3u . 3v ^ 9w _ n ^ 9Hu . 9Hv , „ 31^ . 3c 

 3x 3y 32 3x 3y ' =»" ^* 



3a 3t 



(A-6) 



3u 3uu 3uv ^ 3uw 

 3t 3x 3y 3z 



1 



-»■ — 



H 



3Hu ^ 3(Hu ) ^ 3(Huv) ^ ^ Sua. ^ ,j . 3u H 

 3t 3x' 3y' 3a ^ ' 3a 3t 



(A-7) 



The diffusion terms in the momentum equations involve the second-order 

 derivatives which are: 



3x 3x 



i J_ /h 3 \ 1. /. 3H 3 \ 3 /SH jA 

 H 3x' \ 3x'y "3a y 3x 3x'y " 3x' ^3x30^ 



H Uxy 3a I 3ay " 3x' y3x ia J 



3c 3 

 3x 3a3x' 



(A-8) 



1-^ ^H^ 

 H 3x' ^ 3x'y 



+ Higher Order Terms 



An alternative way to derive the transformed equations is to perform 

 tensor transformation on the dependent as well as the independent variables. 



224 



