Appendix 1 - Y y (1) x Z (X,Y,Z) (2) V (left & right) n z X...

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Y Z X (1) V Ө ∆y (1) (2) n ∆z ∆x (X,Y,Z) How to compute ( 29 CS p e V n dA ρ + ∫∫ u v v ------ (A) cos V n v n θ ⋅ = u v v at plane (1): ( 29 cos 1 1 x V n V V ⋅ = ⋅ = - u v v ------- (B) n Ө V At plane (2), ( 29 cos 1 1 x V n v V ⋅ = ⋅ = u v v ------- (C) V Ө N (2)
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Y Z X Y Z X 2 2 : 2 V : 2 : V mean kinectic energy e gy U gy potential energy U energy = + + internal ------ (D) Applying (A),(B),(C),(D) at planes (1) and (2), one obtains: z y p U gy V p U gy V x x x x x + + + - + + + + ρ 2 V 2 V 2 2 (4) y (3) z x (X,Y,Z) 2 2 V V 2 2 y y y y y p p V gy U V gy U x z +∆ + + + - + + + ∆ ⋅∆ ∆y (5) (6) ∆z ∆x (X,Y,Z) 2 2 V V 2 2 z z z z z p p V gy U V gy U x y +∆ + + + - + + + ∆ ⋅∆
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Dt DT C T k v q ρ = Φ + + where = z T y T x T T , , , ------gradient of a scalar is vector [ ] , , , , T T T k T k k k x y z T T T k T k k k x y z = ∇⋅ = ∇⋅ = z y x , , ? = A where A= (a 1, a 2, a 3 ) = z a y a x a + + 3 2 1 ------ divergence of a vector is scalar vector scalar gradient divergence * [ ] ) ( ) ( ) ( z T k z y T k y x T k x T k + + = : Dt DT Substantial derivative z T u y T u x T u t T z y x + + + = This term vanishes if there is no convective flow contribution q : Heat generation per unit volume unit time Ф : dissipation function + + + + + + + + = 2 2 2 2 2 2 2 z V x V y V z V x V y V μ z V y V x V μ x z z y y x z y x
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From:  chewch@nus.edu.sg [mailto:chewch@nus.edu.sg]  Sent:  Friday, January 15, 2010 9:00 AM Cc:  Lei Chenlu; Tong Yen Wah; Wang Chi-Hwa; Wang Chi-Hwa; Alireza Rezvanpour; Qiao Jian
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This note was uploaded on 01/07/2011 for the course CHBE 123 taught by Professor Teo during the Spring '10 term at National University of Singapore.

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Appendix 1 - Y y (1) x Z (X,Y,Z) (2) V (left & right) n z X...

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