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Old Dominion University

Variational techniques

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Variational Approach To The Volume Viscosity Of Fluids, Allan J. Zuckerwar, Robert L. Ash Jan 2006

Variational Approach To The Volume Viscosity Of Fluids, Allan J. Zuckerwar, Robert L. Ash

Mechanical & Aerospace Engineering Faculty Publications

The variational principle of Hamilton is applied to develop an analytical formulation to describe the volume viscosity in fluids. The procedure described here differs from those used in the past in that a dissipative process is represented by the chemical affinity and progress variable (sometimes called "order parameter") of a reacting species. These state variables appear in the variational integral in two places: first, in the expression for the internal energy, and second, in a subsidiary condition accounting for the conservation of the reacting species. As a result of the variational procedure, two dissipative terms appear in the Navier-Stokes equation ...


Response To "Comment On Variational Approach To The Volume Viscosity Of Fluids" [Phys. Fluids 18, 109101 (2006)], Allen J. Zuckerwar, Robert L. Ash Jan 2006

Response To "Comment On Variational Approach To The Volume Viscosity Of Fluids" [Phys. Fluids 18, 109101 (2006)], Allen J. Zuckerwar, Robert L. Ash

Mechanical & Aerospace Engineering Faculty Publications

We respond to the Comment of Markus Scholle and therewith revise our material entropy constraint to account for the production of entropy. (c) 2006 American Institute of Physics.