Maximum Entropy Production Is Not a Steady State Attractor for 2D Fluid Convection
Multiple authors have claimed that the natural convection of a fluid is a process that exhibits maximum entropy production (MEP). However, almost all such investigations were limited to fixed temperature boundary conditions (BCs). It was found that under those conditions, the system tends to maximiz...
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MDPI AG
2016-12-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/18/12/431 |
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| author | Stuart Bartlett Nathaniel Virgo |
| author_facet | Stuart Bartlett Nathaniel Virgo |
| author_sort | Stuart Bartlett |
| collection | DOAJ |
| description | Multiple authors have claimed that the natural convection of a fluid is a process that exhibits maximum entropy production (MEP). However, almost all such investigations were limited to fixed temperature boundary conditions (BCs). It was found that under those conditions, the system tends to maximize its heat flux, and hence it was concluded that the MEP state is a dynamical attractor. However, since entropy production varies with heat flux and difference of inverse temperature, it is essential that any complete investigation of entropy production allows for variations in heat flux and temperature difference. Only then can we legitimately assess whether the MEP state is the most attractive. Our previous work made use of negative feedback BCs to explore this possibility. We found that the steady state of the system was far from the MEP state. For any system, entropy production can only be maximized subject to a finite set of physical and material constraints. In the case of our previous work, it was possible that the adopted set of fluid parameters were constraining the system in such a way that it was entirely prevented from reaching the MEP state. Hence, in the present work, we used a different set of boundary parameters, such that the steady states of the system were in the local vicinity of the MEP state. If MEP was indeed an attractor, relaxing those constraints of our previous work should have caused a discrete perturbation to the surface of steady state heat flux values near the value corresponding to MEP. We found no such perturbation, and hence no discernible attraction to the MEP state. Furthermore, systems with fixed flux BCs actually minimize their entropy production (relative to the alternative stable state, that of pure diffusive heat transport). This leads us to conclude that the principle of MEP is not an accurate indicator of which stable steady state a convective system will adopt. However, for all BCs considered, the quotient of heat flux and temperature difference F / Δ T —which is proportional to the dimensionless Nusselt number—does appear to be maximized. |
| first_indexed | 2024-04-11T13:58:06Z |
| format | Article |
| id | doaj.art-8486127326214b10b08701d7afea15b4 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T13:58:06Z |
| publishDate | 2016-12-01 |
| publisher | MDPI AG |
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| series | Entropy |
| spelling | doaj.art-8486127326214b10b08701d7afea15b42022-12-22T04:20:11ZengMDPI AGEntropy1099-43002016-12-01181243110.3390/e18120431e18120431Maximum Entropy Production Is Not a Steady State Attractor for 2D Fluid ConvectionStuart Bartlett0Nathaniel Virgo1Earth Life Science Institute, Tokyo Institute of Technology, 2-12-1-I7E-323 Ookayama, Meguro, Tokyo 152-8550, JapanEarth Life Science Institute, Tokyo Institute of Technology, 2-12-1-I7E-323 Ookayama, Meguro, Tokyo 152-8550, JapanMultiple authors have claimed that the natural convection of a fluid is a process that exhibits maximum entropy production (MEP). However, almost all such investigations were limited to fixed temperature boundary conditions (BCs). It was found that under those conditions, the system tends to maximize its heat flux, and hence it was concluded that the MEP state is a dynamical attractor. However, since entropy production varies with heat flux and difference of inverse temperature, it is essential that any complete investigation of entropy production allows for variations in heat flux and temperature difference. Only then can we legitimately assess whether the MEP state is the most attractive. Our previous work made use of negative feedback BCs to explore this possibility. We found that the steady state of the system was far from the MEP state. For any system, entropy production can only be maximized subject to a finite set of physical and material constraints. In the case of our previous work, it was possible that the adopted set of fluid parameters were constraining the system in such a way that it was entirely prevented from reaching the MEP state. Hence, in the present work, we used a different set of boundary parameters, such that the steady states of the system were in the local vicinity of the MEP state. If MEP was indeed an attractor, relaxing those constraints of our previous work should have caused a discrete perturbation to the surface of steady state heat flux values near the value corresponding to MEP. We found no such perturbation, and hence no discernible attraction to the MEP state. Furthermore, systems with fixed flux BCs actually minimize their entropy production (relative to the alternative stable state, that of pure diffusive heat transport). This leads us to conclude that the principle of MEP is not an accurate indicator of which stable steady state a convective system will adopt. However, for all BCs considered, the quotient of heat flux and temperature difference F / Δ T —which is proportional to the dimensionless Nusselt number—does appear to be maximized.http://www.mdpi.com/1099-4300/18/12/431entropy productionconvectionheat transfervariational principle |
| spellingShingle | Stuart Bartlett Nathaniel Virgo Maximum Entropy Production Is Not a Steady State Attractor for 2D Fluid Convection Entropy entropy production convection heat transfer variational principle |
| title | Maximum Entropy Production Is Not a Steady State Attractor for 2D Fluid Convection |
| title_full | Maximum Entropy Production Is Not a Steady State Attractor for 2D Fluid Convection |
| title_fullStr | Maximum Entropy Production Is Not a Steady State Attractor for 2D Fluid Convection |
| title_full_unstemmed | Maximum Entropy Production Is Not a Steady State Attractor for 2D Fluid Convection |
| title_short | Maximum Entropy Production Is Not a Steady State Attractor for 2D Fluid Convection |
| title_sort | maximum entropy production is not a steady state attractor for 2d fluid convection |
| topic | entropy production convection heat transfer variational principle |
| url | http://www.mdpi.com/1099-4300/18/12/431 |
| work_keys_str_mv | AT stuartbartlett maximumentropyproductionisnotasteadystateattractorfor2dfluidconvection AT nathanielvirgo maximumentropyproductionisnotasteadystateattractorfor2dfluidconvection |