Two-phase flow and its applications: Past, present, and future
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Cites background from "Two-phase flow and its applications..."
...Flow regime-based correlations are desired in two-phase flow analyses since a single heat transfer correlation does not apply in all flow regimes (Hewitt, 1983)....
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Cites background from "Two-phase flow and its applications..."
...We define the infinitesimal one-parameter point transformation ?̄?i = yi ( yj,uB; ε ) , (5) ūA = uA ( yj,uB; ε ) , (6) defined in the space of variables { yi,uA } , and ε is an infinitesimal parameter....
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...From (5) and (6), the infinitesimal transformation is defined ?̄?i = y + εξi ( yj,uB ) (7) ūA = uA + εηA ( yj,uB ) (8) with extension in the jet space { yi,uA,uA ,i , ....
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...We say that the system HA remains invariant under the action of the one-parameter point transformation (5) and (6) if and only if H̄A ( ?̄?i, ūA, ūi , ....
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...Under the action of the one-parameter point transformation (5) and (6), the system of differential equations becomes H̄A ( ?̄?i, ūA, ūi , ....
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...that is, X ( HA ) = 0, (12) where denotes the Lie derivative with respect the generator X of the infinitesimal transformation (5) and (6), that is, X = ξi ( yj,uB ) ∂i + ηA ( yj,uB ) ∂A....
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References
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