CE 2004: Heat Transfer Dr. John Brammer

Room 214 Tel. 3380 e-mail j.g.brammer

Heat Exchanger Design – 6 lectures, 2 example classes

Radiation – 2 lectures, 1 example class

Key texts: Coulson & Richardson’s Chemical Engineering

Volume 6, Chapter 12

Holman, Heat Transfer

Butterworth, Introduction to Heat Transfer

Module topics

• Heat exchanger types

• Design of a shell and tube heat exchanger

– tube-side film coefficient

– shell-side film coefficient

– overall heat transfer coefficient

• Heat transfer from finned tubes

• Natural convection

• Radiation heat transfer

What are heat exchangers for?

• To get fluid streams to the right temperature for the next process

• To condense vapours (third year)

• To evaporate liquids (third year)

• To recover heat to use elsewhere

• To reject low-grade heat

• To drive a power cycle – i.e. to heat a working fluid

Concentric tube heat exchanger

• One tube inside another

• Normal size

– 0.25 to 200m2 (2.5 to 2000 ft2) per unit

• Built of carbon steel where possible

– Note multiple units are often used

Advantages/disadvantages of

concentric tube heat exchanger

• Advantages

– Easy to obtain counter-current flow

– Can handle high pressure

– Modular construction

– Easy to maintain and repair

• Disadvantages

– Only moderate e (0.9), T (5K)

– Becomes expensive for large duties (>1MW)

Thermal effectiveness

( )

inin

Cminout

TT

TTp

,2,1

min

e

Stream temperature rise divided by the theoretically

maximum possible temperature rise

T1,in T1,out

T2,out T2,in

Shell and tube heat exchanger

• Size per unit (10 - 1000 m2)

• Easy to build multiple units

• Made of carbon steel where possible

• Essentially multiple concentric tube

Flow in shell-and-tube heat exchanger

Complete shell and tube heat exchanger

Advantages/disadvantages of

shell-and-tube heat exchanger

• Advantages

– Extremely flexible and robust design

– Easy to maintain and repair

– Can be designed to be dismantled for cleaning

– Very many suppliers world-wide

• Disadvantages

– Only moderate e (0.9), T (5K)

– Requires large plot area (removal of bundle)

– Not cheap for lower pressures and temperatures

Plate (or gasketed plate)

heat exchanger

• Plates hung vertically and clamped in a press or frame.

• Gaskets direct the streams between alternate plates and prevent external leakage

• Plates made of stainless steel or higher quality material

• Plates corrugated to give points of support and increase heat transfer

Chevron Washboard

Plate types

• Corrugations on plate improve heat transfer and give rigidity

• Many points of contact and a tortuous flow path

Flow in plate heat exchanger

Alternate plates (often same plate types inverted)

Gaskets arranged

for each stream to

flow between

alternate plates

Advantages/disadvantages of

plate heat exchanger

• Advantages

– High heat transfer, high e (0.95), low T (1K)

– Compact, cheap

– Easily dismantled for cleaning

– Flexible, plates can be added or removed

• Disadvantages

– Limited temperature and pressure (gasket material)

– Limited capacity (port size)

– Prone to blockage (solids), leakage, gasket damage

Air cooled heat exchanger

• Air blown across finned tubes (forced draught type)

• Can suck air across (induced draught)

Finned tubes

Air cooled heat exchanger bundle

Advantages/disadvantages of air

cooled heat exchanger • Advantages

– Air is readily available always

– Low maintenance costs, negligible air side fouling

– Simple mechanical design

– Natural convection operates if power fails

• Disadvantages

– Noisy – low-noise fans are available but inefficient

– Cold weather protection problems

– Less effective than cooling tower

Plate-fin exchangers

• Formed by brazing

aluminium plates separated

by sheets of finning

• Noted for small size and

weight, but limited range

of fluids

• Very high e , very low T

• Main use in cryogenic applications (air liquefaction)

• Must only be used with clean fluids

Cooling towers

• Base filled with packing over which water is sprayed

• Cooling by air flow and evaporation

• Air flow driven by forced or natural convection

• Must make up the cooling water lost by evaporation

Agitated vessels

• Used for batch heating

or cooling of fluids

• An agitator and baffles

promote mixing

• A range of agitators are

used

• Often used for batch

chemical reaction

Distribution of types in terms of market value in Europe

Shell & Tube

42%

Other Tubular

5%

Plate & Frame

13%

Other Plate

4%

Other Proprietary

2%

Air Coolers

10%

Cooling Towers

9%

Waste Heat

Boilers

5%

Other Heat

Recovery

10%

Design method for shell-and-tube

heat exchangers

• Very wide range of temperatures (up to 600oC), pressures (up to 300/1400 bar), fluids, duties

• Can be built in many materials

• Many suppliers

• Repair can be by non-specialists

• Design methods and mechanical codes have been established from many years of experience

Over 80% of new exchangers for oil-refining, chemical,

petrochemical and power companies in Europe are S&T.

