Interdisciplinary Applied Mathematics

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U^



0,


ldP_2


dx


1    32t1


2    72 TbP



___1 д2щ i


2 dxi 2^1 dx2



(15.30)


(15.31a)


(15.31b)


(15.31c)



The second-order conservation equations are


duj2    dwi


dxj    21 dxj


dui2    дпц


1    a


2    dxi


1 d2ui2    1 д


+ 27l^f+ 274^“


j    J



dun    duni


ti 1 -— + ——



dxi



(15.33a)


дт2    дт 2 дР2


7i



<3*7


dxo



i



+



du



Ji



dxi



2



1 д2    1


+ 2^2 (t2t2 + -75Ti2 ) , (15.33b)


where 7n are constants related to the collision integral.


The coefficient functions of the S expansion of the stress tensor Pij and heat flux vector Qi are given as follows:


Pij 1    P1 Sij ,


Pij2 = P2^ij — Y1



duii duji


—1——



dxj,



dxi



n n c    dui2    duj2    2 duk2 c


pij3 = рзSij — 7i ( —H vw- — ——Si



>    (15.34)



-74 Ti



dxJ


f dun duji l dxj    dxj.



dxi



+ 73



3 dxk д2т dx,, dxj



1 52tia 3 dx2 j


Qii = 0,


Qi2 = ~t72



5 dri



4    2 dxi


5    дт2 „    ~    —


Qi3= —Л2Т,775T1W—h -73



5 dT2    5    dri    1 d2uii



4 dxi    4 dxi 2


where y4 and 75 are defined as follows.

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