Terms Of Entropy Production Research Articles

Comments on “Flow, thermal, and entropy generation characteristics inside a porous channel with viscous dissipation” by S. Mahmud and R.A. Fraser [Int. J. Thermal Sciences 44 (2005) 21–32

Hoomen, Merrikh and Ejlali presents comment on the paper on 'Flow, thermal, and entropy generation characteristics inside a porous channel with viscous dissipation' by S. Mahmud and R.A. Fraser. The paper presents closed form solutions to the velocity and temperature distributions that would be very useful for checking numerical computations. The authors have applied the fluid thermal conductivity kf in all of the equations, that should be replaced by the effective thermal conductivity. They have presented the temperature distribution and the Nusselt number as a function of the Darcy number only, inspite of the fact that Re, Pr, and Ec will affect the temperature profile. The authors have applied a clear-fluid compatible term in the entropy production term that has not been already considered in the thermal energy equation. The reliability of the numerical results is questionable though the authors have applied a previously tested numerical scheme.

Entropy production and lost work for some irreversible processes

In this paper we analyze in depth the lost work in an irreversible process (i.e. W Lost = W Re v − W Irrev). This quantity is also called ‘degraded energy’ or ‘energy unavailable to do work’. Usually in textbooks one can find the relation W Lost ≡ TΔSU , which, for many processes, is not suitable for evaluation of the lost work. Here we find for W Lost a more general relation in terms of internal and external entropy production, π int and π ext, quantities which also enable the Clausius inequality to be written in a simple form. Examples are given for elementary processes.

Control of Large-Scale Heat Transport by Small-Scale Mixing

Abstract The equilibrium of an idealized flow driven at the surface by wind stress and rapid relaxation to nonuniform buoyancy is analyzed in terms of entropy production, mechanical energy balance, and heat transport. The flow is rapidly rotating, and dissipation is provided by bottom drag. Diabatic forcing is transmitted from the surface by isotropic diffusion of buoyancy. The domain is periodic so that zonal averaging provides a useful decomposition of the flow into mean and eddy components. The statistical equilibrium is characterized by quantities such as the lateral buoyancy flux and the thermocline depth; here, scaling laws are proposed for these quantities in terms of the external parameters. The scaling theory predicts relations between heat transport, thermocline depth, bottom drag, and diapycnal diffusivity, which are confirmed by numerical simulations. The authors find that the depth of the thermocline is independent of the diapycnal mixing to leading order, but depends on the bottom drag. This dependence arises because the mean stratification is due to a balance between the large-scale wind-driven heat transport and the heat transport due to baroclinic eddies. The eddies equilibrate at an amplitude that depends to leading order on the bottom drag. The net poleward heat transport is a residual between the mean and eddy heat transports. The size of this residual is determined by the details of the diapycnal diffusivity. If the diffusivity is uniform (as in laboratory experiments) then the heat transport is linearly proportional to the diffusivity. If a mixed layer is incorporated by greatly increasing the diffusivity in a thin surface layer then the net heat transport is dominated by the model mixed layer.

Non Equilibrium Thermodynamics and the City: A New Approach to Urban Studies

A city can be conceived as a complex self-adaptive system. The multiple interactions among its structural elements and dynamic agents, its organization on multiple time-space scales, its exchanges with the external context, its irreversible dynamics, are signs of complexity. Some concepts from the evolutionary thermodynamics, such us the theory of dissipative structures, could be extended to the city in order to investigate its behaviour. This theoretical framework suggests to analyze the city in terms of entropy and negentropy production. An emergy analysis (spelled with an "m") of an urban region is presented in order to investigate how cities maintain their organization (and decrease their entropy) by virtue of constant energy inflows from the external environment. As a result, a non-homogeneous spatial pattern of emergy density is shown as an attempt to investigate the multiple relations and energy exchanges that take place in an urban region. This approach to urban studies introduces a new energy-based vision to understand cities.

