Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.mce.biophys.msu.ru/archive/doc15414/doc.pdf Äàòà èçìåíåíèÿ: Wed Sep 26 13:40:48 2007 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 20:04:03 2012 Êîäèðîâêà:

. ., . .

(, )
. , . . , , (, .). . , , . . . . R1 R2 12 = R (.1). z , .
204


. ., . . -- -- 2006, . 2, . 204­215 Krivenko I. V., Smirnova M. A. -- MCE -- 2006, v. 2, p. 204­215

k z. x'y'z' 1. z' k , x' -- E , y' -- H . x1y1z1 x 2 y2 z2 ( x1 x2, y1 y2 ). x1 , k x1O1z, y1 , x1y1z . : r11 , r22 , r .

.1. .

.1 L' , x1O1z x'O1y', L -- x1O1y1 x'O1y'. = 0 ( --

E L' x').

205


6. Part 6. Calculation Methods And Mathematical Modeling

, , :

E + k


( j )2

E = 0, H = 0,


(1) (2) j,

H + k
k(j) --

( j)2

k1 =

, -- . , j=1 -- . ,

i 4 ( + i ), k 2 = i , -- , -- c c

k 2 = - k1 k 2 ,

, -- j : j=0 -- , j=2 -- -

, E j -

E j = E + E ks ,

(3)

E -- , E ks -- , . , E H E H U V [1]. X'Y'Z', , k - -- XkYkZ (k=1,2). j- Pnm (cos j )e im . . .1 -

206


. ., . . -- -- 2006, . 2, . 204­215 Krivenko I. V., Smirnova M. A. -- MCE -- 2006, v. 2, p. 204­215

/2 ­ , , 3/2 O1, X1Y1Z. [2] .

g X'Y'Z' [3]. -

. q j [4]. [5, 6] . [3], = 90, = =0 r . qi, , , E
2

. q

* j



. , . , R1 = 1 . R2 = 1 . R = 20 (R / (R1 + R2) = 10). = 10.6 . T = 273 . = =57.5 /,
207


6. Part 6. Calculation Methods And Mathematical Modeling

1 = 2 = 1.35 103 /. () 1.173 + i 0.0823. ne = 1. = 900 , = 00 . , = 0 . , , q1 = =q2 = 1.5 1012 /3 . qj =qj* I, qj* = 8.657104 -1. I ; . 1 , r. T.

.2. , (r = 0.1Â0.5 ) . 2 r1 = 0.1 ( 1), r2 = 0.2 ( 2), r3 = =0.3 ( 3), r4 = 0.4 ( 4), r5 = 0.5 ( 5). , (10% 208


. ., . . -- -- 2006, . 2, . 204­215 Krivenko I. V., Smirnova M. A. -- MCE -- 2006, v. 2, p. 204­215

) ( (1 = =00) (1 = 1800)). r «» , 2 (1 = 00) > 1(1 = =00), 2 (1 = 1800) < 1(1 = 1800) r1 > r2. [4] , . ( ). , , R / (R1 + R2)= = 3 [3]. 6 Â Â6,2 . , , . , , . . , () , (). , [6], :

T1 - T = 2(ch - cos )

q2 R



2 2

1


n =0



e

( 2 n +1)( 2 - / 2 )

Pn (cos ), (4)

1 ­ ; Rj ­ j - ; q2 ­ , -

209


6. Part 6. Calculation Methods And Mathematical Modeling
2 R 2 + R12 - R2 ; ch 2 = , R ­ 2 RR1 ; , ­ (1 = const, 2 = const ­

), T ­ , . (5) , T1 q2. , , [1] E .
2

, , . , [1], :

~ n (1)

'(1) 1

~ ~ (k (0) R2 ) 1 (n ( 2) k (0) R2 ) - 1(1) (k (0) R2 ) '1 (n ( 2) k (0) R2 ) = 0, (5)
( k (1) k 20 ) ~ = ( 0) (1) , n k k2 ( 2)

