Invariance Properties of the Entropy Production, and the Entropic Pairing of Inertial Frames of Reference by Shear-Flow Systems

Niven, Robert K.

doi:10.3390/e23111515

Cited by 4 publications

(7 citation statements)

References 64 publications

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“…This includes a deep connection to the one-parameter Lie group of point scaling transformations [ 71 , 73 , 74 , 75 ]. Recently, this was shown to enable the non-dimensionalization of a differential equation based on its intrinsic dimensions [ 76 ]. Lie symmetry is therefore an important invariance property of a differential equation, subsuming other invariances such as dimensional scaling, invariance to fixed coordinate displacements, rotations or reflections, and Galilean invariance [ 76 ].…”

Section: Dimensionless Groups and The Principle Of Entropic Similaritymentioning

confidence: 99%

“…First consider internal flows , involving flow in a conduit with solid walls under a pressure gradient (Poiseuille flow). For steady irrotational incompressible flow in a cylindrical pipe, the total entropy production is [ 30 , 76 , 116 , 117 , 118 ]:

where

is the pressure loss [Pa],

is the head loss [m], Q is volumetric flow rate [m

], U is the mean velocity [m s

] and d is the pipe diameter [m]. The head loss by inertial flow is given by the Darcy–Weisbach equation [ 11 , 13 , 15 , 16 , 17 , 18 , 88 ]:

where f is the Darcy friction factor [–] for the inertial regime and L is the pipe length [m].…”

Section: Dispersion Processesmentioning

confidence: 99%

“…Now consider external flows , involving flow around a solid object [ 11 , 13 , 16 , 17 , 18 ]. For a simplified steady one-dimensional flow, the entropy production is [ 30 , 76 , 116 , 117 ]:

where

is the magnitude of the drag force [N] and U is the mean velocity of the ambient fluid [m s

]. The drag force is commonly scaled by the dynamic pressure to give a dimensionless drag coefficient [ 11 , 13 , 93 ]:

where

is the cross-sectional area of the solid normal to the flow [m

].…”

Section: Dispersion Processesmentioning

confidence: 99%

“…Consider a solid object moving at velocity

[m s

] in a uniform flow field of ambient velocity

[m s

], producing the vector drag–lift force

[N] on the object. The vector drag–lift coefficient

and inertial entropy production are [ 76 ]:

while the Stokes viscous force and viscous entropy production for a sphere are:

…”

Section: Dispersion Processesmentioning

confidence: 99%

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Dimensionless Groups by Entropic Similarity: I — Diffusion, Chemical Reaction and Dispersion Processes

Niven

2023

Entropy

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Since the time of Buckingham in 1914, dimensional analysis and similarity arguments based on dimensionless groups have served as powerful tools for the analysis of systems in all branches of science and engineering. Dimensionless groups are generally classified into those arising from geometric similarity, based on ratios of length scales; kinematic similarity, based on ratios of velocities or accelerations; and dynamic similarity, based on ratios of forces. We propose an additional category of dimensionless groups based on entropic similarity, defined by ratios of (i) entropy production terms; (ii) entropy flow rates or fluxes; or (iii) information flow rates or fluxes. Since all processes involving work against friction, dissipation, diffusion, dispersion, mixing, separation, chemical reaction, gain of information or other irreversible changes are driven by (or must overcome) the second law of thermodynamics, it is appropriate to analyze them directly in terms of competing entropy-producing and transporting phenomena and the dominant entropic regime, rather than indirectly in terms of forces. In this study, entropic groups are derived for a wide variety of diffusion, chemical reaction and dispersion processes relevant to fluid mechanics, chemical engineering and environmental engineering. It is shown that many dimensionless groups traditionally derived by kinematic or dynamic similarity (including the Reynolds number) can also be recovered by entropic similarity—with a different entropic interpretation—while many new dimensionless groups can also be identified. The analyses significantly expand the scope of dimensional analysis and similarity arguments for the resolution of new and existing problems in science and engineering.

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Section: Dimensionless Groups and The Principle Of Entropic Similaritymentioning

confidence: 99%

where

is the pressure loss [Pa],

is the head loss [m], Q is volumetric flow rate [m

], U is the mean velocity [m s

] and d is the pipe diameter [m]. The head loss by inertial flow is given by the Darcy–Weisbach equation [ 11 , 13 , 15 , 16 , 17 , 18 , 88 ]:

where f is the Darcy friction factor [–] for the inertial regime and L is the pipe length [m].…”

Section: Dispersion Processesmentioning

confidence: 99%

“…Now consider external flows , involving flow around a solid object [ 11 , 13 , 16 , 17 , 18 ]. For a simplified steady one-dimensional flow, the entropy production is [ 30 , 76 , 116 , 117 ]:

where

is the magnitude of the drag force [N] and U is the mean velocity of the ambient fluid [m s

]. The drag force is commonly scaled by the dynamic pressure to give a dimensionless drag coefficient [ 11 , 13 , 93 ]:

where

is the cross-sectional area of the solid normal to the flow [m

].…”