Local entropy production in turbulent shear flows: A tool for evaluating heat transfer performance

Performance evaluation of heat transfer devices can be based on the overall entropy production in these devices. In our study we therefore provide equations for the systematic and detailed determination of local entropy production due to dissipation of mechanical energy and due to heat conduction, both in turbulent flows. After turbulence modeling has been incorporated for the fluctuating parts the overall entropy production can be determined by integration with respect to the whole flow domain. Since, however, entropy production rates show very steep gradients close to the wall, numerical solutions are far more effective with wall functions for the entropy production terms. These wall functions are mandatory when high Reynolds number turbulence models are used. For turbulent flow in a pipe with an inserted twisted tape as heat transfer promoter it is shown that based on the overall entropy production rate a clear statement from a thermodynamic point of view is possible. For a certain range of twist strength there is a decrease in overall entropy production compared to the case without insert. Also, the optimum twist strength can be determined. This information is unavailable when only pressure drop and heat transfer data are given.

Nonequilibrium Thermodynamics of Spacetime

It has previously been shown that the Einstein equation can be derived from the requirement that the Clausius relation dS=deltaQ/T hold for all local acceleration horizons through each spacetime point, where is one-quarter the horizon area change in Planck units and deltaQ and T are the energy flux across the horizon and the Unruh temperature seen by an accelerating observer just inside the horizon. Here we show that a curvature correction to the entropy that is polynomial in the Ricci scalar requires a nonequilibrium treatment. The corresponding field equation is derived from the entropy balance relation dS=deltaQ/T+diS, where diS is a bulk viscosity entropy production term that we determine by imposing energy-momentum conservation. Entropy production can also be included in pure Einstein theory by allowing for shear viscosity of the horizon.

Modeling of Entropy Production in Turbulent Flows

This article presents new modeling of turbulence correlations in the entropy transport equation for viscous, incompressible flows. An explicit entropy equation of state is developed for gases with the ideal gas law, while entropy transport equations are derived for both gases and liquids. The formulation specifically considers incompressible forced convection problems without a buoyancy term in the y-momentum equation, as density variations are neglected. Reynolds averaging techniques are applied to the turbulence closure of fluctuating temperature and entropy fields. The problem of rigorously expressing the mean entropy production in terms of other mean flow quantities is addressed. The validity of the newly developed formulation is assessed using direct numerical simulation data and empirical relations for the friction factor. Also, the dissipation (ε) of turbulent kinetic energy is formulated in terms of the Second Law. In contrast to the conventional ε equation modeling, this article proposes an alternative method by utilizing both transport and positive definite forms of the entropy production equation.

Entropy Production and Irreversible Processes -from the perspective of continuous topological evolution.

A concept of entropy production associated with continuous topological evolution is deduced (without statistics) from the fact that Cartan-Hilbert 1-form of Action defines a non-equilibrium symplectic system of Pfaff Topological dimension 2n+2. The differential entropy, dS, is composed of the interior product of the non-canonical components of momentum with the components of the differential velocities. An irreversible process can describe entropy production in terms of continuous topological evolution to non-equilibrium but stationary states. An equilibrium system can be defined topologically as a Lagrange submanifold of the 2n+2 topological space, upon which the change in entropy by continuous topological evolution is zero, dSequil=0.

Nonequilibrium thermodynamics of membrane transport

AbstractAll membrane processes are nonequilibrium processes. The transport equation describing a particular membrane process must satisfy the principles of nonequilibrium thermodynamics. However, many expressions for the flux through a membrane as functions of the driving forces can be found in the literature without resorting to nonequilibrium thermodynamics. In fact, the choice of fluxes and driving forces for a particular membrane process frequently seems to be arbitrary and accidental; this is attributed to historical developments. Some exceptions are the cases of reverse osmosis and ultrafiltration processes. Katchalsky and coworkers successfully applied the principles of nonequilibrium thermodynamics by Onsager to analyze reverse osmosis and ultrafiltration processes. A generalized treatise of nonequilibrium thermodynamic analysis is given for all different membrane processes including gas permeation, pervaporation, dialysis, reverse osmosis, ultrafiltration, microfiltration, and electrodialysis. Starting from the entropy production term, fluxes and driving forces are ascertained for each membrane process and the linear expressions between fluxes and driving forces are presented with corresponding coefficients. These are identified with the conventional entities whenever possible. As a consequence of this treatment, flux equations are more generalized to contain additional terms with additional driving forces representing the coupling phenomena. 2004 American Institute of Chemical Engineers AIChE J, 50:862–870, 2004

Computing minimal entropy production trajectories: an approach to model reduction in chemical kinetics.

