Analysis of Radiation Heat Transfer in Furnace

P M V SubbaraoProfessor

Mechanical Engineering Department

Test for Cooling Capacity of Furnace Surface….

Complexity of Gas-Wall Radiation Process

Governing equation in a gas radiation

• For gas radiation governing differential equation is known as Radiative Transfer Equation (RTE)

• The RTE for an absorbing, emitting, gray medium is

• Classification: Basic models and their determinants Based on quadrature set Complex geometry of the furnace

b

II I

S

Face 5

Face 4

Face 1

Face 2

x

y

z

L

W

Face 6

Face 3

South

North

EastWest

Hw

n

e

s

μ

η

ξ

Basic models for RTE in gas radiation

2-Flux4-Flux

MultifluxDOM

MomentModified- Moment

PN - Approx.

ZoneMCM

Numerical(FD, FV)

RTE

Optically Thin Self-absorbing Optically Thick

Directional Averaging Differential Approximation

Energy Hybrid

DTMRay Tracing

Radiation Element

Radiation inside furnace

• Types of radiation: Surface and volumetric radiation

• Characterization of participating media: usually, the radiant energy is

scattered, absorbed and emitted by tiny suspended particles or gases like

CO2 and water vapor, such media are called participating media.

• Gas radiation involved

• Absorption: attenuation of intensity absorption coefficient

• Emission: augmentation of intensity emission coefficient • Scattering scattering coefficient

• Radiant heat transfer occur from the source (Flame) to sink (water walls) in a furnace

Gas radiation-Governing equation

Assumptions:

All six boundaries are diffuse and gray

Absorbing, emitting, non scattering gray medium

Same absorption coefficient at all points

Thermophysical properties e.g. density, specific heat, thermal conductivity and optical property like extinction coefficient are constant.

Absorption coefficient = emission coefficient

Face 5

Face 4

Face 1

Face 2

x

y

z

L

W

Face 6

Face 3

South

North

EastWest

Hw

n

e

s

μ

η

ξ

Co-ordinate system for cubic enclosure

Governing equation for participating media (RTE):

b

II I

S

Where; S is line of sight distance in the direction of propagation of the radiant intensity I

Direction cosine in 2D geometry

cos

sinsin

m

m

]1[ ]2[

]3[]4[

x

y

),(:]4[

),(:]3[

),(:]2[

),(:]1[

),(:

mmQuad

m m mm

m m m b

I I II I

x y z

RTE with consideration of direction cosine

Where Im radiation intensity

Boundary condition

;0,)1( '

'0

'

'

mm

mm

b IwIIm

;0,)1( '

'0

'

'

mm

mm

b IwIIm

At x = 0;

At x = L;

DOM with heat generation

, , 04 m m m

m mmG Id w I

Qq .

GTdITq 4

4

4 44.

25.0

4

4

4

GQ

T

QGT

4

G

Q

Ib

Incident irradiation at the center of each cell containing only gas

(Heat generation per unit volume)

Temperature inside the flame cell

Flame cell

Solution of RTE

• The exact (analytical or numerical) solution of integro- differential radiative transfer equation (RTE) is generally a formidable task.

• Although there have been a few attempts to formulate RTE for non-isothermal rectangular enclosures .

• Explicit solutions are only available for simplified situations such as black walls and constant properties etc.

• There is growing interest in approximate solutions for furnace design and analysis.

• The exact solutions even for these simplest systems are used to serve as benchmarks against which the accuracy of approximate solutions is tested.

Radiation heat transferred to furnace wall

• Radiation heat transfer

• Where eff is the emissivity of flame and water wall system.

• Emissivity of PC flame

• S : Effective thickness of radiant (flame) layer.

kWTTAQ wafleffrad 44

wafl

wafleff

111

kpSfl e1

A

VS 6.3

V is the volume of the gas and A is the enclosing surface area

• K is the coefficient of radiant absorption

• Volume fraction of RO2 & H2O : rRO2 & rH2O

• c1 : 1.0 for coal and 0.5 for wood

• c2 : 0.1 for PC flame, 0.03 for Stoker flame.

h : Concentration of ash particles

• dh : diameter of ash particles : 13 m for PC & 20 m for stoker.

MPam

cckrrkk hhOHROy .

1 10 2122

m.MPa10

100037.011

16.3

168.7

22

2

fe

OHRO

Hy

T

Sprr

rk

3122

5990

hfe

h

dTk

Thermal Efficiency Factor,

• If clean water wall is a perfect black body all radiation falling on it will be absorbed.

• Fouling (leads to drop in emissivity of the wall.

• Water walls consists of tubes which generate an angular coefficient, x.

• Angular coefficient varies with the location of water wall.

• Thermal efficiency factor is defined as the fraction of incident radiation absorbed by the tubes:

• The average thermal efficiency factor is calculated as

A

Axn

iiii

1