The design procedure (single phase)

1. Specification

2. Physical properties

3. Overall heat transfer coefficient estimation

4. Pass arrangement, mean temperature difference

5. Heat transfer area

6. Allocation of fluids

7. Tube size and number

8. Tube-side heat transfer coefficient

9. Tube layout (inc. baffle spacing), shell type

10. Bundle and shell diameter

11. Shell-side heat transfer coefficient

12. Overall heat transfer coefficient

13. Tube-side and shell-side pressure drops

14. Cost estimation

15. Optimisation

Estimate tube-side heat

transfer coefficient

Calculate shell diameter

Estimate tube-side heat

transfer coefficient

• For process fluid, we usually know

– type, mass flow, inlet and outlet temperature, pressure, PMAX

• For service fluid, we usually know

– type, mass flow, inlet temperature, pressure, PMAX

• We must estimate fouling factors

– e.g. water 0.0001-0.00025 m2K/W, air 0.0001-0.0002 m2K/W

• We must calculate duty (i.e. overall heat transfer rate)

– from Q = m1 CP1 T1 for process fluid (CP at mean temp.)

• We must calculate outlet temperature for service fluid

– from T2OUT = (Q / m2 CP2) + T2IN for fluid 2, iterating for CP

• For each fluid, we will need (at mean temperature):

– specific heat, thermal conductivity, density, viscosity

Specification and physical properties

Estimating UO, overall heat transfer

coefficient

• We need to estimate overall heat transfer coefficient at

this stage to allow an initial calculation of total heat

transfer area. A better value will eventually be

calculated, and iterations can be performed if necessary.

• Typical values for overall heat transfer coefficients in

shell-and tube heat exchangers may be obtained from

various sources, e.g.:

– C&R6 Table 12.1 and Figure 12.1

– Perry’s Chemical Engineers’ Handbook, Table 11.3 (7th Edn.)

– Engineering Science Data Unit (Data Item 92013)

Shell-side and tube-side passes

• Generally one or two shell-side passes

• Tube-side passes usually achieved by header partitions

One-pass shell (Type E) Two-pass shell (Type F)

Longitudinal baffle

One tube pass two tube passes four tube passes

Calculation of total heat transfer area

We estimate the area (based on tube O/D) from

)(

)(ln

)()(

INOUT

OUTIN

INOUTOUTINLM

tT

tT

tTtTT

TAUQ OO

For pure counter-flow heat exchangers LMTT

where

For shell-and tube heat exchangers, pure counter-flow only obtained for 1:1 and 2:2 designs (shell:tube passes).

What about other (more common) designs?

HEAT EXCHANGER

SHELL SIDE

TUBE SIDE

TIN TOUT

tIN tOUT

Area for non-counter-flow exchangers

• Theoretical correction factors, FT, have been derived for

each non-counter-flow design of heat exchanger:

LMTOO TFAUQ

• FT values are less than 1, but do not design for FT < 0.8

R=0.1 R=0.8 R=3.0 R=15

FT

0.6

1.0

0.0 1.0 0.5 S

ININ

INOUT

tT

ttS

INOUT

OUTIN

tt

TTR

Allocation of fluids

• Put dirtier stream on the tube side - easier to clean inside the tubes

• Put high pressure stream in the tubes to avoid thick, expensive shell

• When special materials required for one stream (e.g. due to corrosion or very high temperatures), put that one in the tubes to avoid expensive shell

• Cross-flow gives higher film coefficients than flow in tubes, hence put fluid with lowest film coefficient on the shell side

• If no obvious benefit, try streams both ways and see which gives best design

Tube size, tube-side velocity

• Most common tube O/Ds 19.05 and 25.40 mm, with tube

thicknesses 2.11 and 2.77 mm (carbon steel)

• Standard tube lengths 2.44, 3.66, 4.88, 6.10 and 7.31 m

• Total number of tubes given by:

