# Heat transfer in boilers

Mécanique

22 févr. 2014 (il y a 4 années et 4 mois)

142 vue(s)

Heat transfer in
boilers

Heat Engines & Boilers

Co
mbustion chamber calculation

Heat transfer in combustion chamber

Retention time in fire chamber

Flame size variation

Heat transfer forms from gas to solid surface

Convection

By means of

Fluid flow and
conduction through
boundary layer

Electromagnetic

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

T
1

= T
2

Even in case of different
temperatures

T
1

T
2

Absorption

a = I

a
/ I

total

-

absorption coefficient

a = 1

-

black body

Reflection

r = I

r
/ I

total

-

reflection coefficient

r = 1

-

absolute mirror body

Transmission

d = I

d
/ I

total

-

transmission

coefficient

(diffraction)

d = 1

-

transparent body

a + r + d = 1

-

in each case

Radiation emission of black body

The Planck law with Wien type simplification

Where:

c
-

velocity of light in vacuum

c = 299 792 458

3*10
8

[m/s]

h
-

Planck constant

h = 6.625
*10
-
34

[Js]

k

Boltzmann constant

k = 1,38*10
-
23

[J/K]

kT
hc
kT
hc
e
hc
e
hc
I

5
2
5
2
0
2
1
1
2
emission
of black
body

Radiation energy density of black
-
body
-

-

Stefan
-
Boltzman law

where:

-

Stefan
-
Boltzman constant

E
I
d
T
s

4
0

5
6787
10
8
.
W
/
m
K
2

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

where:

-

Emissivity f
actor

A

-

effective water wall surfaces

subject to radiation; [m
2
]

T
f

-

average flame temperatur [K]

T
w

-

average wall temperature [K]

[kW]

T
T
A
Q
4
w
4
f
fw
r

fw
f
w

1
1
1
1

fw
Emissivity factor variation in real

1.
Black body

-

theoretical maximum

2.
Grey body

-

emissivity is constant

3.
Color body

-

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 firs
t

2.
Hot flue
-

Maximal
theoretical
temperature

of flue
-
gas
without any
heat transfer

Calculation of adiabatic flame temperature

Heat flow into the combustion chamber:

where:
-

B: mass flow rate of fuel [ kg/s]

-

v
: specific flue gas amount, [kg
fluegas
/
kg
fuel
]

considering excess air and flue
-
gas recirculation

-

cp
fg
: mean specific heat of flue gas [kJ
\
kg K]

Q
B
H
c
t
c
t
in
i
Lo
pair
hotair
fuel
fuel

pfg
v
in
0
c
B
Q
t

H
eat balance
i
n combustion chamber

Q
r

= Q
in

-

Q
fgout

Outlet flugas heat capacity

where:

fgout
0
pfg
v
4
w
4
f
fw
T
T
c
B
T
T
A

Q
B
c
t
fgout
v
pfg
fgout

fgout
o
f
T
T
T

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

880

830

790

Butane

930

900

870

Ethane

1090

990

910

Methane

990

950

920

Tetrachloromethane

1090

990

920

Toluene

1260

1220

1180

Vinyl chloride

770

740

720

Retention time calculation

s

V
V

=

t
fg
cc
ret

where
:

t
ret

= retention time
[s],

V
cc
=
combustion chamber volume
[m
3
],

V
fg
=
volume flow of flue gas
[m
3
/s].

,
fg
V
dV

=

dt

=

dV

dx
T
V
273A

=

V
dV

=

dt
,
fgN
,
fgN

Integrated from x
=0 to
x=x
out

fgout
0
fgout
0
,
fgN
cc
ret
T
T
ln
T
T
V
V
273
t

Summary

of

c
o
mbustion chamber calculation

You are already familiar with:

Heat transfer in combustion chamber

Flame size variation

Retention time in fire chamber

Con
vective 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
t
t
w
win
wout

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 c
p

kinematic viscosity

etc.

