Fire Chapter 3

Information about Fire Chapter 3

Published on July 30, 2014

Author: pthomp

Source: authorstream.com

Content

PowerPoint Presentation: Fire, Explosions and Process Safety HEAT TRANSFER Dr Pauline Thompson PowerPoint Presentation: Effects of Heat Flux Only 20-30 % of fire fatalities = direct exposure to heat/flame Maximum heat exposure person can endure for an indefinite period without pain is about 1 kWm -2 Radiant Heat Flux (kWm -2 ) Observed effect 0.67 Summer sunshine in the UK a 1.0 Maximum for indefinite skin exposure (without pain) 6.4 Pain after 8 seconds skin exposure b 10.4 Pain after 3 seconds skin exposure 12.5 Volatiles from wood may be ignited by a pilot (see section 4.3) flame (after ~5mins) 16 Blistering of skin after 5 seconds b 29 Wood ignites spontaneously (see section 4.3) after a few minutes 42 Cotton ignites spontaneously after ~5 seconds 52 Fibre board ignites spontaneously after ~ 5 seconds a PowerPoint Presentation: Convective heat transfer Convection = transport of heat by movement of the medium Liquids and gases only Convective flow - energy transport - with bulk movement Convective heat transfer - energy transfer across a phase boundary e.g. from a fluid to a solid or vice versa PowerPoint Presentation: Newton’s Law of Convection Newton’s Law of Convection states where = heat flux - energy transfer per unit area and time (kWm -2 ) h = convective heat transfer coefficient (kWm -2 K -1 ) = temperature difference Tricky to find h – not constant – function of: the system geometry (e.g. angle to flow) the flow characteristics (e.g. the velocity - laminar or turbulent) the properties of the fluid ( e.g. viscosity, thermal conductivity, density, specific heat) the temperature difference h = 0.005-0.025 kWm -2 K -1 - natural convection h = 0.01-0.5 kWm - 2 K -1 - forced convection PowerPoint Presentation: Conduction Conduction is the transfer of heat either by transmission of energy through the elastic binding forces between atoms or by the motion of molecules or free electrons Steady state conduction – Fourier’s equation Where = the heat flux in the x direction k = the thermal conductivity PowerPoint Presentation: Example 1 Example 1. Heat flux through a wall Wall approximated as infinite planar slab of thickness L with surface temperatures T 1 and T 2 Integrate Fourier’s eqn with constant: PowerPoint Presentation: Example 2. Example 2. Heat flux through a composite wall Wall is infinite. T α and T β are the gas temperatures T at each plane within the solid/at surface are T 1 , T 2 , T 3 , T 4 k and h as given. Assume steady state PowerPoint Presentation: Example 2. Example 2. Heat flux through a composite wall Five equations so eliminate intermed Ts 1-4 to get: If know the convective heat transfer coefficients and the thermal conductivities and thickness of all the materials - can estimate heat transfer through the wall Heat flux through wall sometimes as: where R θ is “thermal resistance” PowerPoint Presentation: Non-steady state conduction Infinitesimal volume with no heat generation within the volume itself the conservation of conductive heat flow gives differential operator - spatial dimensions x , y , z α is the thermal diffusivity of the medium ρ = density (kgm -3 ), c = specific heat (kJkg -1 K -1 ), k = thermal conductivity (kWm -1 K -1 ) t = time (seconds) PowerPoint Presentation: Depth of the heated layer Consider semi-infinite solid initially at T 0 heated to T ∞ Boundary conditions at time t and with temperature T at depth x beneath the surface T = T 0 at t = 0; x > 0 T = T  for all t ; x = 0 T = T 0 for all t ; x   Applying the non-steady state equation where erf ( ) is the error function PowerPoint Presentation: Depth of the heated layer Plane at x = L heated to just above T 0 to say 0.5% of ( T ∞ -T 0 ) T L = T 0 + 0.005( T  - T 0 ). Look up in error tables Since temp does not jump to T immediately safe to assume Depth of heated layer related to α PowerPoint Presentation: Thermal penetration time If the ‘thermal penetration time’, t p Characteristic time, t c is approx time heat output significant If heat doesn’t penetrate wall, t c < t p then effective depth L c is the thermal thickness for a barrier for that fire PowerPoint Presentation: Worked example Compare a steel and a concrete wall for a fire with t c = 500s What is the depth of the heated layer, i.e. thermal thickness?  (concrete) = 5.7 x 10 -7 ms -1  (steel) = 1.26 x 10 -5 ms -1 Heated layer penetrated further into steel (no surprise) For t c = 500s, wall thickness L = 0.05 m = 50 mm. What is the thermal penetration time for each material? much faster through steel PowerPoint Presentation: Radiation Transmission of energy by electromagnetic waves No intervening medium is necessary Thermal electromagnetic wavelengths λ = 0.1–100 μ m R + T + a = 1 PowerPoint Presentation: Black bodies Black body α = 1 Perfect emitter  of 1 where ε λ , α λ are the emissivity and absorptivity at wavelength l Total emissive power (Stefan-Boltzmann’s Law) kWm -2 (T is measured in K) where σ = Stefan’s constant = 56.7 x 10-12 kWm -2 K -4 E b is the rate at which energy is emitted from a unit area of a black body into the hemisphere above it at T (K). PowerPoint Presentation: Grey bodies Emissivity (or absorptivity) assumed independent of λ and T Total emissive power where ε lies between 0 and 1 PowerPoint Presentation: Configuration factor Radiation emitted from finite surface to point on 2 nd surface Need to determine a configuration factor ϕ ; value 0-1 accounts for the relative geometries of the two surfaces Radiative flux at point on surface 2 where Values tabulated in Appendix 2 ‘Finite to infinitesimal’ PowerPoint Presentation: Configuration factor Appendix 2 – values for radiation from rectangle Sides L 1 , L 2 Parallel to infinitesimal element of surface area δ A On line perpendicular to corner of rectangle at a distance x Tabulated in the appendix by the values CFs additive PowerPoint Presentation: Configuration factor PowerPoint Presentation: Worked Example Calculate max heat flux at 5m from wall of the building Emissive power of the windows is 170 kWm -2 Wall is symmetrical - maximum flux opposite the central point Two windows = 1m x 1m, located symmetrically, 1m apart Wall 5m long and 3m high PowerPoint Presentation: Worked Example At observation point - contribution Split into rectangles observer perpendicular to one corner From Appendix 2 = 0.009 = 0.003 ϕ = 4(0.009-0.003) = 0.024 As E = 170 kWm -2 at point of observation = 0.024 x 170 kWm -2 = 4.1 kWm -2 (Extreme pain < 30s, Severe burns 20mins) (If L 1 , L 2 give S>1 then reverse) PowerPoint Presentation: Integrated configuration factor Non-infinitesimal receiving area, i.e. ‘finite to finite’ F 1 , 2 is integrated configuration factor value 0 - 1 derived from the expression by symmetry F 1 , 2 A 1 = F 2 , 1 A 2 ( F 1 , 2 A 1 is ‘ exchange area’) Sometimes terms ‘configuration factor ’/‘ integrated configuration factor ’ confused In USA ‘ view factor’ can mean either configuration factor or integrated configuration factor. PowerPoint Presentation: Summary Heat transferred by convection, conduction and radiation. Convection - moving fluid to transmit heat. Flux depends on temperature difference, convective heat transfer coefficient. Conduction in a solid steady-state when heat flux is constant. If know temperature difference, thickness and conductivity of materials can calculate heat flow across composite material. Non-steady state conduction can estimate the thickness of heated layer if know thermal diffusivity of the material. Important to calculate thermal penetration time of a barrier Thermal radiation - no transport medium. The emissive power of a body depends on the temperature and the emissivity. Heat flux received from radiating body at point needs 3-D modelling of geometries of the surfaces to find a configuration factor for each case. Simple geometries from tables. Over an area need integrated configuration factor. PowerPoint Presentation: Discussion Questions Now we recommend: Read through these sections in the notes Tackle the discussion the questions at the end Work with your fellow students on the discussion boards PowerPoint Presentation: Any Questions ? If so – post them in the discussion boards

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