• Tube side velocity then given by:

• For liquids, typically 1.0 < uT < 2.5 m/s

• For vapours and gases, 5 < uT< 70 m/s depending on

pressure

ld

AN

o

OT

2

4

iT

PT

dN

Nmu

Tube-side heat transfer coefficient

• The Dittus-Boelter equation

for non-viscous liquids

n0.8PrReuN 023.0

n = 0.4 for heating, 0.3 for cooling

• The Sieder-Tate equation for viscous liquids

14.0

027.0

W

0.330.8PrReuN

• Useful general form (Colburn)

14.0

W

0.330.8PrReCuN

C = 0.021 (gases), 0.023 (non-viscous liquids), 0.027 (viscous liquids)

Fully developed turbulent flow in smooth pipes (Re > 8000)

NB properties evaluated at mean bulk temperature along pipe

Tube-side heat transfer coefficient

• Heat transfer coefficient for viscous flow can be estimated from:

14.033.0

33.0)(86.1

W

i

L

dPrReuN

or 3.5, whichever larger

• For non-viscous flow, coefficient is 1.62, no correction

• Note that tube length-to-diameter ratio has a large

effect on heat transfer coefficient below ~ 500

• For transition flows (2000 < Re < 8000), evaluate h for

both laminar and turbulent flows and use lower value

Laminar flow in smooth pipes (Re < 2000)

Heat transfer factor, jh

• Heat transfer data may be usefully correlated using a

heat transfer factor, jh, which allows laminar and

turbulent regimes to be represented on one graph

• We then have for non-viscous flow:

33.0

67.0Re62.1

L

dj ih

2.0023.0 eRjh

Laminar:

Turbulent:

PrRe

NuSt,PrSt

14.0

67.0

W

hj

Definition:

Tube arrangements

• Recommended pitch = 1.25 x tube O/D

• Triangular and rotated triangular arrangements give

more tubes per unit area

• Square arrangement gives lower heat transfer rates

• Square and rotated square layouts give cleaning lanes

pitch, p

Triangular Rotated

triangular

Square Rotated

square

transverse pitch, ptr Flow

Tube bundle diameter

• Tube bundle outside diameter given by n

ToB

K

NdD

1

where K and n are empirically derived for triangular and

square arrangements, p = 1.25 do

Tube shell diameter

• Derived from tube bundle diameter plus shell-to-bundle

clearance (shell inside diameter minus bundle outside

diameter)

• Shell-to-bundle

clearance depends on

shell design

– tube bundle removal

(cleaning, tube

repair/replacement)

– differential expansion

Bundle diameter, m

0.2 1.2 0.4 0.6 0.8 1.0

100

0

80

60

40

20 S

he

ll I/

D -

bu

nd

le O

/D, m

m

Pull-through floating head

Split-ring floating head

Outside packed head

Fixed and U-tube

Baffle design

• Typical ratio (DS /lB) 5

• Gives good heat transfer and

acceptable pressure drop

lB

DS

Shell-side (cross-flow) velocity

• The shell-side velocity uS is calculated at the shell equator

using the “minimum cross-flow area” AS

• This is the area without tubes, (DS lB), multiplied by a

blockage factor b which is a function of tube arrangement

p

db o1

p

db o1155.1

p

db o1414.1

Triangular, square

Rotated triangular

Rotated square

• uS is then calculated

using:

S

SA

mu

• typically for liquids,

0.3 m/s < uS < 1.0 m/s

Shell-side heat transfer coefficient using Bell’s method

• Method originally set out by Bell (1960, 1963)

• “Ideal” cross flow coefficients are corrected for

non-idealities which occur in real shell-side flows

• Reasonably accurate while remaining simple and

suitable for manual calculations

• Other methods exist – e.g. Kern’s method (less

accurate), Tinker’s method (complex and tedious)

• Bell gives a similar method for shell-side pressure

drop (see later)

Shell-side non-idealties

Window

effects

Tube

bundle

bypass

Baffle

leakage

Number

of rows

crossed

Bell’s method for shell-side heat

transfer coefficient

LBWNoco FFFFhh

Where

hoc is the heat transfer coefficient for cross-flow over

an idealised tube bank

FN allows for the number of tube rows crossed

FW corrects for some tubes being in the window

FB corrects for bypass flow around the bundle

FL corrects for leakage through and around the baffle

Ideal cross-flow coefficient

14.0

33.0

W

hooc PrRej

k

dhNu

As for tube-side

coefficient:

• Definition of jh same as for tube-side

• jh is similarly plotted against Re - C&R Figure 12.31

• But values are NOT the same as for tube-side !

