scholarly journals A Variational Formulation of Nonequilibrium Thermodynamics for Discrete Open Systems with Mass and Heat Transfer

Entropy ◽  
2018 ◽  
Vol 20 (3) ◽  
pp. 163 ◽  
Author(s):  
François Gay-Balmaz ◽  
Hiroaki Yoshimura
Keyword(s):  
Heat Transfer ◽  
Entropy Production ◽  
Variational Formulation ◽  
Evolution Equations ◽  
Nonequilibrium Thermodynamics ◽  
Open Systems ◽  
Internal Heat ◽  
Nonholonomic Constraints ◽  
Time Dependent ◽  
Nonlinear Constraint

We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for systems with time-dependent nonlinear nonholonomic constraints and time-dependent Lagrangian. For discrete open systems, the time-dependent nonlinear constraint is associated with the rate of internal entropy production of the system. We show that this constraint on the solution curve systematically yields a constraint on the variations to be used in the action functional. The proposed variational formulation is intrinsic and provides the same structure for a wide class of discrete open systems. We illustrate our theory by presenting examples of open systems experiencing mechanical interactions, as well as internal diffusion, internal heat transfer, and their cross-effects. Our approach yields a systematic way to derive the complete evolution equations for the open systems, including the expression of the internal entropy production of the system, independently on its complexity. It might be especially useful for the study of the nonequilibrium thermodynamics of biophysical systems.

Dirac structures and variational formulation of port-Dirac systems in nonequilibrium thermodynamics

2020 ◽  
Vol 37 (4) ◽  
pp. 1298-1347
Author(s):  
François Gay-Balmaz ◽  
Hiroaki Yoshimura
Keyword(s):  
Entropy Production ◽  
Variational Formulation ◽  
Nonequilibrium Thermodynamics ◽  
Open Systems ◽  
Ideal Gas ◽  
Irreversible Processes ◽  
Lagrangian Systems ◽  
Specific Class ◽  
Dirac Structures ◽  
Dirac Systems

Abstract The notion of implicit port-Lagrangian systems for nonholonomic mechanics was proposed in Yoshimura & Marsden (2006a, J. Geom. Phys., 57, 133–156; 2006b, J. Geom. Phys., 57, 209–250; 2006c, Proc. of the 17th International Symposium on Mathematical Theory of Networks and Systems, Kyoto) as a Lagrangian analogue of implicit port-Hamiltonian systems. Such port-systems have an interconnection structure with ports through which power is exchanged with the exterior and which can be modeled by Dirac structures. In this paper, we present the notions of implicit port-Lagrangian systems and port-Dirac dynamical systems in nonequilibrium thermodynamics by generalizing the Dirac formulation to the case allowing irreversible processes, both for closed and open systems. Port-Dirac systems in nonequilibrium thermodynamics can be also deduced from a variational formulation of nonequilibrium thermodynamics for closed and open systems introduced in Gay-Balmaz & Yoshimura (2017a, J. Geom. Phys., 111, 169–193; 2018a, Entropy, 163, 1–26). This is a type of Lagrange–d’Alembert principle for the specific class of nonholonomic systems with nonlinear constraints of thermodynamic type, which are associated to the entropy production equation of the system. We illustrate our theory with some examples such as a cylinder-piston with ideal gas, an electric circuit with entropy production due to a resistor and an open piston with heat and matter exchange with the exterior.

Second Law Analysis of Thermodynamic Cycles for Aero Engines

2015 ◽  
Author(s):  
Eva Kerber ◽  
Bernhard Weigand ◽  
Florian Schmidt ◽  
Stephan Staudacher
Keyword(s):  
Heat Transfer ◽  
Entropy Production ◽  
Internal Heat ◽  
Constant Volume ◽  
Specific Power ◽  
Second Law ◽  
Thermodynamic Cycles ◽  
Heat Addition ◽  
Volume Heat ◽  
Internal Heat Transfer

This paper presents an evaluation of thermodynamic cycles with the help of second law thermodynamics. In common studies thermodynamic cycles are analyzed and judged mostly just by thermal efficiency and specific power output. Another way to describe the efficiency of a cycle and to identify the potential is the analysis of the entropy production of the system. In a previous study a general investigation of thermodynamic cycles was carried out [1]. The promising technologies identified were isothermal compression and expansion, internal heat transfer and constant-volume heat addition. Based on these theoretical and idealized investigations, estimations for component efficiencies and losses were made. The present study investigates the entropy production of the thermodynamic cycles including these promising technologies. This helps to understand the interaction of the components and the effect of single components and their losses on the whole cycle. Furthermore a distinction between internal and external entropy production is made. This identifies which part of the losses occurs in the components and which amount of exergy leaves the system unused. The results finally lead to a gas turbine cycle involving compression with intercooling, internal heat transfer and constant-volume heat addition.

