heat lecture 4

1

Carleton University, 82.575 (CVG7300), Fire Dynamics I, Winter

2002 Lecture # 4

1

Fire Dynamics I

Lecture # 4Heat Transfer:

Convection & RadiationJim Mehaffey

82.575 or CVG7300


2002 Lecture # 4

2

Heat Transfer: Convection & RadiationOutline

• Introduction to heat transfer• Heat transfer by convection• Heat transfer by radiation

2


2002 Lecture # 4

3

Introduction to Heat Transfer• Heat is transferred from regions of high temp to

regions of lower temp.

• All three modes of heat transfer play a role in essentially every fire

• Heat transfer by convection• Heat transfer by radiation• Heat transfer by conduction

• However one mode may predominate at a given stage or given location


2002 Lecture # 4

4

Heat Transfer by Convection• Heat transfer between moving fluid & solid

• Important in small fires early stages of fire and in fires that remain small

• Newton’s Law of heat convection

Eqn (4-1)( )sf TTh "q −=•

)K m(W t coefficienfer heat transh(K) surface solid of etemperaturT

(K) gas of etemperaturT)m(W solid togasflux heat "q

12

s

f

2

−−

−•

=

===

3


2002 Lecture # 4

5

Heat Transfer by Convection• Heat transfer occurs across a boundary layer

• h is not a material constant. It depends on the structure of boundary layer & is a function of– Solid’s surface geometry

(dimensions, angle to flow)– Fluid properties

(thermal conductivity, density, viscosity)– Flow properties

(velocity, nature)


2002 Lecture # 4

6

Convective Heat Transfer Coefficient• Free convection: Fluid moves due to buoyancy

caused by hot (cold) surfaceh = 5 to 25 W m-2 K-1

• Forced convection: Fluid flow not caused by hot (cold) surface (e.g. hot smoke past a sprinkler)

h = 10 to 500 W m-2 K-1

4


2002 Lecture # 4

7

Guidance: Thermal Insulation Studies (6)Wall interior (free convection) h = 8.33 W m-2 K-1

Wall exterior (forced convection: wind) h = 33.3 W m-2 K-1

Ceiling (free convection: heat flow up) h = 9.09 W m-2 K-1

Ceiling (free convection: heat flow down) h = 6.25 W m-2 K-1

Roof (forced convection: wind) h = 33.3 W m-2 K-1

These surfaces are all planar


2002 Lecture # 4

8

Wind Chill Factor: Prior to 2001 (5)• Research in Antarctica on freezing of water in a plastic

cylinder under diverse wind & temp conditions yielded:

C = 0.323 (37.62 + 18.97 v1/2 - v) (33 - T)

C = cooling rate (wind chill factor) (W m-2)v = wind speed (km h-1)T = air temperature (ºC)33 = skin temperature (ºC)

• convective heat transfer coefficient

h(v) = 0.323 (37.62 + 18.97 v1/2 - v)

5


2002 Lecture # 4

9

Wind Chill Factor: Prior to 2001 (5)Convective heat transfer coefficient

h(v) = 0.323 (37.62 + 18.97 v1/2 - v)

v (km / h) h(v) (W m-2 K-1)0 12.21 18.04 23.19 27.616 31.525 34.736 37.349 39.264 40.5


2002 Lecture # 4

10

Wind Chill Factor: Prior to 2001 (5)• Wind chill expressed as temperature was defined as

temperature giving the same cooling rate at average walking speed (vr = 6 - 8 km / h)

h(vr) (33 - Tw) = h(v) (33 - T)

Tw = 33 - {h(v) / h(vr)} (33 - T)

6


2002 Lecture # 4

11

Correlations for h available for many configurations and flow conditions

• Drysdale (1): Table 2.4, page 51• SFPE Handbook (2): Tables 1-3.3 & 1-3.4, pages 1-60

to 61


2002 Lecture # 4

12

Guidance: Fire Scenarios• Wall or ceiling exposed to fire:

h = 25 W m-2 K-1

• Wall or floor exposed to ambient:h = 9 W m-2 K-1

• Wall just above advancing flame:h = 15 W m-2 K-1

• Heat detector / sprinkler immersed in ceiling jet:h ∝ (velocity)1/2

7


2002 Lecture # 4

13

Exposure of Skin to Convection (4)• Tenability limit for exposure of skin to convected heat

is 120ºC, above which pain and burns occur quickly.• Depending on length of exposure, convected heat

below 120ºC may also cause hyperthermia.• For fully clothed people, time for incapacitation (t in

min) is given in terms of T (ºC )

t = (4.1 x 108) T-3.61 Eqn (4-2)

• For unclothed or lightly clothed people, time for incapacitation (t in min) is given in terms of T (ºC )

t = (5 x 107) T-3.4 Eqn (4-3)


2002 Lecture # 4

14

Heat Transfer by Radiation• Transfer of energy by electromagnetic waves (infrared)

• Hot objects emit thermal radiation{Blue (visible) → infrared}

• Colour of hot objectsT = 550°C (823 K) - dull redT = 900°C (1173 K) - cherry redT = 1100°C (1373 K) - orangeT = 1400°C (1673 K) - white

8


2002 Lecture # 4

15

Heat Transfer by Radiation• Flame radiation emitted by soot

• Requires no intervening medium between heat source and receiver

• Dominant mode of heat transfer if fire base ≥ 0.3 m

• Determines growth & spread of fires in compartments

• Accounts for fire spread between buildings


2002 Lecture # 4

16

Thermal Radiation

Eqn (4-4)4TE LawBoltzmann -Stefan theyieldshswavelengtallover gIntegratin

εσ=

0.9)(~ emissivityK m W 10 x 5.67

(K)object of etemperaturT)m(W power emissiveE

428

2

==

==

−−−

−

εσ

9


2002 Lecture # 4

17

ε - Emissivity (absorptivity)