• IMPORTANT: Re is calculated using us, the shell-side velocity calculated at the minimum cross-flow area AS at the equator of the bundle. Also Re and Nu use tube O/D do.

Correction FN:

number of tube rows crossed

Mean h depends on the number of rows

crossed, because of the turbulence generated

as the fluid flows through the bundle

• Re > 2000, turbulent: use C&R Figure 12.32

• 100 < Re < 2000, transition: use FN = 1.0

• Re < 100, laminar: not well established

Note: no. of rows Ncv is

between adjacent baffle tips Ncv

• Use C&R Figure 12.33:

FW plotted against RW, the ratio of the number of tubes in the window zones to the total number in the bundle

Correction FW: window correction factor

Accounts for the flow through

the window zones not being

ideal cross-flow

Example:

RW = 8/28

= 0.286

FW = 1.08

Correction FB: bypass correction factor

Accounts for flow that bypasses the

bundle in a vertical sense – i.e.

through the gap between the bundle

and the shell wall

• Use C&R Figure 12.34:

FB plotted against (AB/AS)

AB is the bundle-shell clearance area = lB(DS – DB)

AS is the minimum cross-flow area

Correction FL: leakage correction factor

Accounts for horizontal leakage flow –

i.e. through the gaps between tube and

baffle, and between baffle and shell

• Atb is the tube-to-baffle clearance area, per baffle

Asb is the shell-to-baffle clearance area, per baffle

AL = Atb + Asb, and AS is the minimum cross-flow area

L

sbtbLL

A

AAF

21

• C&R Figure 12.35 gives

L plotted against (AL/AS)

Overall heat transfer coefficient

UO defined on basis of tube outside area:

i

o

w

o

i

oi

i

o

oO d

d

k

d

d

dr

hr

hUln

2

111

yw

Thot

Tcold

di

do

yw

Next steps

• Compare calculated UO with assumed value

• If necessary, modify design in second iteration

using calculated UO

• But also need to consider tube-side and shell-

side pressure drops – these must remain within

specification

• P = f (velocity, dimensions, friction factor)

Tube-side from familiar pipe flow equations (fluids)

Shell-side using Bell’s method (similar to h)

Tube side pressure drop

• General equation 2

42uρ

d

Lfp

i

837Re,Re

16f

837Re,Re

264.00035.0

42.0f

• Laminar flow

• Turbulent flow in

a rough tube

• Result is corrected by various factors accounting for

tube inlets and outlets, header flow reversal, and

header ports

Shell-side pressure drop by

Bell’s method

• Similar in concept to Bell’s method for hO

• Cross-flow, window, end zone and nozzle pressure

drops calculated separately and summed

OUTIN NNEWBCBS ppppNpNp 2)1(

pC

pW pE

pN

Shell-side pressure drop by

Bell’s method

• Cross-flow and end pressure drops from

correlation for ideal tube bank, corrected for

by-pass and leakage

• Window pressure drop from specific

correlation for window flows, corrected for

leakage only

• Nozzle pressure drops from correlations for

sudden expansions/contractions

Estimating cost

• The cost estimation method given here is based only on equipment cost

• Note: installation costs can be as high as equipment cost in some cases

• Cost estimation often done by multiplying the calculated area, A, by a “cost per unit area”

• But, when comparing exchangers, U and A vary widely from type to type. It is also difficult to define A if there is a complicated extended surface.

• Hence, ESDU give tables of C values where C is the “cost per UA” - using 1992 prices

Heat transfer from finned tubes

• For tube heat transfer where the external fluid is a

gas, and coefficients are very low

• Aim is to maximise heat transfer area per unit tube

volume, by adding transverse fins to outside of tube

L-fins

Formed by tightly

winding L-shaped

strip

G-fins

Formed by locking

strip into groove

on tube

Extruded fins

Formed by

extruding fins on

outer tube

Local heat transfer coefficient for

finned tubes

• Briggs and Young correlation for

banks of tubes in cross-flow with

plain transverse fins

• Length term in Nu and Re is tube o.d.

