Between Waves and Diffusion: Paradoxical Entropy Production in an Exceptional Regime

Hoffmann, Karl Heinz; Kulmus, Kathrin; Essex, Christopher; Prehl, Janett

doi:10.3390/e20110881

Cited by 6 publications

(2 citation statements)

References 31 publications

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“…Entransy dissipation occurs during the heat transfer process as a measure of the irreversibility of heat transfer. The advent of the extreme value principle of entransy dissipation provides a completely different perspective for heat transfer optimization and solves the limitations and backwardness of the previous heat evaluation by virtue of entropy generation and thermal resistance as evaluation indicators, directly eliminating the defect of the entropy production paradox [20,21].…”

Section: Introductionmentioning

confidence: 99%

Symmetric Heat Transfer Pattern of Fuel Assembly Subchannels in a Sodium-Cooled Fast Reactor

et al. 2022

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The method outlined in this paper is convenient and effective for studying the thermal performance of fuel assemblies cooled with sodium fast reactors using the subchannel procedure. To initially study an optimization model for a symmetric single fuel assembly heat transfer pattern analysis in a fast sodium-cooled reactor based on subchannel calculations, this paper innovatively proposes a subchannel heat transfer analysis method with the entransy dissipation theory, which can solve the limitations and inaccuracies of the traditional entropy method such as poor applicability for heat transfer processes without functional conversion and the paradox of entropy production of heat exchangers. The symmetric distributions of the thermal-hydraulic parameters such as coolant flow rate, coolant temperature, cladding temperature, and fuel pellet temperature were calculated, and the entransy dissipation calculation method corresponding to the fuel assembly subchannels was derived based on the entransy theory. The effect of subchannel differences on the thermal-hydraulic parameters and the symmetric distribution pattern of entransy dissipation during the cooling process of the fuel assembly was analyzed and compared from the symmetrical arrangement of subchannels in the axial and radial directions.

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Section: Introductionmentioning

confidence: 99%

Symmetric Heat Transfer Pattern of Fuel Assembly Subchannels in a Sodium-Cooled Fast Reactor

et al. 2022

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“…According to References [10,11], the entropy production rate of the time-fractional diffusion equation increases with increasing of β from one (diffusion) to two (wave propagation) that results in the so called entropy production paradox. Many efforts were put into "resolving" of this paradox (see e.g., [12] and references therein). However, as mentioned above, this paradox does not appear in the dimensions two and three, i.e., in the cases that are important for applications.…”

Section: Introductionmentioning

confidence: 99%

Entropy Production Rates of the Multi-Dimensional Fractional Diffusion Processes

Luchko

2019

Entropy

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Our starting point is the n-dimensional time-space-fractional partial differential equation (PDE) with the Caputo time-fractional derivative of order β , 0 < β < 2 and the fractional spatial derivative (fractional Laplacian) of order α , 0 < α ≤ 2 . For this equation, we first derive some integral representations of the fundamental solution and then discuss its important properties including scaling invariants and non-negativity. The time-space-fractional PDE governs a fractional diffusion process if and only if its fundamental solution is non-negative and can be interpreted as a spatial probability density function evolving in time. These conditions are satisfied for an arbitrary dimension n ∈ N if 0 < β ≤ 1 , 0 < α ≤ 2 and additionally for 1 < β ≤ α ≤ 2 in the one-dimensional case. In all these cases, we derive the explicit formulas for the Shannon entropy and for the entropy production rate of a fractional diffusion process governed by the corresponding time-space-fractional PDE. The entropy production rate depends on the orders β and α of the time and spatial derivatives and on the space dimension n and is given by the expression β n α t , t being the time variable. Even if it is an increasing function in β , one cannot speak about any entropy production paradoxes related to these processes (as stated in some publications) because the time-space-fractional PDE governs a fractional diffusion process in all dimensions only under the condition 0 < β ≤ 1 , i.e., only the slow and the conventional diffusion can be described by this equation.

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A new truncated M-fractional derivative for air pollutant dispersion

et al. 2019

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Between Waves and Diffusion: Paradoxical Entropy Production in an Exceptional Regime

Cited by 6 publications

References 31 publications

Symmetric Heat Transfer Pattern of Fuel Assembly Subchannels in a Sodium-Cooled Fast Reactor

Symmetric Heat Transfer Pattern of Fuel Assembly Subchannels in a Sodium-Cooled Fast Reactor

Entropy Production Rates of the Multi-Dimensional Fractional Diffusion Processes

A new truncated M-fractional derivative for air pollutant dispersion

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