IV. Radiation Heat Transfer IV. Radiation Heat Transfer
IV. Radiation Heat Transfer IV. Radiation Heat Transfer
IV. Radiation Heat Transfer IV. Radiation Heat Transfer
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<strong>IV</strong>. <strong>Radiation</strong> <strong>Heat</strong> <strong>Transfer</strong>H1d. Forest Fire Example (cont.)2F21=H2+ x2+ x + ∆x−2∆x2 2( x + (x + ∆x)+ H )FTake limit as ∆x →0.x ∆x1 d=2 dx2 2( x − H + x )1 ⎡= ⎢1−2 ⎢⎣x /H ⎤⎥2(x /H) + 1⎥⎦21 (<strong>IV</strong>.C.8)The irradiation on the ground adistance x from the fire islesson 28G1 ⎡2 ⎢⎣x /H ⎤⎥(x /H) + 1 ⎥ ⎦42 ⎢1−σT2f= (<strong>IV</strong>.C.9)<strong>IV</strong>. <strong>Radiation</strong> <strong>Heat</strong> <strong>Transfer</strong>d. Forest Fire Example (cont.)Consider the time to ignition. Assume the followingproperties for wood and flame.T f = 1250 K (1800°F) k = 0.24 W/(m k)H = 5 m ρ = 500 kg/m 3x = 2 m c = 2800 J/(kg K)α= 0.17 x 10 -6 m 2 /s ε = 1Ignition temperature, T ig = 530 K (500°F)Initial temperature of wood, T 0 = 300 KRecall (I.I.4)T(0,t) − T02G2(αt/ π)=k1/ 2(<strong>IV</strong>.C.10)lesson 286
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