Abstract The formalism of the internal variable theory is applied to extend Navier-Stokes equations. The internal variable theory provides a thermodynamically consistent derivation of constitutive relations and equations of motion without a priori specifying the nature of internal variables. Both single and dual internal variables cases are thoroughly examined. The similarities and differences of the approaches are emphasized. In the single internal variable framework, the elimination of the internal variable results in Maxwell-type constitutive relations and hyperbolic equations of motion. The dual internal variable technique enables us to create even more sophisticated fluid flow models with coupled equations for fluid motion and internal variable evolution.
{"title":"Internal Variables as a Tool for Extending Navier-Stokes Equations","authors":"A. Berezovski","doi":"10.1515/jnet-2021-0089","DOIUrl":"https://doi.org/10.1515/jnet-2021-0089","url":null,"abstract":"Abstract The formalism of the internal variable theory is applied to extend Navier-Stokes equations. The internal variable theory provides a thermodynamically consistent derivation of constitutive relations and equations of motion without a priori specifying the nature of internal variables. Both single and dual internal variables cases are thoroughly examined. The similarities and differences of the approaches are emphasized. In the single internal variable framework, the elimination of the internal variable results in Maxwell-type constitutive relations and hyperbolic equations of motion. The dual internal variable technique enables us to create even more sophisticated fluid flow models with coupled equations for fluid motion and internal variable evolution.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":null,"pages":null},"PeriodicalIF":6.6,"publicationDate":"2022-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47179329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Some tools of Non-Equilibrium Thermodynamics of closed discrete systems are considered: the non-equilibrium state space, the non-equilibrium entropy as a state function and its connection with the entropy production, Clausius’ inequality, equilibrium and accompanying processes. Why can the thermostatic temperature be used successfully in thermal engineering even in cases of non-equilibrium?
{"title":"Thermodynamical Foundations of Closed Discrete Non-Equilibrium Systems","authors":"W. Muschik","doi":"10.1515/jnet-2021-0064","DOIUrl":"https://doi.org/10.1515/jnet-2021-0064","url":null,"abstract":"Abstract Some tools of Non-Equilibrium Thermodynamics of closed discrete systems are considered: the non-equilibrium state space, the non-equilibrium entropy as a state function and its connection with the entropy production, Clausius’ inequality, equilibrium and accompanying processes. Why can the thermostatic temperature be used successfully in thermal engineering even in cases of non-equilibrium?","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":null,"pages":null},"PeriodicalIF":6.6,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46829129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In a series of papers we have obtained results for nonlinear heat transport when thin wires exchange heat non-linearly with the surroundings, with particular attention to propagating solitons. Here we obtain and discuss new results related to the propagation of nonlinear heat fronts and some conceptual aspects referring to the application of the second principle of thermodynamics to some nonlinear steady states related to non-propagating solitons.
{"title":"Nonlinear Thermal Transport with Inertia in Thin Wires: Thermal Fronts and Steady States","authors":"M. Sciacca, D. Jou","doi":"10.1515/jnet-2021-0069","DOIUrl":"https://doi.org/10.1515/jnet-2021-0069","url":null,"abstract":"Abstract In a series of papers we have obtained results for nonlinear heat transport when thin wires exchange heat non-linearly with the surroundings, with particular attention to propagating solitons. Here we obtain and discuss new results related to the propagation of nonlinear heat fronts and some conceptual aspects referring to the application of the second principle of thermodynamics to some nonlinear steady states related to non-propagating solitons.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":null,"pages":null},"PeriodicalIF":6.6,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48945838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Editorial","authors":"V. Klika, M. Pavelka","doi":"10.1515/jnet-2022-5003","DOIUrl":"https://doi.org/10.1515/jnet-2022-5003","url":null,"abstract":"","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":null,"pages":null},"PeriodicalIF":6.6,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48344902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The general concept of temperature is thermodynamically defined in equilibrium somehow predictable even for non-equilibrium; however, it presents some still controversial aspects, as has been shown in a number of studies and reviews that have been published so far. Equilibrium concepts are often extrapolated to apply in micro-localized equilibrium and then appended to non-equilibrium in its entirety, which helps to define out-of-equilibrium temperature on both the macroscopic and microscopic bases. Unfortunately, these theoretical analyses do not provide any guidance on how to assess and understand temperature in practical measurements, such as for conventional thermal analysis. Insufficient use of alternative thermodynamic attitudes is evident especially in the field of thermophysical studies, which do not use static measurements, because they usually involve heating from an external source, i. e., the effect of thermal dynamics on the laboratory sample. This paper presents the applied nonequilibrium thermodynamic concept, historically known as thermotics. This approach takes into account the existence of gradients and heat fluxes, which it assesses from the point of view of the average user, and considers additional influences, going beyond the description of thermodynamics in traditional textbooks. The goal is to extend their validity, even to the state of constant first-time derivatives. At the same time, it points to changes in the temperature due to thermal inertia, which has long been ignored, suggesting that the heat spreads immediately. Moreover, special techniques enabling measurements during its extreme changes probably then require an alternative concept for temperature (tempericity). This opinion paper may provide stimuli for further discussion with regard to the practice of measurements done in the customary nonisothermal mode.