BAYESIAN ESTIMATION OF A TIME DEPENDENT INTERNAL HEAT SOURCE IN A HETEROGENEOUS MEDIA

2016 ◽  
Author(s):  
Carolina Palma Naveira Cotta ◽  
Kelvin Chen ◽  
Christopher Tostado ◽  
Philippe Rollemberg d'Egmont ◽  
Fernando Duda ◽  
...  
Keyword(s):  
Heat Source ◽  
Bayesian Estimation ◽  
Heterogeneous Media ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Time Dependent

scholarly journals A Computational Study on the Role of Parameters for Identification of Thyroid Nodules by Infrared Images (and Comparison with Real Data)

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4459
Author(s):  
José R. González ◽  
Charbel Damião ◽  
Maira Moran ◽  
Cristina A. Pantaleão ◽  
Rubens A. Cruz ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thyroid Nodules ◽  
Numerical Study ◽  
Computational Study ◽  
Internal Heat ◽  
Heat Transfer Process ◽  
The Body ◽  
Physical Parameters ◽  
Infrared Sensors ◽  
Wide Range

According to experts and medical literature, healthy thyroids and thyroids containing benign nodules tend to be less inflamed and less active than those with malignant nodules. It seems to be a consensus that malignant nodules have more blood veins and more blood circulation. This may be related to the maintenance of the nodule’s heat at a higher level compared with neighboring tissues. If the internal heat modifies the skin radiation, then it could be detected by infrared sensors. The goal of this work is the investigation of the factors that allow this detection, and the possible relation with any pattern referent to nodule malignancy. We aim to consider a wide range of factors, so a great number of numerical simulations of the heat transfer in the region under analysis, based on the Finite Element method, are performed to study the influence of each nodule and patient characteristics on the infrared sensor acquisition. To do so, the protocol for infrared thyroid examination used in our university’s hospital is simulated in the numerical study. This protocol presents two phases. In the first one, the body under observation is in steady state. In the second one, it is submitted to thermal stress (transient state). Both are simulated in order to verify if it is possible (by infrared sensors) to identify different behavior referent to malignant nodules. Moreover, when the simulation indicates possible important aspects, patients with and without similar characteristics are examined to confirm such influences. The results show that the tissues between skin and thyroid, as well as the nodule size, have an influence on superficial temperatures. Other thermal parameters of thyroid nodules show little influence on surface infrared emissions, for instance, those related to the vascularization of the nodule. All details of the physical parameters used in the simulations, characteristics of the real nodules and thermal examinations are publicly available, allowing these simulations to be compared with other types of heat transfer solutions and infrared examination protocols. Among the main contributions of this work, we highlight the simulation of the possible range of parameters, and definition of the simulation approach for mapping the used infrared protocol, promoting the investigation of a possible relation between the heat transfer process and the data obtained by infrared acquisitions.

Laminar boundary layers behind detonation waves

1983 ◽  
Vol 387 (1793) ◽  
pp. 331-349 ◽  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Boundary Layers ◽  
Flow Analysis ◽  
Time Dependent ◽  
Detonation Waves ◽  
Planar Geometry ◽  
Laminar Boundary Layers ◽  
Spherical Detonation ◽  
Layer Flow

New solutions are presented for non-stationary boundary layers induced by planar, cylindrical and spherical Chapman-Jouguet (C-J) detonation waves. The numerical results show that the Prandtl number ( Pr ) has a very significant influence on the boundary-layer-flow structure. A comparison with available time-dependent heat-transfer measurements in a planar geometry in a 2H 2 + O 2 mixture shows much better agreement with the present analysis than has been obtained previously by others. This lends confidence to the new results on boundary layers induced by cylindrical and spherical detonation waves. Only the spherical-flow analysis is given here in detail for brevity.

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