# Averaging formulation of governing equations

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:[[Volume averaging|Volume averaging]], [[Lagrangian Averaging|Lagrangian averaging]], and [[Basics of Boltzmann statistical averaging|Boltzmann statistical averaging]]. | :[[Volume averaging|Volume averaging]], [[Lagrangian Averaging|Lagrangian averaging]], and [[Basics of Boltzmann statistical averaging|Boltzmann statistical averaging]]. | ||

*[[Multi-fluid model]] | *[[Multi-fluid model]] | ||

- | :[[Multi- | + | :[[Multi-fluid_model#Continuity_Equation|Continuity equation]], [[Multi-fluid_model#Momentum_Equation|momentum equation]], [[Multi-fluid_model#Energy_Equation|energy equation]],and [[Multi-fluid_model#Species|conservation of species]]. |

*[[Homogeneous model]] | *[[Homogeneous model]] | ||

- | :[[ | + | :[[Homogeneous_model#Continuity_Equation|Continuity equation]], [[Homogeneous_model#Momentum_Equation|momentum equation]], [[Homogeneous_model#Energy_Equation|energy equation]], and [[Homogeneous_model#Species|conservation of species]]. |

*'''[[Governing Equations for Porous Media|Porous media]]''' | *'''[[Governing Equations for Porous Media|Porous media]]''' | ||

- | :[[Basics of porous media|Basics]], [[ | + | :[[Basics of porous media|Basics]], [[Governing_Equations_for_Porous_Media#Conservation_of_Mass|continuity equation]], [[Governing_Equations_for_Porous_Media#Conservation_of_Momentum|momentum equation]], [[Governing_Equations_for_Porous_Media#Energy_Equation|energy equation]], and [[Governing_Equations_for_Porous_Media#Species|conservation of species]]. |

*[[Boltzmann statistical averaging]] | *[[Boltzmann statistical averaging]] | ||

- | :[[Boltzmann | + | :[[Boltzmann Equation]], [[Lattice Boltzmann Model (LBM)]], and [[LBM for multiphase flows]]. |

+ | |||

+ | ==References== | ||

+ | |||

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

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+ | ==Further Reading== | ||

+ | |||

+ | ==External Links== |

## Current revision as of 13:43, 5 August 2010

Many multiphase-flow problems encountered in engineering – such as those with dispersed and mixed phases – have extremely complicated and deformable interfaces. It is not always possible to solve the local instance fluid flow, because the difficulty associated with interface tracking exceeds present computational capability. Fortunately, information about the discontinuity of properties at the interfaces and the exact locations of the interfaces are not always of interest to practical engineers. The macroscopic aspects of multiphase flow are more important to the design and operation of a multiphase system. Appropriate averaging can obtain the mean values of flow and thermal properties and eliminate the need to explicitly track interfaces and/or the local instance fluctuations of properties.

## References

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