Legitimacy of the Local Thermal Equilibrium Hypothesis in Porous Media: A Comprehensive Review
Local thermal equilibrium (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>T</mi><mi>E</mi></mrow></semantics></math></inline-formula&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/14/23/8114 |
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| author | Gazy F. Al-Sumaily Amged Al Ezzi Hayder A. Dhahad Mark C. Thompson Talal Yusaf |
| author_facet | Gazy F. Al-Sumaily Amged Al Ezzi Hayder A. Dhahad Mark C. Thompson Talal Yusaf |
| author_sort | Gazy F. Al-Sumaily |
| collection | DOAJ |
| description | Local thermal equilibrium (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>T</mi><mi>E</mi></mrow></semantics></math></inline-formula>) is a frequently-employed hypothesis when analysing convection heat transfer in porous media. However, investigation of the non-equilibrium phenomenon exhibits that such hypothesis is typically not true for many circumstances such as rapid cooling or heating, and in industrial applications involving immediate transient thermal response, leading to a lack of local thermal equilibrium (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>T</mi><mi>E</mi></mrow></semantics></math></inline-formula>). Therefore, for the sake of appropriately conduct the technological process, it has become necessary to examine the validity of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>T</mi><mi>E</mi></mrow></semantics></math></inline-formula> assumption before deciding which energy model should be used. Indeed, the legitimacy of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>T</mi><mi>E</mi></mrow></semantics></math></inline-formula> hypothesis has been widely investigated in different applications and different modes of heat transfer, and many criteria have been developed. This paper summarises the studies that investigated this hypothesis in forced, free, and mixed convection, and presents the appropriate circumstances that can make the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>T</mi><mi>E</mi></mrow></semantics></math></inline-formula> hypothesis to be valid. For example, in forced convection, the literature shows that this hypothesis is valid for lower Darcy number, lower Reynolds number, lower Prandtl number, and/or lower solid phase thermal conductivity; however, it becomes invalid for higher effective fluid thermal conductivity and/or lower interstitial heat transfer coefficient. |
| first_indexed | 2024-03-10T04:54:14Z |
| format | Article |
| id | doaj.art-59a8348f276e480eb4b06bc8cf3408ea |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-10T04:54:14Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-59a8348f276e480eb4b06bc8cf3408ea2023-11-23T02:22:59ZengMDPI AGEnergies1996-10732021-12-011423811410.3390/en14238114Legitimacy of the Local Thermal Equilibrium Hypothesis in Porous Media: A Comprehensive ReviewGazy F. Al-Sumaily0Amged Al Ezzi1Hayder A. Dhahad2Mark C. Thompson3Talal Yusaf4Energy and Renewable Energies Technology Centre, University of Technology, Baghdad 19006, IraqDepartment of Electrochemical Engineering, University of Technology, Baghdad 19006, IraqMechanical Engineering Department, University of Technology, Baghdad 19006, IraqDepartment of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC 3800, AustraliaSchool of Engineering and Technology, Central Queensland University, Brisbane, QLD 4009, AustraliaLocal thermal equilibrium (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>T</mi><mi>E</mi></mrow></semantics></math></inline-formula>) is a frequently-employed hypothesis when analysing convection heat transfer in porous media. However, investigation of the non-equilibrium phenomenon exhibits that such hypothesis is typically not true for many circumstances such as rapid cooling or heating, and in industrial applications involving immediate transient thermal response, leading to a lack of local thermal equilibrium (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>T</mi><mi>E</mi></mrow></semantics></math></inline-formula>). Therefore, for the sake of appropriately conduct the technological process, it has become necessary to examine the validity of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>T</mi><mi>E</mi></mrow></semantics></math></inline-formula> assumption before deciding which energy model should be used. Indeed, the legitimacy of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>T</mi><mi>E</mi></mrow></semantics></math></inline-formula> hypothesis has been widely investigated in different applications and different modes of heat transfer, and many criteria have been developed. This paper summarises the studies that investigated this hypothesis in forced, free, and mixed convection, and presents the appropriate circumstances that can make the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>T</mi><mi>E</mi></mrow></semantics></math></inline-formula> hypothesis to be valid. For example, in forced convection, the literature shows that this hypothesis is valid for lower Darcy number, lower Reynolds number, lower Prandtl number, and/or lower solid phase thermal conductivity; however, it becomes invalid for higher effective fluid thermal conductivity and/or lower interstitial heat transfer coefficient.https://www.mdpi.com/1996-1073/14/23/8114convection heat transferporous media<i>LTE</i><i>LTNE</i> |
| spellingShingle | Gazy F. Al-Sumaily Amged Al Ezzi Hayder A. Dhahad Mark C. Thompson Talal Yusaf Legitimacy of the Local Thermal Equilibrium Hypothesis in Porous Media: A Comprehensive Review Energies convection heat transfer porous media <i>LTE</i> <i>LTNE</i> |
| title | Legitimacy of the Local Thermal Equilibrium Hypothesis in Porous Media: A Comprehensive Review |
| title_full | Legitimacy of the Local Thermal Equilibrium Hypothesis in Porous Media: A Comprehensive Review |
| title_fullStr | Legitimacy of the Local Thermal Equilibrium Hypothesis in Porous Media: A Comprehensive Review |
| title_full_unstemmed | Legitimacy of the Local Thermal Equilibrium Hypothesis in Porous Media: A Comprehensive Review |
| title_short | Legitimacy of the Local Thermal Equilibrium Hypothesis in Porous Media: A Comprehensive Review |
| title_sort | legitimacy of the local thermal equilibrium hypothesis in porous media a comprehensive review |
| topic | convection heat transfer porous media <i>LTE</i> <i>LTNE</i> |
| url | https://www.mdpi.com/1996-1073/14/23/8114 |
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