theoretical
temperature
of flue-gas
without any
heat transfer
Calculation of adiabatic flame temperature
• Heat flow into the combustion chamber:
Qin  B  Hi     Lo  cpair  thotair  c fuel  t fuel
• adiabatic flame temperature
Qin
t0 
B  v  c pfg
• 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]
Heat balance in combustion chamber

Qr = Qin - Qfgout
4
f
 fw    A  T  T
4
w
 B    c
v
pfg
 T0  T fgout 
Outlet flugas heat capacity
Qfgout  B   v  cpfg  t fgout
where:
T f  To  T fgout
Emissivity
variation in
case of
different
fuels
Flame size
variation
Flame size variation
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
Butane
880
930
830
900
790
870
Ethane
Methane
Tetrachloromethane
1090
990
1090
990
950
990
910
920
920
Toluene
Vinyl chloride
1260
770
1220
740
1180
720
Retention time calculation
V cc
s 
t ret =
V fg
where:
tret = retention time [s],
Vcc = combustion chamber volume [m3],
Vfg = volume flow of flue gas [m3/s].
dV
dt = ,
V fg
dV = Adx
dt =
Integrated from x=0 to x=xout
tret
dV
273A
=
dx
,
,
V fgN V fgN T
273 Vcc
T0
 ,
ln
V fgN T0  T fgout  T fgout
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
Convective heat transfer calculation
• Definition of convective surfaces
• Types and arrangements of convective
heating surfaces
• Calculation method
• Heat balance
• Radiation / Convective heat transfer
variation
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.
Flue-gas flow can be inside tubes
Convective
heating
surface
construction
Fluegas is
streaming
around water
tubes
Convective heating surface construction
Typical superheater arrangements
Tube
arrangement
examples
Finned watertube type
heating surface constructions
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
- mass flow rate
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:
 fg 
 fgin   fgout
2
t win  t wout
tw 
2
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.
Heat transfer coefficient calculation
There are several semi empirical equation to determine heat transfer coefficient.
For this dimensionless numbers are used.
Most commonly used dimensionless numbers:
 L
- Nusselt number:
Nu 

- Reynolds number
Re 
- Prandtl number
Pr 
w L

a

Explanation of different quantities
Where:  - heat transfer coefficient
L - specific size
 - thermal conductivity
w - fluid flow velocity
 - kinematic viscosity
a - temperature conductivity a 

  cp
where:  - density of the fluid
cp - specific heat at constant pressure
Turbulent fluid flow inside tubes
0.43  Pr 
0.8

Nu  0.021  Re  Pr  
 Prw 
0.25
l
valid for: 104  Re  5  105 and 0. 6  Pr  2500
where: - L specific size
- t standard temperature
- Prw
- l
- inside tube diameter
- fluid average temperature
- Prandtl number at the wall temperature
- coefficient against long/diameter ratio
l
 1   l  1.5
d
l
 50   l  1. 0
d
Fluid flow around (between) tubes
Tubes in series arrangement:
 Pr 

Nu  0.23  Re 0.65  Pr 0.33  
 Prw 
Tubes in staggered (chequerred) arrangement:
0.6
0.33  Pr 

Nu  0.41  Re  Pr  
 Prw 
0.25
 
0.25
 
valid for: 2  102  Re  2  105
where: - w specific velocity - fluid flow velocity in the narrowest cross-section
- 
- coefficient according to the angle including between the
fluid flow and tubes
 = 90° -  = 1.0
 = 10° -  = 0.56
Heat transfer coefficient in case of water boiling
  2. 8  p 0.176  q 0.7 [ W / m 2  K ] valid at: 0.2 bar < p < 98 bar
  1. 27  q 0.75  e
p
62
[W / m2  K] valid at: 6.0 bar < p < 173 bar
where - p - saturated pressure [bar]
- q - heat flux
[W/m2]
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: 5000 <  < 20000 W/m2K
• In case of water flow:
500 <  < 2000 W/m2K
• In case of steam flow:
100 <  < 1000 W/m2K
• In case of air or flue gas: 10 <  <
200 W/m2K
Heat transmission coefficient
Heat transmission coefficient
U
1
i 1
 
 fg
i  w
1
[W/m 2 K]
where: fg - flue gas heat transfer coefficient
w - water/steam side heat transfer coefficient
 - thickness of the tube or other surface
(In case of soot or scale coating possibility
also has to be taken into account.)
 - thermal conductivity
Convective heat transfer
q  U  (t fg  tm ) 
  fg  (t fg  tW 1 ) 

  (tW 1  tW 2 ) 

  m  (tW 2  tm ) 
Convective heat transfer modification in case of
deposit formation
flue gas side
medium side
Transferred heat
Qtransferred  U  F  t ln
where: k - heat transmission coefficient
F - heating surface area
t greatest  t smallest
tln- logharitmical temperature difference t ln 
t greatest
ln
t smallest
Simple heat balance
Three types of heat quantities have to be equal: Q fg  Qtransferred  Qwater / steam
Flue gas heat:
Q fg  B  v'  c pfg  t fgin  t fgout  [kW]
where : B - mass flow rate of fuel [kg/s]
v' - specific mass flow rate of fuel [kg/s]
c pfg - specific heat of flue gas [kJ/kg  K]
t fg - flue gas temperature [ C]
Water/steam:
Q water / steam  m w  hwout  hwin  [kW]
where : m w - mass flow rate of steam or water [kg/s]
hw - water/steam enthalpy [kJ/kg]
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
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)
Thank You for Your Attention !
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