• For perfect emitter, blackbody, ε =1

• For most building materials, ε ~ 0.9Usually tarnished (oxidized) early in fire exposures


2002 Lecture # 4

18

ε - Emissivity (absorptivity) (7)

10


2002 Lecture # 4

19

Directional Radiation• Surface 1 radiates with emmissive power E1

• What is radiant heat flux (kW m-2) falling on a point near the centre of surface 2

= E1 F1-d2 Eqn (4-5)

F1-d2 = configuration factor, accounts for spatial relationship between emitter & receiver

q" d21

•

−

2

r

1

θ1

θ2

q" d21

•

−

12

211

d21dA

r cos cos

Eq" ∫=•

− πθ θ


2002 Lecture # 4

20

Configuration Factor F1-d2 (1)

11


2002 Lecture # 4

21



2002 Lecture # 4

22


12


2002 Lecture # 4

23

Addition of Configuration Factors

Ftot-d5 = F1-d5 + F2-d5 + F3-d5 + F4-d5 Eqn (4-6)


2002 Lecture # 4

24

Radiant Exposure of Skin (4)• Tenability limit for exposure of skin to radiant heat is

< 2.5 kW m-2 Eqn (4-7)• Below 2.5 kW m-2, exposure can be tolerated for 30

min without affecting the time available for for escape

• Above 2.5 kW m-2, the time to burning of skin(t in min),

due to radiant heating ( in kW m-2) decreases rapidly as follows

t = 4 { }-1.35 Eqn (4-8)

q" d21

•

−

q" d21

•

−

q" d21

•

−

13


2002 Lecture # 4

25

Radiant Exposure of Wood (1)

• Volatiles from wood may be ignited by pilot after prolonged exposure if

> 12.5 kW m-2 Eqn (4-9)

• 12.5 kW m-2 is the critical radiant flux for the ignition of wood

• Volatiles from wood ignite spontaneously after prolonged exposure if

> 29 kW m-2 Eqn (4-10)

q" d21

•

−

q" d21

•

−


2002 Lecture # 4

26

Spatial Separation between Buildings

• Philosophy based on experiments conducted by NRC referred to as the St. Lawrence Burns

• For office building, assume radiating surfaces (windows) can be characterized by E = 170 kW m-2

• Separation between buildings must ensure heat flux at target building is less than critical radiant flux for piloted ignition of wood (12.5 kW m-2)

14


2002 Lecture # 4

27


2002 Lecture # 4

28

15


2002 Lecture # 4

29


2002 Lecture # 4

30

16


2002 Lecture # 4

31


2002 Lecture # 4

32

17


2002 Lecture # 4

33


2002 Lecture # 4

34

18


2002 Lecture # 4

35


2002 Lecture # 4

36

Radiation: Surface 1 → Surface 2• Surface 1 radiates with emissive power E1

• Radiant heat transfer (kW) from surface 1 to surface 2

Eqn (4-11)

• where F1-2 = configuration factor

Eqn (4-12)

21q −

•

FAE 211121q −−

•

=

212

21

1

21 dAdA r

cos cosA1

F ∫ ∫=− πθ θ

19


2002 Lecture # 4

37

Configuration Factor F1-2 (1)


2002 Lecture # 4

38


20


2002 Lecture # 4

39



2002 Lecture # 4

40

Configuration Factor Algebra

• Reciprocity rule:

A1 F1-2 = A2 F2-1 Eqn (4-13)

• Summation rule:

Eqn (4-14)∑ =−j

ji 1F

21


2002 Lecture # 4

41

Infinite Parallel Plates• Radiative heat transfer is a two-way process• Surfaces 1 and 2 both emit and absorb energy

(net) = net heat transfer leaving surface 1 (kW m-2)

Eqn (4-15)

Eqn (4-16)

q"1•

[ ]42

411,21 TT(net)q" −=

•

σε

1111

212,1

−+=εεε

[ ] (net)q"TT(net)q" 14

14

21,22

••

−=−= σε


2002 Lecture # 4

42

Hot Object in Large Room• Radiative heat transfer is a two-way process• Object and “room” 2 both emit and absorb energy

T1 = Temp of object (K)T2 = Temp of “room” (K)

• (net) = net heat transfer leaving surface 1 (kW m-2)

• For hot object in a large room

Eqn (4-17)

q"1•

[ ]42

4111 TT(net)q" −=

•

σε

22


2002 Lecture # 4

43

Radiation from Luminous Flamesand Hot Smoky Gases

• Luminosity is net effect of emission from soot particles (10-100 nm)

ε = 1 - e-KL Eqn (4-18)

K = effective emission coefficient (m-1)

L = mean beam length (m)


2002 Lecture # 4

44

L = Mean Beam Length (m)

23


2002 Lecture # 4

45

K = Effective Emission Coefficient (m-1)


2002 Lecture # 4

46

References1. D. Drysdale, An Introduction to Fire Dynamics,Wiley, 1999, Chap 12. A. Atreya, “Convection Heat Transfer” Section 1 / Chapter 3, SFPE

Handbook, 2nd Ed. (1995)3. C.L. Tien, K.Y. Lee and A.J. Stretton, “Radiation Heat Transfer”

Section 1 / Chapter 4, SFPE Handbook, 2nd Ed. (1995)4. ISO/DTS 13571, “Life threat from fires - guidance on the estimation

of the time available for escape using fire data”.5. http://www.msc.ec.gc.ca/windchill6. Timber Design Manual7. J.P. Holman, Heat Transfer

heat lecture 4

Documents