2/9/06 KEY CONCEPTS FROM LAST TIME blackbody Planck's law Wien's disp. law Stefan-Boltzmann law solid angle intensity emissive power I_λ = Power radiated / Projected area = P_λ / dA_d * dλ * dΩ = P_λ' / dA * cos θ * dλ * dΩ P_λ' = I_λ * dA * cos θ * dλ * dΩ P_λ = ∫ I_λ * dA * cos θ * dλ * dΩ E_bλ = πI_bλ Lambert's Law: Lambert's surface Intensity is a scalar WHY DOES IT VARY IN DIFFERENT DIRECTIONS? PHASE SPACE (wx, wy, wz) f(x, y, z, vx, vy, vz, t) (x, y, z) t DIST. FUNCT HOW TO MAKE A BLACK BODY "HOLRAM" RADIATION PRESSURE FΔt = Δp = Δmv, no rest mass so p = h/λ P_r = ∫ I_λ / hν * h/λ * cos θ dΩ = 2πI_b / hc P_r = 2E_b / 3c FOR VISIBLE LIGHT => LUMINOUS INTENSITY L_λ = K_λ * I_λ LUMINOUS EFFICIENCY K_max = 683 lm/W * FOR 60W LIGHT BULB -> 840 lumen -> 3W 0.4 0.565 0.7 [μm] EMISSIVITY E' = (I_λ cos θ dA dλ dΩ) / (I_bλ cos θ dA dλ dΩ) = P_λ / P_bλ ε' = I_λ / I_bλ "SPECTRAL-DIRECTIONAL EMISSIVITY" ε_λ = ∫ ε'λ cos θ dΩ / ∫ cos θ dΩ ε = ∫ ε_λ E_bλ dλ / ∫ E_bλ dλ DIFFUSE ε' = ε_λ GRAY ε' = ε DIFFUSE-GRAY ε' = ε (IDEAL SITUATION) REFLECTION COULD BE BOUND BY A PARTICULAR REGION REFLECTION ABSORPTION TRANSMISSION ABSORPTIVITY α_λ' = H_aλ' / I_λ α_λ = H_aλ / H_λ SPECTRAL DIR. IRRADIATION α_λ'(T, θ, ψ, λ) SPECTRAL-DIRECTIONAL-HEMISPHERICAL EMISS. α_λ = ∫ dI_λ cos θ_r dΩ_r / H_λ dΩ_i = ∫ φ_λ'' cos θ_r dΩ_r / π WILL GET 8 VERSIONS, BECAUSE NOW, REFLECTION IS DIRECTIONALLY DEPENDENT. FROM AN NER BALANCE ε + α + τ = 1 ε'_λ + α'_λ + τ'_λ = 1 IF OPAQUE, THEN τ = 0 AND ε + α = 1 KIRCHHOFF'S LAW ε'_λ(T,θ,φ) = α'_λ(T,θ,φ) BLACK BODY ε'_λ(T) = α'_λ(T) IF LINEAR, ONLY EMITTER TEMP. MATTERS IF DIFFUSE GRAY, ε = ε_λ **IF GEOMETRY OF STRUCTURE IS IMPORTANT, PPL. WILL USE** "TRANSMITTANCE" "REFLECTANCE" "ABSORPTANCE" "EMITTANCE" RADIATION TRANSFER q' = εE_b(T) - αE_b(T₀) BLACK SURROUNDINGS T₀ q' = εσ(T⁴ - T₀⁴) SANITY CHECK: WHEN T = T₀ NO HEAT TRANSFER FOR 2 SURFACES.... T₁, A₁ I = P' / (cos θ₁ dA₁ dΩ₁) T₂, A₂ L = cos θ₁ dA₁ / S₂ P' = I dA₁ cos θ₁ dΩ₁ P_tot = ∫∫ I dA₁ cos θ₁ dΩ₁ F₁₂ dA₁ = ∫∫ P' / P_tot * cos θ₁ dΩ₁ "view factor"

Lecture 2 Notes: View Factor and Simple Radiative Transfer

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