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## Flow Exergy as a Lagrangian for the Navier-Stokes Equations for Incompressible Flow

#### Enrico Sciubba [1]

##### 129 557

A novel variational derivation of the Navier-Stokes equations for incompressible flows is presented and discussed. The Lagrangian density is obtained from the exergy balance equation written for both the (Lagrangian) steady and quasi-stationary isothermal flows of an incompressible fluid. The exergy of a fluid mass (composed of a kinetic, a pressure-work, a diffusive, and a dissipative portion, the latter being the result of viscous irreversibility) is derived first, and it is then shown that a formal minimisation of the exergy variation (i.e. destruction) generates, without recurring to “local potentials”, the Navier-Stokes equations of motion under the given assumptions. The acceleration being held constant, the proposed variational method can be classified as a “restricted” principle.

The problem is also briefly discussed both in its historical perspective and in its possible formal and practical implications.

Navier-Stokes variational, Navier-Stokes Lagrangian, Exergy-based Lagrangian
Primary Language en Regular Original Research Article Author: Enrico Sciubba Publication Date: September 1, 2004
 Bibtex @ { ijot76673, journal = {International Journal of Thermodynamics}, issn = {1301-9724}, eissn = {2146-1511}, address = {Uluslararası Uygulamalı Termodinamik Derneği İktisadi İşletmesi}, year = {2004}, volume = {7}, pages = {115 - 122}, doi = {}, title = {Flow Exergy as a Lagrangian for the Navier-Stokes Equations for Incompressible Flow}, key = {cite}, author = {Sciubba, Enrico} } APA Sciubba, E . (2004). Flow Exergy as a Lagrangian for the Navier-Stokes Equations for Incompressible Flow. International Journal of Thermodynamics, 7 (3), 115-122. Retrieved from http://dergipark.org.tr/ijot/issue/5753/76673 MLA Sciubba, E . "Flow Exergy as a Lagrangian for the Navier-Stokes Equations for Incompressible Flow". International Journal of Thermodynamics 7 (2004): 115-122 Chicago Sciubba, E . "Flow Exergy as a Lagrangian for the Navier-Stokes Equations for Incompressible Flow". International Journal of Thermodynamics 7 (2004): 115-122 RIS TY - JOUR T1 - Flow Exergy as a Lagrangian for the Navier-Stokes Equations for Incompressible Flow AU - Enrico Sciubba Y1 - 2004 PY - 2004 N1 - DO - T2 - International Journal of Thermodynamics JF - Journal JO - JOR SP - 115 EP - 122 VL - 7 IS - 3 SN - 1301-9724-2146-1511 M3 - UR - Y2 - 2019 ER - EndNote %0 International Journal of Thermodynamics Flow Exergy as a Lagrangian for the Navier-Stokes Equations for Incompressible Flow %A Enrico Sciubba %T Flow Exergy as a Lagrangian for the Navier-Stokes Equations for Incompressible Flow %D 2004 %J International Journal of Thermodynamics %P 1301-9724-2146-1511 %V 7 %N 3 %R %U ISNAD Sciubba, Enrico . "Flow Exergy as a Lagrangian for the Navier-Stokes Equations for Incompressible Flow". International Journal of Thermodynamics 7 / 3 (September 2004): 115-122. AMA Sciubba E . Flow Exergy as a Lagrangian for the Navier-Stokes Equations for Incompressible Flow. International Journal of Thermodynamics. 2004; 7(3): 115-122. Vancouver Sciubba E . Flow Exergy as a Lagrangian for the Navier-Stokes Equations for Incompressible Flow. International Journal of Thermodynamics. 2004; 7(3): 122-115.