Governing Equation for Multicomponent System

The conservation equations (mass, momentum, energy) are primarily considered for fluids of uniform and homogeneous composition. Here, we examine how these conservation equations change when two or more species are present and when chemical reactions may also take place. In a multicomponent mixture, transfer of mass takes place whenever there is a spatial gradient in the mixture properties, even in the absence of body forces that act differently upon different species. In fluid flows, the mass transfer will generally be accompanied by a transport of momentum and may further be combined with a transport of heat. For a multicomponent fluid, conservation relations can be written for individual species. Let m, be the species velocities and Pi the species density where the index i, is used to represent the fth species. 

For single-component system, the mass conservation equation is 

Suppose if species are produced by chemical reaction, say, at a mass rate r,- kilogram per cubic meter second, then we have 

Using mass average velocity (pu = I,pjUj) and flux with respect to mass average velocity 

Note that equation (4.26) is identical to the mass conservation equation (4.21) for pure fluid, that is, single-component system. 

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