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€ € *We can also write these on a spectral basis as well. 19 Radia%on Heat Transfer Reﬂec%vity 20 Radia%on Heat Transfer Transmissivity Solar Irradia%on 21 Example 2 • Assume solar irradia%on is propor%onal to a blackbody with a temperature of 5800 K, is incident upon a quartz glass window with a transmissivity of 0.93 over the bandwidth 0.2 µm – 4 µm and approximately 0, elsewhere in the spectrum. What is the total transmissivity of the glass. 22 Radia%on Heat Transfer • Kirchoﬀ’s Law and Grey Surfaces – Kirchoﬀ’s Law in radia%on states either α = ε, or αλ = ελ, for diﬀuse surfaces in thermal equilibrium. – It can be shown that it holds in general for any condi%on, since α and ε only depend on the surface condi%on and its temperature. – It is also valid under condi%ons illustrated below, i.e. αλ and ελ independent of λ over the spectral regions of irradia2on and emission, providing we have diﬀuse surfaces and diﬀuse irradia2on. 23 Radia%on Heat Transfer • Radia2on Exchange: – We now consider essen%al concepts for diﬀuse radiant exchange between surfaces. – These include the concepts of surface Radiosity and View Factor. – We will present the basic exchange equa%ons for enclosures with both black surfaces and grey surfaces. – In general we assume surfaces are at ﬁxed uniform temperatures, but we may also specify heat ﬂuxes. – We will also limit our analysis to two and three surface systems. 24 Radia%on Heat Transfer • Surface Radiosity: is the combined eﬀect of reﬂected incident radia%on (ρG) and surface radia%on emission (E). In other words the rate at which radia%on leaves a surface: J = E + ρG € 25 Radia%on Heat Transfer • View Factors: 1
Fij =
Ai
1
F ji =
Aj ȹ cosθ i cosθ j ȹ
dqi → j = J i ȹ ȹdAi dA j
πR 2
ȹ Ⱥ
ȹ cosθ j cosθ i ȹ
dq j → i = J j ȹ ȹdA j dAi
πR 2
ȹ Ⱥ
€
qi → j
Fij =
Ai J i ȹ cosθ i cos θ j dAi dA j ȹ
∫∫ ȹ ȹ
πR 2
ȹ Ⱥ
ȹ cosθ j c...
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This document was uploaded on 02/14/2014 for the course ENGR 6901a at Memorial University.
 Fall '12
 DrMuzychka
 Heat Transfer

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