Heat transfer coefficient calculation

There are several semi empirical equation to determine heat transfer coefficient.

For th
is dimensionless numbers are used.

Most commonly used dimensionless numbers:

-
Nusselt number:
Nu
L

-
Reynolds number
Re

w
L

-
Prandtl number
Pr

a

Explanation of different quant
i
ties

Where:

-

heat transfer coefficient

L
-
specific size

-
thermal conductivity

w
-
fluid flow velocity

-
kinematic viscosity

a
-
temperature conductivity
a
c
p

where:

-
density of the fluid

c
p

-
specific heat at constant pressure

Turbulent fluid flow inside tubes

l
25
.
0
w
43
.
0
8
.
0
Pr
Pr
Pr
Re
021
.
0
Nu

valid for:
10
5
10
0
6
2500
4
5

Re
.
Pr
and

where:
-
L specific size
-
inside tube diameter

-
t standard temperature
-
fluid average temperature

-
Pr
w

-
Prandtl number at the wall temperature

-

l

-
coefficient against long/diameter ratio

l
d
l
d
l
l

1
1
5
50
1
0

.
.

Fluid flow around (between) tubes

Tubes in series arrangement:

25
.
0
w
33
.
0
65
.
0
Pr
Pr
Pr
Re
23
.
0
Nu

Tubes in staggered (chequerred) arrangement:

25
.
0
w
33
.
0
6
.
0
Pr
Pr
Pr
Re
41
.
0
Nu

valid for:
2
10
2
10
2
5

Re

where:
-
w specific velocity
-
fluid
flow velocity in the narrowest cross
-
section

-

-
coefficient according to the angle including between the

fluid flow and tub
es

= 90°
-

= 1.0

= 10°
-

= 0.56

Heat transfer coefficient in case of water boiling

2
8
0
176
0
7
.
.
.
p
q
[
W
/
m
K
]
2

valid at: 0.2 bar < p < 98 bar

1
27
0
75
.
.
q
e
[
W
/
m
K
]
p
62
2

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/m
2
K

In case of water flow: 500 <

<

2000 W/m
2
K

In case of steam flow: 100 <

<

1000 W/m
2
K

In case of air or flue gas: 10 <

<

200 W/m
2
K

Heat transmission coefficient

Heat
transmission coefficient

K]
[W/m

1
1
1
2

w
i
i
fg
U

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

al
so has to b
e taken
into
account
.)

-
thermal conductivity

Convective heat transfer

)
(
)
(
)
(
)
(
2
2
1
1
m
W
m
W
W
W
fg
fg
m
fg
t
t
t
t
t
t
t
t
U
q

Convective heat transfer modification in case of
deposit formation

flue gas side

medium side

Transferred heat

ln
t
F
U
Q
d
transferre

where: k
-
heat transmission coefficient

F
-
heating surface area

tln
-
logharitmical temperature difference

t
t
t
t
t
greatest
smallest
greatest
smallest
ln
ln

Simple heat balance

Thr
ee types of heat quantities have to be equal:
Q
Q
Q
fg
transferred
water
steam

/

Flue gas heat:

C]
[

e
temperatur

gas

flue

-

t

K]
[kJ/kg

gas

flue

of

heat

specific
-

c

[kg/s]

fuel

of

rate

flow

mass

specific
-

[kg/s]

fuel

of

rate

flow

mass

-

B

:
where
[kW]

t
t
c

B
Q
fg
pfg
'
v
fgout
fgin
pfg
'
v
fg

Water/steam:

[kJ/kg]
enthalpy

am
water/ste
-

h

[kg/s]
or water

steam
of

rate

flow

mass

-

m

:
where
[kW]

h
h
m
Q
w
w
win
wout
w
steam
/
water

Radiation / Convective heat transfer variation

Radiation and convective heat transfer has different
principal

Radiation heat transfer is proportional with
~
T
4

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

c
on
vective 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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