~ n

(1)

k ( 2) k = (0) kk

(0) 2 ( 2) 2

, (j) ­ ,

(j = 0, 1, 2), n ( z ) = z hn ( z ), n ( z ) = z jn ( z ) . (5), , , [1]. , . , -, , ; -, ,

210


. ., . . -- -- 2006, . 2, . 204­215 Krivenko I. V., Smirnova M. A. -- MCE -- 2006, v. 2, p. 204­215

; -, , . , . , , . , , . , ( , ). , , .., . ­ [7], , . , (90 70 ) 5 10 , . , . , , . . 3. 211


6. Part 6. Calculation Methods And Mathematical Modeling

[8­10]. , , . . , 9 .

.3.

212


. ., . . -- -- 2006, . 2, . 204­215 Krivenko I. V., Smirnova M. A. -- MCE -- 2006, v. 2, p. 204­215

.4. 5 . 4, 5, -- 1. 1. 1 2,3,7,8 1,4,5,6,9 2 1,4,5,6,9 2,3,7,8 3 1,2,4,7 3,5,6,8,9 4 3,4,6,7 1,2,5,8,9 5 2,3,5,6,9 1,4,7,8 6 2,3,7,8 ­ 7 1,4,5,6,9 ­ 8 1,2,4,7 ­ 9 3,4,6,7 ­ 10 2,3,5,6,9 ­ 11 ­ 2,3,7,8 12 ­ 1,4,5,6,9 13 ­ 3,5,6,8,9 14 ­ 1,4,7,8 15 ­ 1,2,3,6,7,9 ­ ­ ­ ­ ­ 1,4,5,6,9 2,3,7,8 3,5,6,8,9 1,2,5,8,9 1,4,7,8 1,4,5,6,9 2,3,7,8 1,2,4,7 2,3,5,6,9 4,5,8

, , , , , ­ . (213


6. Part 6. Calculation Methods And Mathematical Modeling

) 1,5 . , ( ).

.5. 7
( 03-01-00324) 1. ., . . ­ .: , 1970. 850 . 2. .. . -- .: , 1956. -- 588 . 3. .., .., .., .. // .1997..71.N 12. -- .2270­2274. 4. .. . -- .: , 1983. -- 190 . 5. .., .. . ­ .-. . «- ». -- : , 1999. -- . 24­25.
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. ., . . -- -- 2006, . 2, . 204­215 Krivenko I. V., Smirnova M. A. -- MCE -- 2006, v. 2, p. 204­215

6. Krivenko I.V., Klinger A.V., Uvarova L.A. Two disperse particles in the field of the electromagnetic radiation. / In collected articles «Mathematical Modeling: Problems, Methods, Applications». 2001. -- P. 231­243. 7. .. // . -- .8. -- 2000. -- .9. 8. M.A.Smirnova. Mathematical models nonlinear heat transfer in an inhomogeneous dispersible system. Mathematical Models Non-Linear Excitations, Transfer, Dynamics, and Control in Condensed Systems and Other Media, edited by Uvarova et al., Kluwer Academic / Plenum Publishtrs, New York, 1999. -- P.129­134. 9. .. . « , , , ». -- .: «», 2000. -- .106.. 10. M.A.Smirnova. Heat transfer in disperse systems of various structures and configurations./In collected articles «Mathematical Modeling: Problems, Methods, Applications». -- New York ­ Boston ­ Dordrecht ­ London ­ Moscow: KLUWER ACADEMIC/PLENUM PUBLISHERS, 2001. -- P. 99­111.

MODELING OF HEAT TRANSFER IN AEROSOL SYSTEMS IN A FIELD OF THE ELECTROMAGNETIC RADIATION UNDER VARIOUS CONDITIONS AND CALCULATION OF THE TEMPERATURE IN POLIDISPERSE SYSTEMS Krivenko I. V., Smirnova M. A.

Russia, Tver

The influence of electromagnetic radiation on disperse systems and mechanisms of induced physical processes in disperse particles is investigated. The theoretical and numerical methods of the decision of a thermal task with sources initiated by electromagnetic radiation are offered.
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