Advanced experimental techniques in chemistry and physics provide increasing access to detailed deterministic mass action models for chemical reaction kinetics. Especially in complex technical or biochemical systems the huge amount of species and reaction pathways involved in a detailed modeling approach call for efficient methods of model reduction. These should be automatic and based on a firm mathematical analysis of the ordinary differential equations underlying the chemical kinetics in deterministic models. A main purpose of model reduction is to enable accurate numerical simulations of even high dimensional and spatially extended reaction systems. The latter include physical transport mechanisms and are modeled by partial differential equations. Their numerical solution for hundreds or thousands of species within a reasonable time will exceed computer capacities available now and in a foreseeable future. The central idea of model reduction is to replace the high dimensional dynamics by a low dimensional approximation with an appropriate degree of accuracy. Here I present a global approach to model reduction based on the concept of minimal entropy production and its numerical implementation. For given values of a single species concentration in a chemical system all other species concentrations are computed under the assumption that the system is as close as possible to its attractor, the thermodynamic equilibrium, in the sense that all modes of thermodynamic forces are maximally relaxed except the one, which drives the remaining system dynamics. This relaxation is expressed in terms of minimal entropy production for single reaction steps along phase space trajectories.

Entropy production of diffusion in spatially periodic deterministic systems.

This paper presents an ab initio derivation of the expression given by irreversible thermodynamics for the rate of entropy production for different classes of diffusive processes. The first class is Lorentz gases, where noninteracting particles move on a spatially periodic lattice, and collide elastically with fixed scatterers. The second class is periodic systems, where N particles interact with each other, and one of them is a tracer particle that diffuses among the cells of the lattice. We assume that, in either case, the dynamics of the system are deterministic and hyperbolic, with positive Lyapunov exponents. This work extends methods originally developed for a chaotic two-dimensional model of diffusion, the multi-baker map, to higher-dimensional, continuous-time dynamical systems appropriate for systems with one or more moving particles. Here we express the rate of entropy production in terms of hydrodynamic measures that are determined by the fractal properties of microscopic hydrodynamic modes that describe the slowest decay of the system to an equilibrium state.

An irreversible thermodynamic approach to normal grain growth with a pinning force

The formalism of the Thermodynamic Theory of Irreversible Processes is applied to grain growth in the presence of a pinning force due to a particle dispersion. The Irreversible Thermodynamics treatment is able to show that both Burke's law and Zener type expressions have a sound thermodynamical basis. Particle pinning models are interpreted in terms of the irreversible entropy production that takes place as the grain boundary bypasses a particle.

Modeling the Air-Cooled Gas Turbine: Part 1—General Thermodynamics

AbstractThis paper is Part I of a study concerned with developing a formal framework for modeling air-cooled gas turbine cycles and deals with basic thermodynamic issues. Such cycles involve gas mixtures with varying composition which must be modeled realistically. A possible approach is to define just two components, air and gas, the latter being the products of stoichiometric combustion of the fuel with air. If these components can be represented as ideal gases, the entropy increase due to compositional mixing, although a true exergy loss, can be ignored for the purpose of performance prediction. This provides considerable simplification. Consideration of three idealized simple cycles shows that the introduction of cooling with an associated thermal mixing loss does not necessarily result in a loss of cycle efficiency. This is no longer true when real gas properties and turbomachinery losses are included. The analysis clarifies the role of the cooling losses and shows the importance of assessing performance in the context of the complete cycle. There is a strong case for representing the cooling losses in terms of irreversible entropy production as this provides a formalized framework, clarifies the modeling difficulties, and aids physical interpretation. Results are presented that show the effects on performance of varying cooling flowrates and cooling losses. A comparison between simple and reheat cycles highlights the ro^le of the thermal mixing loss. Detailed modeling of the heat transfer and cooling losses is discussed in Part II of this paper.

