Next Article in Journal
Matching Users’ Preference under Target Revenue Constraints in Data Recommendation Systems
Previous Article in Journal
Entropy Value-Based Pursuit Projection Cluster for the Teaching Quality Evaluation with Interval Number
Previous Article in Special Issue
Entropy Generation Analysis and Thermodynamic Optimization of Jet Impingement Cooling Using Large Eddy Simulation
Article Menu
Issue 2 (February) cover image

Export Article

Open AccessArticle
Entropy 2019, 21(2), 204; https://doi.org/10.3390/e21020204

On Entropic Framework Based on Standard and Fractional Phonon Boltzmann Transport Equations

Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
*
Author to whom correspondence should be addressed.
Received: 22 January 2019 / Revised: 16 February 2019 / Accepted: 18 February 2019 / Published: 21 February 2019
(This article belongs to the Special Issue Entropy Generation and Heat Transfer)
Full-Text   |   PDF [260 KB, uploaded 21 February 2019]

Abstract

Generalized expressions of the entropy and related concepts in non-Fourier heat conduction have attracted increasing attention in recent years. Based on standard and fractional phonon Boltzmann transport equations (BTEs), we study entropic functionals including entropy density, entropy flux and entropy production rate. Using the relaxation time approximation and power series expansion, macroscopic approximations are derived for these entropic concepts. For the standard BTE, our results can recover the entropic frameworks of classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT) as if there exists a well-defined effective thermal conductivity. For the fractional BTEs corresponding to the generalized Cattaneo equation (GCE) class, the entropy flux and entropy production rate will deviate from the forms in CIT and EIT. In these cases, the entropy flux and entropy production rate will contain fractional-order operators, which reflect memory effects. View Full-Text
Keywords: entropy density; entropy flux; entropy production rate; classical irreversible thermodynamics (CIT); extended irreversible thermodynamics (EIT); phonon heat transport; Boltzmann transport equation (BTE) entropy density; entropy flux; entropy production rate; classical irreversible thermodynamics (CIT); extended irreversible thermodynamics (EIT); phonon heat transport; Boltzmann transport equation (BTE)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Li, S.-N.; Cao, B.-Y. On Entropic Framework Based on Standard and Fractional Phonon Boltzmann Transport Equations. Entropy 2019, 21, 204.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top