{"title":"Thermotics As an Alternative Nonequilibrium Thermodynamic Approach Suitable for Real Thermoanalytical Measurements: A Short Review","authors":"J. Šesták, R. Černý","doi":"10.1515/jnet-2021-0074","DOIUrl":"https://doi.org/10.1515/jnet-2021-0074","url":null,"abstract":"Abstract The general concept of temperature is thermodynamically defined in equilibrium somehow predictable even for non-equilibrium; however, it presents some still controversial aspects, as has been shown in a number of studies and reviews that have been published so far. Equilibrium concepts are often extrapolated to apply in micro-localized equilibrium and then appended to non-equilibrium in its entirety, which helps to define out-of-equilibrium temperature on both the macroscopic and microscopic bases. Unfortunately, these theoretical analyses do not provide any guidance on how to assess and understand temperature in practical measurements, such as for conventional thermal analysis. Insufficient use of alternative thermodynamic attitudes is evident especially in the field of thermophysical studies, which do not use static measurements, because they usually involve heating from an external source, i. e., the effect of thermal dynamics on the laboratory sample. This paper presents the applied nonequilibrium thermodynamic concept, historically known as thermotics. This approach takes into account the existence of gradients and heat fluxes, which it assesses from the point of view of the average user, and considers additional influences, going beyond the description of thermodynamics in traditional textbooks. The goal is to extend their validity, even to the state of constant first-time derivatives. At the same time, it points to changes in the temperature due to thermal inertia, which has long been ignored, suggesting that the heat spreads immediately. Moreover, special techniques enabling measurements during its extreme changes probably then require an alternative concept for temperature (tempericity). This opinion paper may provide stimuli for further discussion with regard to the practice of measurements done in the customary nonisothermal mode.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":null,"pages":null},"PeriodicalIF":6.6,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48097957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We show that a confined viscous liquid emits a dynamic thermal response upon applying a low frequency (∼1 Hz) shear excitation. Hot and cold thermal waves are observed in situ at atmospheric pressure and room temperature, in a viscous liquid (polypropylene glycol) at various thicknesses ranging from 100 µm up to 340 µm, upon applying a mechanical oscillatory shear strain. The observed thermal effects, synchronous with the mechanical excitation, are inconsistent with a viscous behaviour. It indicates that mesoscopic liquids are able to (partly) convert mechanical shear energy in non-equilibrium thermodynamic states. This effect called thermo-elasticity is well known in solid materials. The observation of a thermal coupling to the mechanical shear deformation reinforces the assumption of elastically correlated liquid molecules. The amplitude of the thermo-elastic waves increases linearly by increasing the shear strain amplitude up to a transition to a non-linear thermal behavior, similar to a transition from an elastic to plastic regime. The thermo-elastic effects do not give rise to any change in stress measurements and thus the dynamic thermal analysis provides unique information about dynamic liquid properties.
