Fire Dynamics I

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Fire Dynamics I

• Lecture 4
• Heat Transfer
• Convection Radiation
• Jim Mehaffey
• 82.575 or CVG7300

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• Heat Transfer Convection Radiation
• Outline
• Introduction to heat transfer
• Heat transfer by convection
• Heat transfer by radiation

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• 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

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• Heat Transfer by Convection
• Heat transfer between moving fluid solid
• Important in small fires early stages of fire and
  in fires that remain small
• Newtons Law of heat convection
• Eqn (4-1)

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• 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
• Solids surface geometry
• (dimensions, angle to flow)
• Fluid properties
• (thermal conductivity, density, viscosity)
• Flow properties
• (velocity, nature)

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• Convective Heat Transfer Coefficient
• Free convection Fluid moves due to buoyancy
  caused by hot (cold) surface
• h 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

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• 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

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• 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)

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• Wind Chill Factor Prior to 2001 (5)
• Convective heat transfer coefficient
• h(v) 0.323 (37.62 18.97 v1/2 - v)

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• 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)

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• 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

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• 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

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• 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)

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• Heat Transfer by Radiation
• Transfer of energy by electromagnetic waves
  (infrared)
• Hot objects emit thermal radiation
• Blue (visible) ? infrared
• Colour of hot objects
• T 550C (823 K) - dull red
• T 900C (1173 K) - cherry red
• T 1100C (1373 K) - orange
• T 1400C (1673 K) - white

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• 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

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• Thermal Radiation
• Eqn (4-4)

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• ? - Emissivity (absorptivity)
• For perfect emitter, blackbody, ? 1
• For most building materials, ? 0.9
• Usually tarnished (oxidized) early in fire
  exposures

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• ? - Emissivity (absorptivity) (7)

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• 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

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• Configuration Factor F1-d2 (1)

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• Configuration Factor F1-d2 (1)

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• Configuration Factor F1-d2 (3)

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• Addition of Configuration Factors
• Ftot-d5 F1-d5 F2-d5 F3-d5
  F4-d5 Eqn (4-6)

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

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• Radiant Exposure of Wood (1)
• Volatiles from wood may be ignited by pilot after
  prolonged exposure if
• gt 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
• gt 29 kW m-2 Eqn (4-10)

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• 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)

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• 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)

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• Configuration Factor F1-2 (1)

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• Configuration Factor F1-2 (1)

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• Configuration Factor F1-2 (3)

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• Configuration Factor Algebra
• Reciprocity rule
• A1 F1-2 A2 F2-1 Eqn (4-13)
• Summation rule
• Eqn (4-14)

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• 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)

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• 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)

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• Radiation from Luminous Flames
• and Hot Smoky Gases
• Luminosity is net effect of emission from soot
  particles (10-100 nm)
• ? 1 - e-KL Eqn (4-18)
• K effective emission coefficient (m-1)
• L mean beam length (m)

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• L Mean Beam Length (m)

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• K Effective Emission Coefficient (m-1)

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• References
• 1. D. Drysdale, An Introduction to Fire
  Dynamics,Wiley, 1999, Chap 1
• 2. 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/windchill
• 6. Timber Design Manual
• 7. J.P. Holman, Heat Transfer