Radiative heat flux

The heat flux, E, from BLEVEs is in the range 200 to 350 kW/m is much higher than in pool fires because the flame is not smoky. Roberts (1981) and Hymes (1983) estimate the surface heat flux as the radiative fraction of the total heat of combustion according to equation 9.1-32, where E is the surface emitted flux (kW/m ), M is the mass of LPG in the BLEVE (kg) h, is the heat of combustion (kJ/kg), is the maximum fireball diameter (m) f is the radiation fraction, (typically 0.25-0.4). t is the fireball duration (s). The view factor is approximated by equation 9.1-34. where D is the fireball diameter (m), and x is the distance from the sphere center to the target (m). At this point the radiation flux may be calculated (equation 9.1-30). 

Experiments can be performed where chemical, convective and radiative heat release rates can be measured at various external heat flux values. Linear relationships should be found for the experimental data, where the slope is equal to xj (AH /L). 

Convective heating in fire conditions is principally under natural convection conditions where for turbulent flow, a heat transfer coefficient of about 10 W/m2 K is typical. Therefore, under typical turbulent average flame temperatures of 800 °C, we expect convective heat fluxes of about 8 kW/m2. Consequently, under turbulent conditions, radiative heat transfer becomes more important to fire growth. This is one reason why fire growth is not easy to predict. 

Note that if this net flux is for a heat flux meter cooled at 7 ,XJ, the ambient temperature, the gage directly measures the external incident radiative and flame heat fluxes. 

The net heat flux is taken here to represent radiative heating in an environment at Tcx, with an initial temperature T,yj as well. From Equation (7.20) a more general form can apply if the flame heat flux is taken as constant. This nonlinear problem cannot yield an analytical solution. To circumvent this difficulty, the radiative loss term is approximated by a linearized relationship using an effective coefficient, hr ... 

The Ahmad and Faeth [18] data encompass alcohols saturated into an inert wall of xp up to 150 mm and xf up to 450 mm. Typically, qf is roughly constant over the visible flame extension (4) with values of between 20 and 30 kW/m2. The same behavior is seen for the radiatively enhanced burning of solid materials - again showing q values of 20-30 kW/m2 over 4 for Xf up to 1.5 m. These data are shown in Figure 8.13. Such empirical results for the flame heat flux are useful for obtaining practical estimates for upward flame spread on a wall. 

The inclusion of radiative heat transfer effects can be accommodated by the stagnant layer model. However, this can only be done if a priori we can prescribe or calculate these effects. The complications of radiative heat transfer in flames is illustrated in Figure 9.12. This illustration is only schematic and does not represent the spectral and continuum effects fully. A more complete overview on radiative heat transfer in flame can be found in Tien, Lee and Stretton [12]. In Figure 9.12, the heat fluxes are presented as incident (to a sensor at T,, ) and absorbed (at TV) at the surface. Any attempt to discriminate further for the radiant heating would prove tedious and pedantic. It should be clear from heat transfer principles that we have effects of surface and gas phase radiative emittance, reflectance, absorptance and transmittance. These are complicated by the spectral character of the radiation, the soot and combustion product temperature and concentration distributions, and the decomposition of the surface. Reasonable approximations that serve to simplify are ... 

Radiation increases with scale while convection drops as the diameter increases. Local resolution of these flame heat fluxes were estimated by Orloff, Modak and Alpert [15] for a burning 4 m vertical wall of PMMA. It is clearly seen that flame radiative effects are significant relative to convection. 

Solution At extinction we expect the flame to be small so we will assume no flame radiative heat flux and Xr = 0. This is not a bad approximation since near extinction soot is reduced and a blue flame is common. For PMMA, Ij., = 1- Substituting values into Equation (9.79), we obtain (approximating Lm L)... 

PMMA bums in air at an average m" — 15 g/m2 s. Air temperature is 20 °C and the heat transfer coefficient is 15 W/m2 K. Determine the net radiative heat flux to the fuel surface. What amount comes from the flame ... 

A polypropylene square slab, 0.3 m on a side, bums in a steady manner. Polypropylene does not char, and it can be considered that its radiation characteristics do not vary, with the flame radiative fraction at 0.38 and the flame incident heat flux to the fuel surface at 25 kW/m2. It burns in a wind as shown in various conditions as specified. Its convective heat transfer coefficient can be taken as 50 W/m2 K. The properties of polypropylene are listed as follows. 

A conservative estimate of the resulting surface temperature is obtained by assuming no convective heat losses from the target structures. Equation 5-23 is used to calculate the surface temperature of the equipment due to an incident radiative heat flux from the fire and accounting for only radiation losses from the target. 

With aflame length of 13.9 m, the jet flame will impinge on the steel structure overhead. Consequently, the steel will see high convective and radiative heat fluxes on the order of 200 kW/m. Since the structure will be exposed to direct flame impingement, the expected failure time would be 3-4 minutes (Table 5-7) or less due to the high heat flux from the jet fire, depending on the type of steel structure and design factor of safety. 

If this excess absorption by clouds is ultimately shown to be a real phenomenon, then an increased cloud formation and extent due to anthropogenic emissions may alter the radiative balance of the atmosphere not only through increased reflectance but also through increased absorption of solar radiation. Such an effect could impact atmospheric temperatures, their vertical distribution, and circulation, as well as surface wind speeds and the surface latent heat flux (Kiehl et al., 1995). Hence establishing if this is truly excess absorption, and if so, its origins, is a critical issue that remains to be resolved. 

Surface S6 is in direct contact with the gas. In this case there is a mass continuity with the channel flow, insulation for the electric and ionic current current, while the heat flux is composed of two terms, one considering the heat flux exiting the gas channel, plus one heat source represented by the radiative heat from the current collector ... 

The heat flux at any given surface is comprised of both convective and radiative components. The convective heat flux between the gas and solid is obtained through the use of a convective coefficient ... 

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