{"title":"Thermal Shear Waves Induced in Mesoscopic Liquids at Low Frequency Mechanical Deformation","authors":"E. Kume, L. Noirez","doi":"10.1515/jnet-2021-0091","DOIUrl":"https://doi.org/10.1515/jnet-2021-0091","url":null,"abstract":"Abstract We show that a confined viscous liquid emits a dynamic thermal response upon applying a low frequency (∼1 Hz) shear excitation. Hot and cold thermal waves are observed in situ at atmospheric pressure and room temperature, in a viscous liquid (polypropylene glycol) at various thicknesses ranging from 100 µm up to 340 µm, upon applying a mechanical oscillatory shear strain. The observed thermal effects, synchronous with the mechanical excitation, are inconsistent with a viscous behaviour. It indicates that mesoscopic liquids are able to (partly) convert mechanical shear energy in non-equilibrium thermodynamic states. This effect called thermo-elasticity is well known in solid materials. The observation of a thermal coupling to the mechanical shear deformation reinforces the assumption of elastically correlated liquid molecules. The amplitude of the thermo-elastic waves increases linearly by increasing the shear strain amplitude up to a transition to a non-linear thermal behavior, similar to a transition from an elastic to plastic regime. The thermo-elastic effects do not give rise to any change in stress measurements and thus the dynamic thermal analysis provides unique information about dynamic liquid properties.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":null,"pages":null},"PeriodicalIF":6.6,"publicationDate":"2022-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42055871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this work, an analytical analysis of the dynamics of a van der Waals gas flow passing through a direct shock wave was performed. For this purpose, modified Rankine-Hugoniot conditions were used. The influence of parameters α and β of the van der Waals model and the pressure jump in the shock adiabat was analyzed. Relations for the velocity jump in flow were obtained, and the influence of parameters α and β on the velocity jump was revealed. Calculations made it possible to estimate the limits of applicability of the van der Waals model, within which it adequately describes the physics of the process under consideration.
{"title":"Shock Wave in van der Waals Gas","authors":"A. Avramenko, I. V. Shevchuk, N. Dmitrenko","doi":"10.1515/jnet-2021-0099","DOIUrl":"https://doi.org/10.1515/jnet-2021-0099","url":null,"abstract":"Abstract In this work, an analytical analysis of the dynamics of a van der Waals gas flow passing through a direct shock wave was performed. For this purpose, modified Rankine-Hugoniot conditions were used. The influence of parameters α and β of the van der Waals model and the pressure jump in the shock adiabat was analyzed. Relations for the velocity jump in flow were obtained, and the influence of parameters α and β on the velocity jump was revealed. Calculations made it possible to estimate the limits of applicability of the van der Waals model, within which it adequately describes the physics of the process under consideration.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":null,"pages":null},"PeriodicalIF":6.6,"publicationDate":"2022-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47293871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D. Peschka, Andrea Zafferi, L. Heltai, Marita Thomas
Abstract We present a framework to systematically derive variational formulations for fluid-structure interaction problems based on thermodynamical driving functionals and geometric structures in different coordinate systems by suitable transformations within this formulation. Our approach provides a promising basis to construct structure-preserving discretization strategies.
{"title":"Variational Approach to Fluid-Structure Interaction via GENERIC","authors":"D. Peschka, Andrea Zafferi, L. Heltai, Marita Thomas","doi":"10.1515/jnet-2021-0081","DOIUrl":"https://doi.org/10.1515/jnet-2021-0081","url":null,"abstract":"Abstract We present a framework to systematically derive variational formulations for fluid-structure interaction problems based on thermodynamical driving functionals and geometric structures in different coordinate systems by suitable transformations within this formulation. Our approach provides a promising basis to construct structure-preserving discretization strategies.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":null,"pages":null},"PeriodicalIF":6.6,"publicationDate":"2022-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43348850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Faraz Ahmad, F. Ahmed, H. Ali, Zabdur Rehman, Muhammad Suleman, Izaz Raouf
Abstract The aim of this paper is to numerically analyze the hydrothermal behavior of different cross-sectional geometries of microchannel heat sinks (MCHSs) and conduct a comparative analysis of traditional and non-traditional designs using ANSYS Fluent. It is expected that the proposed design discussed in this paper will improve the performance of MCHSs by maximizing the cooling capability and minimizing the thermal resistance and entropy generation rate, thus leading to better energy efficiency. The channel designs include a rectangular microchannel (RMC), a circular microchannel (CMC), an elliptical microchannel (EMC), a trapezoidal microchannel (TMC), a hexagonal microchannel (HMC), and a new microchannel (NMC) which has a plus-like shape. The discussed geometry of the NMC is designed in such a way that it maximizes the cross-sectional area and the wetted perimeter of the channel, keeping the hydraulic diameter constant ( D h = 412{D_{h}}=412 µm). The performance of various channels is compared on the basis of pressure drop, wall temperature, thermal enhancement factor, thermal resistance, thermal transport efficiency, and entropy generation rates. It has been observed that the NMC is capable of cooling effectively and it can achieve a minimum wall temperature of 305 K, thus offering the lowest thermal resistance ( R th {R_{mathrm{th}}}), irreversible heat loss, and entropy generation rate. Moreover, the NMC has achieved the highest value of the thermal enhancement factor, i. e., 1.13, at Re = 1 , 000mathrm{Re}=1,000. Similarly, it has the highest thermal transport efficiency of almost 97 % at Re = 1 , 000mathrm{Re}=1,000, followed by the TMC and the RMC. Overall, the NMC has achieved the best performance in all aspects, followed by the RMC and TMC. The performance of the EMC, the CMC, and the HMC was found to be the worst in this study.