Section: Dispersion Processesmentioning

confidence: 99%

“…Consider a solid object moving at velocity

[m s

] in a uniform flow field of ambient velocity

[m s

], producing the vector drag–lift force

[N] on the object. The vector drag–lift coefficient

and inertial entropy production are [ 76 ]:

while the Stokes viscous force and viscous entropy production for a sphere are:

…”

Section: Dispersion Processesmentioning

confidence: 99%

See 2 more Smart Citations

Dimensionless Groups by Entropic Similarity: I — Diffusion, Chemical Reaction and Dispersion Processes

Niven

2023

Entropy

Self Cite

View full text Add to dashboard Cite

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“…Термодинамічні особливості екологічних систем досліджуються з різних позицій. У роботі [5] розглядаються інваріантні властивості термодинамічного виробництва ентропії в її глобальних (інтегральних), локальних (диференціальних), білінійних і макроскопічних формулюваннях, включаючи масштабування розмірів, інваріантність до фіксованих переміщень, обертання або відображення координат, антисиметрію часу, інваріантність Галілея і симетрію точки Лі. За допомогою аналізу різних підсистем зсувного потоку представлено ряд керівних принципів для опису їх ентропійних властивостей сполучення та джерел негентропії.…”

Section: аналіз останніх досліджень і публікаційunclassified

Thermodynamic aspects of the systems approach in ecology

Bezsonnyi

Tretyakov

Sherstyuk

et al. 2022

Visnyk of V.N. Karazin Kharkiv National University, Series Geology. Geography. Ecology

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Purpose. research from thermodynamic positions of the properties of ecological systems of various types under the influence of anthropogenic factors. Methods. Analytical-synthetic method, analysis of information sources, entropy analysis. Results. The effect of an anthropogenic factor on the ecosystem will result in a decrease in the antientropy of the components. The response of the ecosystem will be different depending on the strength and duration of the disturbance. With a strong and sufficiently long impact, the antientropy of the components falls while preserving the organization of the ecosystem until the too low level of the antientropy of the components does not include their own regulatory reactions aimed at restraining the fall of the antientropy even to the detriment of the organization of the system. The organization begins to fall. Since the influence is strong enough and does not stop, the regulatory mechanisms of the components are not able to stabilize the antientropy. The process of falling anti-entropy and organization continues, the system is irreversibly going to its demise. With an average strength, but long-term impact, the components manage to stabilize their anti-entropy at some sub-optimal, but acceptable level at the expense of energy reserves while preserving the organization. However, if the influence continues and does not weaken, the components, not being able to return their antientropy to the original optimal level, sooner or later cannot cope with the continuous perturbation, and their antientropy begins to fall again, now together with the organization. With a weak or short-term impact, the components, adapting to new conditions, return the antientropy to the optimal level (with a strong or medium impact, this is possible only after its termination before irreversible changes in the system). In this case, the organization of the system remains constant, since the disturbing action in this case did not lead the ecosystem beyond the effective operation of homeostatic mechanisms. Thus, the critical moment when an anthropogenic factor acts on an ecosystem is the beginning of the fall of its organization, when homeostasis has completely exhausted itself in countering the disturbance, and the ecosystem begins to irreversibly degrade. So, to control the state of the ecosystem exposed to the anthropogenic factor, it is enough to monitor the organization of the system: if it does not decrease, we can talk about relative well-being, but if the organization falls, the ecosystem is on the verge of death, and it is necessary to take measures to save it. However, the periodic and fairly frequent measurement of the organization of the ecosystem is a task, although one that does not cause fundamental difficulties, but is very time-consuming, primarily due to finding the average module of the correlation coefficients of the parameters. Determining the complexity of the ecosystem according to the formula, although associated with certain difficulties associated with finding the number of connections, does not require time-consuming mathematical processing.

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On the Validity of a Linearity Axiom in Diffusion and Heat Transfer

et al. 2022

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In this work, the linearity axiom of irreversible thermodynamics for diffusion and heat transfer has been re-examined. It is shown that this axiom is compatible with the entropy production invariance principle with respect to a reference quantity for diffusion and heat transfer in the Euclidean space. Moreover, the underlying relations of the other principles of irreversible thermodynamics for multi-component diffusion and heat transfer, such as the quasi-equilibrium and the Onsager reciprocal relations (ORR) with the entropy production invariance, are re-examined. It was shown that the linearity principle postulates for diffusion and heat transfer and could be directly derived from the entropy production invariance axiom. It is believed that this work could not only be used for the drying of polymer coatings but also for pedagogical purposes. It may also be generalized; thus, leading to a generalized framework for irreversible thermodynamics.

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Invariance Properties of the Entropy Production, and the Entropic Pairing of Inertial Frames of Reference by Shear-Flow Systems

Cited by 4 publications

References 64 publications

Dimensionless Groups by Entropic Similarity: I — Diffusion, Chemical Reaction and Dispersion Processes

Dimensionless Groups by Entropic Similarity: I — Diffusion, Chemical Reaction and Dispersion Processes

Thermodynamic aspects of the systems approach in ecology

On the Validity of a Linearity Axiom in Diffusion and Heat Transfer

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