Question

Measurement of the spectral, directional absorptivity of a certain non-reflecting surface shows that directional and spectral dependencies may be model as the product of two independent functions:

αλ, α(λ)α(Θ) α = 0.9 α=0.5 α(0) α(λ) α=0.1 α = 0 λ λ=1 μm θ θ=20° θ =70°

This surface is irradiated by diffuse blackbody radiation at a temperature of 5800 K. Note that the intensity of ideal radiation can be calculated at I_b= E_b/pi(W/m² -sr). The surface is at a uniform temperature of 300 K.

Determine the rate that energy is absorbed by the surface (W/m² )

Determine the net radiation heat flux to/from the surface (W/m² ).

Answer 1

sop Given that Loo 2(1). 10) that means albsorphinity of sentence funcbon of 9th and onentation, co). body spuckel and directional dependent Surface temperature of differed block! look body To=5800k Surface temperature of non black body 11:0) reflecting block body Ts = 300k. Energy radialed by 5-67X10-8 blouk body. Ev sots" Ey x58" 15 p^ Eb: 64164532 32 W/m2 Torstensity of ladialon from black body Top 1 اگ I 64164532-32 T Ij = 20424204.98 l maso the given surfaces Now for applying wein's displaumunt law, ATs = 2998 um =1300) = 2898 um

= q. 66 um .. 4(1) - 0.9 Xx,o ts. the 0.9.0 (O) t&aid=9(1):100) value of onentation is not give co w with vertical) from Icrichoff's laws enie 4,0 Go -0.9.410) => Energy Rate absorbed by surface. Dans = The Is 0.9410) X 20424 204.98 Odbs. = 18381784.48 (40) L m2 Ary taking plate to be homontal vertical (6) - 0.1 . Oabsb. = 183817884.48 X01 Qabul = 1838178.448 il m2 → finding the heat flux net from the surface.

( Q the nat Dobe Q Emitted 18381984.48 210) here x g_91869.5 (coorI boo Ofux 18381 371.14 20 hon nek me. for with vertical. (R (0) = 0.1) o 6) (Ofwer) net • 1838 131-14 X 0.1 (Ojhe Dret = 1838137.114 W ma be

As you can see the orientation is not given so I have to give the answer in function of angle but for standard vertical plate case I have given the answer you can apply the same steps to get answers for new orientations. Please forgive me for any calculation mistake and do comment for any short of queries.