Internal Entropy Production in Magnetic Systems

In the framework of the mathematically and conceptually simple two-level mean-field model of an electronic spin system characterised by the spin-lattice relaxation time, actual magnetic phenomena have been evaluated within the language of irreversible thermodynamics, namely in terms of internal entropy production. A suitable description of both reversible and irreversible magnetization processes is presented which enables one to distinguish between them. It is suggested that, on the basis of this model, the majority of the phenomena observed in magnetic systems, for example, the construction of hysteresis loops, the energy balance of magnetization processes, the Steinmetz rule, etc., should be experimentally evaluated.

Dissipation in Laplacian fields across irregular boundaries.

The entropy production associated to a Laplacian field distributed across irregular boundaries is studied. In the context of the active zone approximation an explicit expression is given for the entropy production in terms of geometry, whose relation to the variational formulation is discussed. It is shown that the entropy production diminishes for successive prefractal generations of the same fractal generator, so that the final fractal object is expected to dissipate less than all previous ones. The relevance of this result in the abundance of fractal surfaces or interfaces observed in nature is discussed.

Nonequilibrium Thermodynamics of Autowaves of Laminar Combustion

Within the framework of the Zel'dovich–Frank‐Kamenetskii theory of thermal propagation of flame, thermodynamic properties of an open nonlinear system are considered, and nonequilibrium entropy of a steady combustion wave is constructed. The nonequilibrium dynamic system is analyzed qualitatively and quantitatively, and the distribution functions of local entropy production in terms of the spatial variable are constructed. It is shown that total entropy production in the system is a functional on integral curves that possess extreme properties, and its minimum corresponds to a unique physically sustainable solution of the problem. The procedure of “cutting” (vanishing) of the reaction rate is justified by methods of nonequilibrium thermodynamics. A variational formulation of the problem is presented for calculation of a steady combustion wave.

The combined relaxation and vanishing Debye length limit in the hydrodynamic model for semiconductors

The combined relaxation and vanishing Debye length limit for the hydrodynamic model for semiconductors is considered in both the unipolar and the bipolar case. The resulting limit problems are non-linear drift driven hyperbolic equations. We make use of non-standard entropy functions and the related entropy productions in order to obtain uniform estimates. In the bipolar case additional time-dependent L∞-type estimates, available from the existence theory, are needed in order to control the entropy production terms. Finally, strong convergence of the electric field allows the limit towards the limiting problem. Copyright © 2001 John Wiley & Sons, Ltd.

Dissipation Trends in a Shallow Water Model

Abstract The formalism of irreversible thermodynamics is applied to the shallow water model. Entropy production and entropy flow terms are identified, describing the ways dissipation and exchange processes unfold in space and time. Explicit evaluations are carried out in the case of Lorenz’s nine-mode truncation and in the quasigeostrophic limit of the model. A number of systematic trends are identified by studying the way dissipation and kinetic energy vary as the forcing is increased and the system undergoes qualitative changes of behavior between different regimes, from simple symmetric flow to intermittent chaos. The constraints imposed by thermodynamics on the structure of the model equations and, especially, on the parameterization schemes are brought out.

A Cauchy inequality for the Boltzmann equation

The distance to a set of Maxwellians is determined for a family of functions with bounded mass, energy and a small entropy production term. Functions with small masses are close to the null Maxwellian. Functions with masses bounded from below by a constant are approached by functions proportional to the gain term of the Boltzmann operator, taking advantage of its regularity. For these regularizations, the integrands of the entropy production term are small everywhere. Hence classical arguments can be used to obtain the closedness to the set of Maxwellians.

A Cauchy inequality for the Boltzmann equation

The distance to a set of Maxwellians is determined for a family of functions with bounded mass, energy and a small entropy production term. Functions with small masses are close to the null Maxwellian. Functions with masses bounded from below by a constant are approached by functions proportional to the gain term of the Boltzmann operator, taking advantage of its regularity. For these regularizations, the integrands of the entropy production term are small everywhere. Hence classical arguments can be used to obtain the closedness to the set of Maxwellians. Copyright © 2000 John Wiley & Sons, Ltd.