An Integral Variational Equation for Transport Processes in a Moving Fluid

1989 ◽  
Vol 56 (1) ◽  
pp. 208-210 ◽  
Author(s):  
E. S. Geskin
Keyword(s):  
Energy Dissipation ◽  
Lagrangian Density ◽  
Variational Equation ◽  
Boundary Energy ◽  
Minimum Energy ◽  
Transport Processes ◽  
Lagrange Equations ◽  
Flow Through ◽  
Moving Fluid ◽  
Minimum Energy Dissipation

An integral variational equation can adequately describe heat, mass, and momentum transfer in a moving chemically reactive fluid. The Euler-Lagrange equations corresponding to the suggested variational equation are identical to the equations of entropy, momentum, angular momentum, and mass balance. The constructed Lagrangian density relates energy change in the system to the work and energy dissipation of the system. For steady-state processes, the Lagrangian density includes convective energy flow through the system boundary, energy dissipation in the system, and work of the system. The proposed variational equation is equivalent to the expansion of the principle of minimum energy dissipation.

On the Variational Principle and Lagrange Equations in Studies of Gasdynamic Lubrication

1964 ◽  
Vol 31 (1) ◽  
pp. 43-46 ◽  
Author(s):  
L. N. Tao
Keyword(s):  
Variational Formulation ◽  
Lagrangian Density ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Minimum Energy ◽  
Classical Dynamics ◽  
Lagrange Equations ◽  
Rayleigh Principle ◽  
Special Case ◽  
Minimum Energy Dissipation

The paper is concerned with the variational formulation in studies of gasdynamic lubrication. It is shown that Reynolds’ equation of lubrication is equivalent to a set of Lagrange equations similar to those in classical dynamics. The Lagrangian and the dissipation-production are defined. Furthermore, based on the Hamiltonian principle for the field of a continuum, the Lagrangian density and the dissipation-production density are established. This formulation includes the incompressible problem, which is obtainable from the Helmholtz-Rayleigh principle of minimum energy-dissipation, as a special case. Hence a unification of the variational methods for both gasdynamic and hydrodynamic lubrication is accomplished.

Computational Evolution of Optimal Iceform Shapes Over a Flat Plate

1991 ◽  
Author(s):  
Ronald S. LaFleur
Keyword(s):  
Energy Dissipation ◽  
Flat Plate ◽  
Thermal Field ◽  
Fluid Dynamic ◽  
Minimum Energy ◽  
Thermal Parameter ◽  
Thermal Constraints ◽  
Ice Water ◽  
Nonlinear Geometric ◽  
Minimum Energy Dissipation

Abstract This paper presents the computational evolution of minimum energy dissipation iceform contours. The ice/water interface is shaped according to fluid dynamic and heat transfer characteristics of the flow field near the interface. A Couette iceform design model is used to approximate flow and thermal field behavior near the interface. The theory used to calculate the interface shape is based on a wedge model of the ice contour over a cold flat plate. The steady state ice profile is calculated when Reynolds number and the thermal parameter are selected. The generation function, designation function and energy dissipation are related to the nonlinear geometric development. An optimal preprocess criterion is prescribed as zero evolution length. The result is optimal geometries that are adapted to the flow and thermal constraints.

scholarly journals On using the minimum energy dissipation to estimate the steady-state of a flow network and discussion about the resulting power-law:application to tree-shaped networks in HVAC systems

Energy ◽  
2019 ◽  
Vol 172 ◽  
pp. 181-195 ◽  
Author(s):  
Víctor-Manuel Soto-Francés ◽  
José-Manuel Pinazo-Ojer ◽  
Emilio-José Sarabia-Escrivá ◽  
Pedro-Juan Martínez-Beltrán
Keyword(s):  
Steady State ◽  
Energy Dissipation ◽  
Minimum Energy ◽  
Hvac Systems ◽  
Flow Network ◽  
Minimum Energy Dissipation

Study On the Damage Evolution Equation of Rockburst

2008 ◽  
Vol 33-37 ◽  
pp. 663-668
Author(s):  
Quan Sheng Liu ◽  
Bin Liu ◽  
Wei Gao
Keyword(s):  
Energy Dissipation ◽  
Evolution Equation ◽  
Damage Evolution ◽  
Minimum Energy ◽  
Strength Criterion ◽  
Internal Variable ◽  
Total Strength ◽  
Damage Evolution Equation ◽  
Traditional Research ◽  
Minimum Energy Dissipation

This paper introduces the principle of minimum energy dissipation and its general procedures to establish development equation of internal variable. With the accepted viewpoint that the damage is only mechanics of energy dissipation during the rockburst and utilizing the total strength criterion based on released strain energy, the general damage evolution equation is deduced. Compared with the traditional research method of damage evolution equation, this method has universal and objective characteristics.

Micromagnetic study of minimum-energy dissipation during Landauer erasure of either isolated or coupled nanomagnetic switches

2014 ◽  
Vol 90 (10) ◽  
Author(s):  
M. Madami ◽  
M. d’Aquino ◽  
G. Gubbiotti ◽  
S. Tacchi ◽  
C. Serpico ◽  
...  
Keyword(s):  
Energy Dissipation ◽  
Minimum Energy ◽  
Minimum Energy Dissipation

Analysis and Comparison on Typical Methods for Predicting Composite Roughness of River

2012 ◽  
Vol 518-523 ◽  
pp. 4111-4114
Author(s):  
Liang Zhong ◽  
Guang Xiang Xu ◽  
Feng Zeng
Keyword(s):  
Energy Dissipation ◽  
Minimum Energy ◽  
Weighted Average ◽  
Necessary And Sufficient Condition ◽  
Weighted Average Method ◽  
Single Cross Section ◽  
Single Cross ◽  
Necessary And Sufficient ◽  
Minimum Energy Dissipation ◽  
Resistance Equation

Composite roughness is an important parameter in river hydraulic calculations. In this paper, various typical methods for predicting composite roughness of river were summarized, including Einstein Method, Lotter Method, JIANG Method and Weighted Average Method, their theoretical rigors were discussed from both perspectives of minimum energy dissipation principle and analytical analysis, and their calculation precisions were verified by a large number of flume test data. Research shows that Einstein Method complies with the principle of minimum energy dissipation, also is the necessary and sufficient condition of resistance equation having unique solution, and its calculation precision is higher, therefore, Einstein Method is more suitable for composite resistance calculation of river with single cross section.

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