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A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Absorbing media, interaction phenomena in, Absorption of thermal radiation: Absorption coefficient, Absorption spectra in gases, Absorptivity: Acentric factor: Acetaldehyde: Acetic acid: Acetic anhydride: Acetone: Acetonitrile: Acetophenone: Acetylene: Acetylenes Ackerman correction factor in condensation, Acoustic methods, for fouling mitigation, Acoustic vibration of heat exchangers, Acrolein: Acrylic acid: Active systems for augmentation of heat transfer: Additives: Adiabatic flows, compressible, in duct, Admiralty brass, Advanced models for furnaces, Agitated beds, heat transfer to, Agitated vessels, Ahmad scaling method for critical heat flux in flow boiling of nonaqueous fluids, Air: Air-activated gravity conveyor, Air-cooled heat exchangers: Air preheaters, fouling in, Albedo for single scatter in radiation, Alcohols: Aldehydes: Aldred, D L, Allyl alcohol: Allyl chloride (-chloropropane) Alternating direction (ADR) method, for solution of implicit finite difference equations, Aluminum, spectral characteristics of anodized surfaces, Aluminum alloys, thermal and mechanical properties, Aluminium brass, Ambrose-Walton corresponding states method, for vapour pressure, Amides: Amines: Ammonia: tert-Amyl alcohol: Analogy between heat and mass and momentum transfer Analytical solution of groups, for calculation of thermodynamic Anelasticity, Angled tubes, use in increasing flooding rate in reflux condensation, Aniline: Anisotropy of elastic properties, Annular distributor in shell-and-tube heat exchangers, Annular ducts: Annular (radial) fins, efficiency Annular flow (gas-liquid): Annular flow (liquid-liquid), Annular flow (liquid-liquid-gas), Anti-foulants, Antoine equation, for vapour pressure, Aqueous solutions, as heat transfer media, Arc welding of tubes into tube sheets: Archimedes number, Area of tube outside surface in shell-and-tube heat exchangers: Argon: Arithmetic mean temperature difference, definition, Armstrong, Robert C Aromatics: ASME VIII code, for mechanical design of shell-and-tube heat exchangers: Assisted convection: Attachment, of fouling layers, Augmentation of heat transfer
Augmentation of Heat Transfer Condensation Enhancement Augmentation of Boiling and Evaporation active systems for: entropy generation in,
EGM at the elemental level
in boiling, in condensation, in kettle reboilers, in microfluidic systems, nanoparticles for, passive systems for: phase change materials for, in shell-and-tube heat exchangers using low finned tubes, system impact of,
Austenitic stainless steels, Average phase velocity in multiphase flows, Axial flow reboilers, Axial wire attachments, for augmentation of condensation, Azeotropes, condensation of

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HEDH
A
Absorbing media, interaction phenomena in, Absorption of thermal radiation: Absorption coefficient, Absorption spectra in gases, Absorptivity: Acentric factor: Acetaldehyde: Acetic acid: Acetic anhydride: Acetone: Acetonitrile: Acetophenone: Acetylene: Acetylenes Ackerman correction factor in condensation, Acoustic methods, for fouling mitigation, Acoustic vibration of heat exchangers, Acrolein: Acrylic acid: Active systems for augmentation of heat transfer: Additives: Adiabatic flows, compressible, in duct, Admiralty brass, Advanced models for furnaces, Agitated beds, heat transfer to, Agitated vessels, Ahmad scaling method for critical heat flux in flow boiling of nonaqueous fluids, Air: Air-activated gravity conveyor, Air-cooled heat exchangers: Air preheaters, fouling in, Albedo for single scatter in radiation, Alcohols: Aldehydes: Aldred, D L, Allyl alcohol: Allyl chloride (-chloropropane) Alternating direction (ADR) method, for solution of implicit finite difference equations, Aluminum, spectral characteristics of anodized surfaces, Aluminum alloys, thermal and mechanical properties, Aluminium brass, Ambrose-Walton corresponding states method, for vapour pressure, Amides: Amines: Ammonia: tert-Amyl alcohol: Analogy between heat and mass and momentum transfer Analytical solution of groups, for calculation of thermodynamic Anelasticity, Angled tubes, use in increasing flooding rate in reflux condensation, Aniline: Anisotropy of elastic properties, Annular distributor in shell-and-tube heat exchangers, Annular ducts: Annular (radial) fins, efficiency Annular flow (gas-liquid): Annular flow (liquid-liquid), Annular flow (liquid-liquid-gas), Anti-foulants, Antoine equation, for vapour pressure, Aqueous solutions, as heat transfer media, Arc welding of tubes into tube sheets: Archimedes number, Area of tube outside surface in shell-and-tube heat exchangers: Argon: Arithmetic mean temperature difference, definition, Armstrong, Robert C Aromatics: ASME VIII code, for mechanical design of shell-and-tube heat exchangers: Assisted convection: Attachment, of fouling layers, Augmentation of heat transfer
Augmentation of Heat Transfer Condensation Enhancement Augmentation of Boiling and Evaporation active systems for: entropy generation in,
EGM at the elemental level
in boiling, in condensation, in kettle reboilers, in microfluidic systems, nanoparticles for, passive systems for: phase change materials for, in shell-and-tube heat exchangers using low finned tubes, system impact of,
Austenitic stainless steels, Average phase velocity in multiphase flows, Axial flow reboilers, Axial wire attachments, for augmentation of condensation, Azeotropes, condensation of
B C D E F G H I J K L M N O P Q R S T U V W X Y Z
A Augmentation of heat transfer entropy generation in,
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EGM at the elemental level

DOI 10.1615/hedhme.a.000127

1.8.2 Entropy Generation Minimization at the Elemental Level

Adrian Bejan

A. Entropy generation is proportional to lost work

We begin with a brief look at why in EGM we must rely on heat transfer and fluid mechanics, not just thermodynamics. Consider the open thermodynamic system (control volume) shown in Figure 1, where, for simplicity, only one of the heat transfer interactions \(\dot{Q}_{i}\) (i = 0, 1, ..., n) is shown. Each heat transfer interaction \(\dot{Q}_{i}\) is accompanied by the entropy transfer \(\dot{Q}_{i}\) /Ti, where Ti is the absolute temperature of the boundary point crossed by \(\dot{Q}_{i}\). The thermodynamic analysis of the system is based on three statements, mass conservation, the first law, and the second law Bejan (1988).

\[\label{eq1} \frac{\partial \mbox{M}}{\partial t} = \sum\limits_{\rm in}\dot{m} - \sum\limits_{\rm out}\dot{m}\tag{1}\]

\[\label{eq2} \frac{\partial \mbox{E}}{\partial \mbox{t}} = \sum\limits_{{\rm i} = 0}^ {\rm n} \dot {Q}_{i} - \dot{\rm W} + \sum\limits_{{\rm in}}\dot{m}\left(h + 1/2V^{2} + {\rm gz}\right) - \sum\limits_{out}\dot{m}\left(h + 1/2V^{2} + gz\right)\tag{2}\]

\[\label{eq3} \frac{\partial S}{\partial t} \geq \sum\limits_{i = 0}^{n}\frac{\dot{Q}_{i}}{T_{i}} + \sum\limits_{in}\dot{m}s - \sum\limits_{out}\dot{m}s\tag{3}\]

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