• Cross-flow Re taken at AS (no fins)

• h is referenced to fin area

tf pf

lf

1134.02.0

33.0681.0134.0

f

f

f

ff

t

p

l

tpPrReuN

Overall heat transfer coefficient

from finned tubes

i

o

w

o

i

oi

i

o

oO d

d

k

d

d

dr

hr

hUln

2

111

o

o

rh

1is referenced to un-finned tube area BUT assumes

We use:

f

of

ff

o

o A

Ar

hEr

h

111

Af = fin area

Ao = bare tube area,

Ef = fin effectiveness

(< 1, typically 0.95)

( )Pr,GrNu f

Heat

high density

low density

where Gr is Grashof number

2

23

Gr

Tlg

forcesviscous

forcesbuoyancy

From a dimensional analysis of natural convection:

= coefficient of volume expansion g = gravity

l = characteristic length T = Tsurface Tdistant fluid

Natural convection

( )nPrGrNu C

Many workers have studied

natural convection from

various surfaces to a range

of fluids. Generally:

Natural convection

where values for C and n

are tabulated for different

geometries and regimes –

see C&R Vol. 1 Table 9.5 Results for natural convection from

horizontal surfaces

Natural convection

Fluids between two surfaces

For heat transfer between two large parallel plates where

surface dimensions are large compared to separation:

1kQ

Q

( ) 25.0PrGr15.0

kQ

Q

( ) 33.0PrGr05.0

kQ

Q

Gr Pr < 103

104 < Gr Pr < 106

Gr Pr > 106

Where Qk is the rate heat

would be transferred by

conduction alone, and Q

is the actual rate.

Characteristic length in

Gr is plate separation.

Natural convection from pipes to air

Calculation of heat loss to environment from pipes

Geometry Gr Pr C'' n

Vertical

tubes

109 1.37 0.25

> 109 1.24 0.33

Horizontal

tubes

109 1.32 0.25

> 109 1.24 0.33

then h = C'' (T )n l (3n-1) where

Assume the environment is air at 294K

Radiation heat transfer

• Black body radiation

• Radiation properties

• Grey bodies and real surfaces

• The view factor

• Radiation exchange between two surfaces

• Two-surface enclosures

• Gas radiation

• Furnaces and fired heaters

Radiation heat transfer

The Electromagnetic Spectrum

3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12

Thermal

radiation

Infrared Ultra-

violet

rays

X-rays

Radio

wavesVisible

log , m

3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12

Thermal

radiation

Infrared Ultra-

violet

rays

X-rays

Radio

wavesVisible

3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -123 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -123 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12

Thermal

radiation

Infrared Ultra-

violet

rays

X-rays

Radio

wavesVisible

log , m

Energy density of radiation per

unit area per unit wavelength

f (wavelength,

temperature) =

Stefan-Boltzmann law for

black body radiation

If we integrate the function for energy density over all

wavelengths, the total energy Eb (W/m2) is given by:

4TEb

= 5.669 x 10-8 W/m2K4 (Stefan-Boltzmann constant)

T is absolute temperature, K

Eb is the emissive power of an ideal radiator, i.e one that

absorbs all radiation incident on it and radiates across the

whole spectrum – the so-called black body

Energy distribution - black body

Wien’s law:

Tmax = 0.00288

0

10

20

30

40

50

60

0

2 4 6 8 10

Wavelength (m)

1400K

1100K

850K

550K

Mo

nochro

matic e

mis

siv

e p

ow

er

(kW

/m2.

m)

Radiation properties

= reflectivity

(fraction reflected)

= absorptivity

(fraction absorbed)

= transmissivity

(fraction transmitted)

+ + = 1

Incident radiation Reflected

Absorbed

Transmitted

• For opaque bodies, = 0 (we will only consider opaque bodies)

• For black bodies, = 0, = 0, = 1

• Reflected radiation can be diffuse (uniform in all directions) or

specular (angle of reflection = angle of incidence)

Kirchhoff’s identity

Body of area A in a black enclosure,

receiving radiant flux G and emitting

emissive power E, at equilibrium.

is the emissivity of the

body, e

EA = GA

If replace body with black body of

same size,

EbA = GA (as = 1)

GA EA

body

black enclosure

bE

E

bE

E

and e =

Thus

Grey bodies and real surfaces

The monochromatic emissivity, e, is defined as the

ratio of the monochromatic emissive power of the

body to that of a black body at the same temperature

and wavelength:

ebE

E

• For grey bodies, e = constant (< 1) and

• For real surfaces, e = f (, T) constant

• Tabulated values for many real surfaces

4εTσE

Energy distribution - real surfaces

0

10

20

30

40

50

60

Mo

nochro

matic e

mis

siv

e p

ow

er

(kW

/m2.

m)

0

2 4 6 8 10

Wavelength (m)

e = e = 1 (black body)

e = e = 0.6 (grey body)

real surface

The view factor

(also known as shape, angle or geometric factor)

The view factor, Fij, is the fraction of the radiation

leaving surface i that strikes surface j directly.

