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Research Papers: Heat and Mass Transfer

Study of Nonequilibrium Size and Concentration Effects on the Heat and Mass Diffusion of Indistinguishable Particles Using Steepest-Entropy-Ascent Quantum Thermodynamics

[+] Author and Article Information
Guanchen Li

Mem. ASME
Center for Energy Systems Research,
Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: guanchen@vt.edu.edu

Michael R. von Spakovsky

Professor
Fellow ASME
Center for Energy Systems Research,
Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: vonspako@vt.edu.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received February 3, 2017; final manuscript received April 30, 2017; published online June 27, 2017. Assoc. Editor: Ravi Prasher.

J. Heat Transfer 139(12), 122003 (Jun 27, 2017) (8 pages) Paper No: HT-17-1062; doi: 10.1115/1.4036735 History: Received February 03, 2017; Revised April 30, 2017

Conventional first-principle approaches for studying nonequilibrium processes depend on the mechanics of individual particles or quantum states and as a result require many details of the mechanical features of the system to arrive at a macroscopic property. In contrast, thermodynamics, which has been successful in the stable equilibrium realm, provides an approach for determining macroscopic properties without the mechanical details. Nonetheless, this phenomenological approach is not generally applicable to a nonequilibrium process except in the near-equilibrium realm and under the local equilibrium and continuum assumptions, both of which limit its ability to describe nonequilibrium phenomena. Furthermore, predicting the thermodynamic features of a nonequilibrium process (of entropy generation) across all scales is difficult. To address these drawbacks, steepest-entropy-ascent quantum thermodynamics (SEAQT) can be used. It provides a first-principle thermodynamic-ensemble based approach applicable to the entire nonequilibrium realm even that far-from-equilibrium and does so with a single kinematics and dynamics, which crosses all temporal and spatial scales. Based on prior developments by the authors, SEAQT is used here to study the heat and mass diffusion of indistinguishable particles. The study focuses on the thermodynamic features of far-from-equilibrium state evolution, which is separated from the specific mechanics of individual particle interactions. Results for nonequilibrium size (volume) and concentration effects on the evolutionary state trajectory are presented for the case of high temperature and low particle concentration, which, however, do not impact the generality of the theory and will in future studies be relaxed.

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References

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Figures

Grahic Jump Location
Fig. 1

Temperature evolutions for the boson systems (solid line) and that for the fermion systems (dashed line). The concentration is high, because eγ∼10.

Grahic Jump Location
Fig. 2

Particle number evolutions for the boson systems (solid line) and that for the fermion systems (dashed line). The concentration is high, because eγ∼10.

Grahic Jump Location
Fig. 3

Temperature evolutions for the boson systems (solid line) and that for the fermion systems (dashed line). The solid line and the dashed line converge. The concentration is low, because eγ≫1.

Grahic Jump Location
Fig. 4

Particle number evolutions for the boson systems (solid line) and that for fermion systems (dashed line). The solid line and the dashed line converge. The concentration is low, because eγ≫1.

Grahic Jump Location
Fig. 5

Temperature evolutions for the boson systems for the four cases. γa and γb increase and, thus, concentration decreases from the bottom curve to the top one for system a and from the top curve to the bottom one for system b. γa−γb is kept constant. The curves for the two low concentration cases converge.

Grahic Jump Location
Fig. 6

Normalized particle number evolutions for the boson systems for the four cases. γa and γb increase and, thus, concentration decreases from the bottom curve to the top one for system a and from the top curve to the bottom one for system b. γa−γb is kept constant. The curves for the two low concentration cases converge.

Grahic Jump Location
Fig. 7

Temperature evolutions for the boson systems for different volumes and the same (γa,γb). The curves of the three cases converge.

Grahic Jump Location
Fig. 8

Normalized particle number evolution evolutions for boson systems for different volumes and the same (γa,γb). The curves of the three cases converge.

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