# Differential formulation of governing equations

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==Continuity Equation== | ==Continuity Equation== | ||

- | <center><math>\frac{{D\rho }}{{Dt}} + \rho \nabla \cdot {{\mathbf{V}}_{rel}} = 0 | + | <center><math>\frac{{D\rho }}{{Dt}} + \rho \nabla \cdot {{\mathbf{V}}_{rel}} = 0 </math></center> |

''See Main Article'' [[Continuity equation]] | ''See Main Article'' [[Continuity equation]] | ||

## Revision as of 09:05, 27 June 2010

The microscopic (differential) formulations to be presented here include conservation equations and jump conditions. The former apply within a particular phase, and the latter are valid at the interface that separates two phases. The phase equations for a particular phase should be the same as those for a single-phase system. Most textbooks (e.g., White, 1991; Incropera and DeWitt, 2001; Bejan, 2004; Kays *et al*., 2004) obtain the governing equations for a single-phase system by performing mass, momentum, and energy balances for a microscopic control volume. We will obtain the conservation equations by using the integral equations for a finite control volume that includes only one phase. Jump conditions at the interface will be obtained by applying the conservation laws at the interfaces.

## Contents |

## Continuity Equation

*See Main Article* Continuity equation

## Momentum Equation

*See Main Article* Momentum equation

## Energy Equation

*See Main Article* Energy equation

## Entropy Equation

*See Main Article* Entropy

## Conservation of mass species equation

*See Main Article* Conservation of Mass Species

## References

Bejan, A., 2004, *Convection Heat Transfer*, 3^{rd} ed., John Wiley & Sons, New York.

Faghri, A., and Zhang, Y., 2006, *Transport Phenomena in Multiphase Systems,* Elsevier, Burlington, MA

Faghri, A., Zhang, Y., and Howell, J. R., 2010, *Advanced Heat and Mass Transfer,* Global Digital Press, Columbia, MO.

Incropera, F.P., and DeWitt, D.P., 2001, *Fundamentals of Heat and Mass Transfer*, 5^{th} ed., John Wiley & Sons, New York.

Kays, W.M., Crawford, M.E., and Weigand, B., 2004, *Convective Heat Transfer*, 4^{th} ed., McGraw-Hill, New York, NY.

White, F.M., 1991, *Viscous Fluid Flow*, 2^{nd} ed., McGraw-Hill, New York.