By definition, the energy leaving surface 1 and arriving

at surface 2 is Q12 = Eb1A1F12

And the energy leaving surface 2 and arriving at

surface 1 is Q21 = Eb2A2F21

So the net exchange is Qnet 12 = Eb1A1F12 – Eb2A2F21

The view factor

Net exchange is Qnet 12 = Eb1A1F12 – Eb2A2F21

But if T1 = T2, then Qnet 12 = 0 and Eb1= Eb2

So A1F12 = A2F21, or more generally AmFmn = AnFnm

This is known as The Reciprocity Rule

F can be easily derived

for simple geometries:

otherwise results are

presented graphically dA1

A2

D

R

e.g. small-area

element to disk

22

2

124 DR

DF

The view factor

The Summation Rule

The sum of the view factors from surface i of an enclosure to all

surfaces of the enclosure, including to itself, must equal unity

11

N

j

ijF

The Superposition Rule

The view factor from a surface i to a surface j is equal to the

sum of the view factors from surface i to the parts of surface j

Nijijijij FFFF ...21

The Symmetry Rule

Two or more surfaces that possess symmetry about a third

surface will have identical view factors from that surface

Radiation exchange between two

“enclosed” surfaces

“Enclosed” surfaces exchange heat with each other only

One or both surfaces

grey:

More complex – we use the

concept of radiosity

Both black surfaces: Easy, as no radiation is reflected,

re-absorbed, re-reflected etc. etc.

( )4

2

4

1121

4

2212

4

112121 TTFATFATFAQnet

4

112121 TFAQ

4

221212 TFAQ and:

Radiation exchange between

two “enclosed” grey surfaces

( )( ) ( ) 222121111

4

2

4

112

/1/1/1 AFAA

TTQ

eeee

We will consider four special cases of a two-surface enclosure:

• Small convex object in a large enclosure

• Infinitely large parallel plates

• Infinitely long concentric cylinders

• Concentric spheres

Making use of the concept of radiosity, the total flux leaving a

surface, we can show that for two enclosed grey surfaces:

Two-surface enclosures

( )( ) ( ) 222121111

4

2

4

112

/1/1/1 AFAA

TTQ

eeee

1

2 Q Small convex object in a large enclosure

F12 = 1, A1/A2 0 ( )4

2

4

11112 TTAQ e

1

2

Q

Infinitely large parallel plates

F12 = 1, A1 = A2 ( )1/1/1 21

4

2

4

112

ee

TT

A

Q

Two-surface enclosures

( )( ) ( ) 222121111

4

2

4

112

/1/1/1 AFAA

TTQ

eeee

Infinitely long concentric cylinders

F12 = 1

A1/A2 = r1/r2

( )( ) 2121

4

2

4

1

1

12

/1/1/1 rr

TT

A

Q

ee

Concentric spheres

F12 = 1

A1/A2 = (r1/r2)2

2

1

Q

2

1

Q ( )( )( )2

2121

4

2

4

1

1

12

/1/1/1 rr

TT

A

Q

ee

Gas radiation

• Most monatomic and diatomic gases are transparent to

thermal radiation.

• HOWEVER many polyatomic gases are not, both

absorbing and emitting considerable amounts at

certain frequencies

• and e are functions of (Pgl), where Pg is gas partial

pressure and l is path length through gas. Curves are

available for certain gases (e.g. H2O).

• If the gas is particle-laden (e.g. flame), then further

emission/absorption, f(particle concentration, size)

Furnace and fired heater design

Radiant heat exchangers, in which the

source of heat is the combustion of a fuel

• Fired heaters

Process stream heated by passage through a

coil or tube-bank enclosed in a furnace: wide

variety of applications

• Steam boilers

For raising saturated or superheated steam for

use in processes or for power generation

Fired heaters

Radiant

tubes

Radiant

coil

Radiant

tubes

Convection

bank

Burner Burner Burners

all radiant,

vertical tubes

all radiant,

helical coil

radiant/convective,

helical coil