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By R. T. Lahey Jr., D. A. Drew (auth.), Jeffery Lewins, Martin Becker (eds.)

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T. LAHEY AND D. A. k (rl/P l Ai") + (rl/P1Ai" )2]/2 (132a) and e 2i h g + [U~ + 2 u • n (r /p A~") + (r2/p2A~,,)2]/2 -1 -i -k 2 2 1 1 (132b) in which saturated conditions are assumed at the interface. The interfacial heat fluxes can be modelled as. q" (133 ) k, 1 where the interfacial heat transfer coefficient (H'k) depends on the flow regime. 5 - v -1 I (134c) Since the vapor phase is essentially saturated for one component bubbly flow, the interfacial heat transfer coefficient, Hi2 , is often taken to be a very large value.

X,t) /:'P k . ~k /:, 1- 1 /:, 1 q" k. ai/V 1- 1 k w /:, . , · i . -k. 'Vd /:'P /:, <_k_>. rk Pk 1 1 1 V w I IV /:, 'L·d [/:'P k . J(~,t) /:, 1 V Sf 1- a. (x,t) 1- If a. (x,t) ~k /:,~d k. 1 (m" /:'~k. ::'k dS, (65d) 1 ~k W (65c) dS, ~k 1- V a. (x,t) ~k (65b) dS, . q" V a. (x,t) ~k If 1 -1 ff 1 /:, 1 d /:, r\ -k. v. 1 w . ,9;"k dS ' . i . ::'k dS k/P k ) dS (65e) (65f) (65g) THREE-DIMENSIONAL CONSERVATION EQUATION 21 The conservation equations tabulated in Equations (36), (52) and (64) are instantaneous volume-averaged equations.

That is, (68) Using the time-averaging defined in equation (66), the time and volume averaged conservation equations can be readily derived. It should be noted that space~and time-averaging is known (1) to be commutative, thus the order of these operations is immaterial. This point will be discussed further in Section 6. A. Three-dimensional Space and Time Averaged Mass Conservation Equation From Equations d at B. [Bk

] + (36) and (66), we obtain 1 V V· [V Bk

] = r k (69) • Three-dimensional Space and Time Averaged Momentum Conservation Equation From Equations (52) and (66) we obtain d dt S' -k w w I I + -1 V • [Bk<~k>] + Bk

+ r ~kir + ~~d k k V i + ~~d w + ~~ + w <1 > • =k i SI I -k i I (70) 23 THREE-DIMENSIONAL CONSERVATION EQUATION C.

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