OCR Text |
Show Continuity Equation: d d;(p~) = 0 . pV = COilS!. Energy Equation: - k-d2T+ pC YrnI~T +dq-"""= O d;r2 P dx dx Dimensionless parameters: the optical thickness t = ~x ; to = ~L the extinction coefficient ~ = lCabs + a sca the single scattering albedo C1)o = a scalP 9=L . 91 =!L T2' T2 N - conduCDO" - ~ 1 - rad,anon - O~ 2 Eqn. (2) can be dimensionless as N - corrw.cDO" _ pe"V 2 - rad,anon - o~ (ii) Boundary Value Problems of Nonlinear Ordinary Differential Equations Eqn. (3) can be rearranged as N d2e'+1 N dO,.1 (1 )(94 \II) 0 - 1 t.h2 + 2-;;;- + - C1)o ,+1 - T 1+1 = Incident radiation '1';+1 = G..:. = 211E'l(t) + 21'lE'l(to -t)+2J~[(1-C1)o)9~(t)+ :°'l',(t)] OJ 2 .El(t-t)dt+2J~0[(I-C1)o)9;(t)+ :°'1',(/)] ·E1(t-t)dt The radiosities of the two boundary surfaces 11 =E 1 91 + 2(I-E 1 ) (J'lE) (to) + J~O[(1 - C1)o)9:(t) + :0'1' ;(1)] . E2(t)dt} Boundary Conditions: 9(0) = 9 1 9(to) = 1.0 (iii) The Numerical Procedures: (1) (2) (3) (4) (5) I. The function 9,(t), 'I',(t) are initially assumed and inserted into Eqn. (6) to calculate 11 ,J2 . 3 |