Reynolds Transport Theorem
المؤلف:
Leal, L. G
المصدر:
Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes. New York: Cambridge University Press, 1999
الجزء والصفحة:
...
23-7-2018
1799
Reynolds Transport Theorem
The Reynolds transport theorem, also called simply the Reynolds theorem, is an important result in fluid mechanics that's often considered a three-dimensional analog of the Leibniz integral rule. Given any scalar quantity 
associated with a moving fluid, the general form of Reynolds transport theorem says
Here, 
is the convective derivative, 
is the usual gradient, 
denotes the material volume at time 
, and 
denotes the velocity vector.
Because of its relation to the Leibniz rule, the Reynolds transport theorem is sometimes called the Leibniz-Reynolds transport theorem.
Worth noting is the large number of variants of Reynolds transport theorem present in the literature. Indeed, the formula is extremely general and can be applied to a variety of contexts in vastly many circumstances. As such, different literature will inevitably have equations which often look different than the above equation in both appearance and complexity.
REFERENCES:
Gray, D. "Why the Balance Principle Should Replace the Reynolds Transport Theorem." 2008. http://tinyurl.com/q324mw3.
Leal, L. G. Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes. New York: Cambridge University Press, 1999.
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