{"title":"Effect of Cross-Sectional Geometry on Hydrothermal Behavior of Microchannel Heat Sink","authors":"Faraz Ahmad, F. Ahmed, H. Ali, Zabdur Rehman, Muhammad Suleman, Izaz Raouf","doi":"10.1515/jnet-2021-0067","DOIUrl":"https://doi.org/10.1515/jnet-2021-0067","url":null,"abstract":"Abstract The aim of this paper is to numerically analyze the hydrothermal behavior of different cross-sectional geometries of microchannel heat sinks (MCHSs) and conduct a comparative analysis of traditional and non-traditional designs using ANSYS Fluent. It is expected that the proposed design discussed in this paper will improve the performance of MCHSs by maximizing the cooling capability and minimizing the thermal resistance and entropy generation rate, thus leading to better energy efficiency. The channel designs include a rectangular microchannel (RMC), a circular microchannel (CMC), an elliptical microchannel (EMC), a trapezoidal microchannel (TMC), a hexagonal microchannel (HMC), and a new microchannel (NMC) which has a plus-like shape. The discussed geometry of the NMC is designed in such a way that it maximizes the cross-sectional area and the wetted perimeter of the channel, keeping the hydraulic diameter constant ( D h = 412{D_{h}}=412 µm). The performance of various channels is compared on the basis of pressure drop, wall temperature, thermal enhancement factor, thermal resistance, thermal transport efficiency, and entropy generation rates. It has been observed that the NMC is capable of cooling effectively and it can achieve a minimum wall temperature of 305 K, thus offering the lowest thermal resistance ( R th {R_{mathrm{th}}}), irreversible heat loss, and entropy generation rate. Moreover, the NMC has achieved the highest value of the thermal enhancement factor, i. e., 1.13, at Re = 1 , 000mathrm{Re}=1,000. Similarly, it has the highest thermal transport efficiency of almost 97 % at Re = 1 , 000mathrm{Re}=1,000, followed by the TMC and the RMC. Overall, the NMC has achieved the best performance in all aspects, followed by the RMC and TMC. The performance of the EMC, the CMC, and the HMC was found to be the worst in this study.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":null,"pages":null},"PeriodicalIF":6.6,"publicationDate":"2022-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42492276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The relation between heat flux and temperature gradient has been considered as a constitutive structure or as a balance law in different approaches. Both views may allow a description of heat conduction characterized by finite speed propagation of temperature disturbances. Such a result, which overcomes Fourier’s drawback of infinite speed propagation, can be obtained also by considering insufficient the representation of a conductor, even when it is considered to be rigid, rather than the sole relation between heat flux and temperature gradient. We comment this last view and describe the intersection with previous proposals. Eventually, we show how under Fourier’s law we can have traveling-wave-type temperature propagation when thermal microstructures are accounted for.
{"title":"Sources of Finite Speed Temperature Propagation","authors":"P. M. Mariano, M. Spadini","doi":"10.1515/jnet-2021-0078","DOIUrl":"https://doi.org/10.1515/jnet-2021-0078","url":null,"abstract":"Abstract The relation between heat flux and temperature gradient has been considered as a constitutive structure or as a balance law in different approaches. Both views may allow a description of heat conduction characterized by finite speed propagation of temperature disturbances. Such a result, which overcomes Fourier’s drawback of infinite speed propagation, can be obtained also by considering insufficient the representation of a conductor, even when it is considered to be rigid, rather than the sole relation between heat flux and temperature gradient. We comment this last view and describe the intersection with previous proposals. Eventually, we show how under Fourier’s law we can have traveling-wave-type temperature propagation when thermal microstructures are accounted for.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":null,"pages":null},"PeriodicalIF":6.6,"publicationDate":"2022-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44048481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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