Analytical irreversible thermodynamics in conduction-radiative heat transfer of neutral gases through a lens of thermal radiation fields
An analytical investigation has been conducted on the steady-state conduction and a diluted gas exposed to a thermal radiation field experiences radiative heat transfer. Analytical solutions have been derived for the transport Boltzmann BGK partial differential equations system. The investigation de...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-06-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124000597 |
| _version_ | 1797213297526702080 |
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| author | Taha Z. Abdel Wahid Rashid Jan M.K. Hadhouda Ahmed Refaie Ali |
| author_facet | Taha Z. Abdel Wahid Rashid Jan M.K. Hadhouda Ahmed Refaie Ali |
| author_sort | Taha Z. Abdel Wahid |
| collection | DOAJ |
| description | An analytical investigation has been conducted on the steady-state conduction and a diluted gas exposed to a thermal radiation field experiences radiative heat transfer. Analytical solutions have been derived for the transport Boltzmann BGK partial differential equations system. The investigation delves into the irreversible thermodynamic behavior of the system through the utilization of the Liu-Lees model, which employs two-stream Maxwellian distribution functions. The moment approach is utilized to predict the behavior of macroscopic gas parameters like temperature, concentration, and Fourier heat flux. This process entails substituting these parameters into the two-stream Maxwellian distribution functions to analyze the system's non-equilibrium thermodynamic characteristics, which encompass gas particles and the heated plate. Through this analysis, kinetic coefficients, entropy, entropy flux, entropy production, and thermodynamic forces are determined. The investigation assesses the validation of Onsager's reciprocity relation, the Boltzmann H-theorem, the Le Chatelier principle, and the second law of thermodynamics within the system. Furthermore, the Gibbs formula is employed to estimate the ratios between various contributions to internal energy changes, which are determined by the total derivatives of extensive parameters. The non-equilibrium velocity distribution function was calculated for the first time, and its behavior was compared with that of the equilibrium one using 3D graphics. The behavior of the computed variables is predicted through graphical analysis and discussion of the results. |
| first_indexed | 2024-04-24T10:56:02Z |
| format | Article |
| id | doaj.art-1cd52fc35df14a6d9f1a62a49959ff71 |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-04-24T10:56:02Z |
| publishDate | 2024-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-1cd52fc35df14a6d9f1a62a49959ff712024-04-12T04:46:04ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-06-0110100673Analytical irreversible thermodynamics in conduction-radiative heat transfer of neutral gases through a lens of thermal radiation fieldsTaha Z. Abdel Wahid0Rashid Jan1M.K. Hadhouda2Ahmed Refaie Ali3Mathematics and Computer Science Department, Faculty of Science, Menoufia University, Shebin El-Kom 32511, EgyptInstitute of Energy Infrastructure (IEI), Department of Civil Engineering, College of Engineering, Universiti Tenaga Nasional (UNITEN), Putrajaya Campus, Jalan IKRAM-UNITEN, Kajang, Selangor 43000, MalaysiaBasic Sciences Department, El Gazeera High Institute for Engineering and Technology, Cairo, EgyptMathematics and Computer Science Department, Faculty of Science, Menoufia University, Shebin El-Kom 32511, Egypt; Corresponding author.An analytical investigation has been conducted on the steady-state conduction and a diluted gas exposed to a thermal radiation field experiences radiative heat transfer. Analytical solutions have been derived for the transport Boltzmann BGK partial differential equations system. The investigation delves into the irreversible thermodynamic behavior of the system through the utilization of the Liu-Lees model, which employs two-stream Maxwellian distribution functions. The moment approach is utilized to predict the behavior of macroscopic gas parameters like temperature, concentration, and Fourier heat flux. This process entails substituting these parameters into the two-stream Maxwellian distribution functions to analyze the system's non-equilibrium thermodynamic characteristics, which encompass gas particles and the heated plate. Through this analysis, kinetic coefficients, entropy, entropy flux, entropy production, and thermodynamic forces are determined. The investigation assesses the validation of Onsager's reciprocity relation, the Boltzmann H-theorem, the Le Chatelier principle, and the second law of thermodynamics within the system. Furthermore, the Gibbs formula is employed to estimate the ratios between various contributions to internal energy changes, which are determined by the total derivatives of extensive parameters. The non-equilibrium velocity distribution function was calculated for the first time, and its behavior was compared with that of the equilibrium one using 3D graphics. The behavior of the computed variables is predicted through graphical analysis and discussion of the results.http://www.sciencedirect.com/science/article/pii/S2666818124000597Partial differential equationsBoltzmannHeat transferMolecular gasMaxwellian distributionRadiation flux |
| spellingShingle | Taha Z. Abdel Wahid Rashid Jan M.K. Hadhouda Ahmed Refaie Ali Analytical irreversible thermodynamics in conduction-radiative heat transfer of neutral gases through a lens of thermal radiation fields Partial Differential Equations in Applied Mathematics Partial differential equations Boltzmann Heat transfer Molecular gas Maxwellian distribution Radiation flux |
| title | Analytical irreversible thermodynamics in conduction-radiative heat transfer of neutral gases through a lens of thermal radiation fields |
| title_full | Analytical irreversible thermodynamics in conduction-radiative heat transfer of neutral gases through a lens of thermal radiation fields |
| title_fullStr | Analytical irreversible thermodynamics in conduction-radiative heat transfer of neutral gases through a lens of thermal radiation fields |
| title_full_unstemmed | Analytical irreversible thermodynamics in conduction-radiative heat transfer of neutral gases through a lens of thermal radiation fields |
| title_short | Analytical irreversible thermodynamics in conduction-radiative heat transfer of neutral gases through a lens of thermal radiation fields |
| title_sort | analytical irreversible thermodynamics in conduction radiative heat transfer of neutral gases through a lens of thermal radiation fields |
| topic | Partial differential equations Boltzmann Heat transfer Molecular gas Maxwellian distribution Radiation flux |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124000597 |
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