Integral governing equations

From Thermal-FluidsPedia

Revision as of 03:34, 27 June 2010 by Yuwen Zhang (Talk | contribs)
Jump to: navigation, search


Transformation Formula

A fixed-mass system describes an amount of matter that can move, flow and interact with the surroundings, but the control volume approach depicts a region or volume of interest in a flow field, which is not unique and depends on the user. So conservation laws for a fixed-mass system need to be transformed to apply to a control volume. The transformation Formula allows one to mathematically and physically link the conservation laws for a control volume with that of a fixed-mass system.

See Main Article Transformation formula

Continuity Equation

The law of the conservation of mass dictates that mass may be neither created nor destroyed. For a control volume that contains only one phase, the integral continuity equation is

\frac{\partial }{{\partial t}}\int_V {\rho dV + \int_A {\rho ({{\mathbf{V}}_{rel}} \cdot {\mathbf{n}})dA} }  = 0     \qquad \qquad(1)

See Main Article Integral continuity equation


See Main Article Momentum


See Main Article Energy


See Main Article Entropy

Conservation of Mass Species

See Main Article Conservation of Mass Species