This investigation provides an approach towards identification, selection or construction of certain unconstrained controls called Carnot variables which are particularly suitable for easy ...determining of power limits in various power systems. Applying these controls we develop a unified analysis of how various transfer phenomena (heat, mass and electric charge transfer) effect power limits in various energy converters, such as thermal, chemical and radiation engines and fuel cells. We present diverse pseudo-Carnot structures for converters’ efficiencies and apply them in estimating irreversible power limits in steady state systems. Power limits are determined for steady thermal systems propelled by differences of temperatures and for steady chemical systems driven by differences of chemical potentials. Radiation engines are treated as systems described by Stefan–Boltzmann equations. We show that both chemical and electrochemical energy generators (fuel cells) satisfy similar principles of modeling and apply similar schemes of power evaluation as thermal machines. Based on a systematic application of Carnot controls (as variables which satisfy identically the internal entropy constraint) we construct, in fact, a methodologically novel, coherent approach to the family of power systems. Such approach has the virtue of reducing the number of controls and is superior to the traditional approach, which works with an enlarged number of traditional constrained controls. We believe that, because of its formal lucidity, the new approach also improves our understanding of the role of various energy transfer phenomena in power systems.
We consider typical problems of the field called the finite time thermodynamics (also called the optimization thermodynamics). We also outline selected formal methods applied to solve these problems ...and discuss some results obtained. It is shown that by introducing constraints imposed on the intensity of fluxes and on the magnitude of coefficients in kinetic equations, it is possible not only to investigate limiting possibilities of thermodynamic systems within the considered class of irreversible processes, but also to state and solve problems whose formulation has no meaning in the class of reversible processes. This article is part of the themed issue 'Horizons of cybernetical physics'.
This paper represents the research direction which deals with various computer aided energy converters, in particular thermal or chemical engines and fuel cells. Applying this general framework we ...can derive formulae for a family of converters’ efficiencies and apply them to estimate irreversible power limits in practical systems. Thermal engines can be analyzed as linear units and radiation engines may be treated as Stefan-Boltzmann systems. We can also consider power limits for thermal systems as those propelled by differences of temperatures and chemical ones as those driven by differences of chemical potentials. In this paper we focus on fuel cells which are the electrochemical energy generators. We show that fuel cells satisfy the same modeling principles and apply similar computer schemes as thermal machines.
We apply thermodynamic analysis in modeling, simulation and optimization of radiation engines as non-linear energy converters. We also perform critical analysis of available data for photon flux and ...photon density that leads to exact numerical value of photon flux constant. Basic thermodynamic principles lead to expressions for converter’s efficiency and generated work in terms of driving energy flux in the system. Steady and dynamical processes are investigated. In the latter, associated with an exhaust of radiation resource measured in terms of its temperature decrease, real work is a cumulative effect obtained in a system composed of a radiation fluid, sequence of engines, and an infinite bath. Variational calculus is applied in trajectory optimization of relaxing radiation described by a pseudo-Newtonian model. The principal performance function that expresses optimal work depends on thermal coordinates and a dissipation index,
h, in fact a Hamiltonian of the optimization problem for extremum power or minimum entropy production. As an example of work limit in the radiation system under pseudo-Newtonian approximation the generalized exergy of radiation fluid is estimated in terms of finite rates quantified by Hamiltonian
h. The primary results are dynamical equations of state for radiation temperature and work output in terms of process control variables. In the second part of this paper these equations and their discrete counterparts will serve to derive efficient algorithms for work optimization in the form of Hamilton–Jacobi–Bellman equations and dynamic programming equations. Significance of non-linear analyses in dynamic optimization of radiation systems is underlined.
We treat simulation and power optimization of nonlinear, steady and dynamical generators of mechanical energy, in particular radiation engines. In dynamical cases, associated with downgrading of ...resources in time, real work is a cumulative effect obtained from a nonlinear fluid, set of engines, and an infinite bath. Dynamical state equations describe resources upgrading or downgrading in terms of temperature, work output and process controls. Recent formulae for converter’s efficiency and generated power serve to derive Hamilton–Jacobi equations for the trajectory optimization. The relaxation curve of typical nonlinear system is non-exponential. Power extremization algorithms in the form of Hamilton–Jacobi–Bellman equations (HJB equations) lead to work limits and generalized availabilities. Optimal performance functions depend on end states and the problem Hamiltonian,
h. As an example of limiting work from radiation, a generalized exergy flux of radiation fluid is estimated in terms of finite rates quantified by Hamiltonian
h.
In many systems governing HJB equations cannot be solved analytically. Then the use of discrete counterparts of these equations and numerical methods is recommended. Algorithms of discrete dynamic programming (DP) are particularly effective as they lead directly to work limits and generalized availabilities. Convergence of these algorithms to solutions of HJB equations is discussed. A Lagrange multiplier
λ helps to solve numerical algorithms of dynamic programming by eliminating the duration constraint. In analytical discrete schemes, the Legendre transformation is a significant tool leading to the original work function.
We define and analyze thermodynamic limits for various traditional and work-assisted processes of sequential development with finite rates important in engineering and biology. The thermodynamic ...limits are expressed in terms of classical exergy change and a residual inevitable minimum of dissipated exergy, or some extension including time penalty. We consider processes with heat and mass transfer that occur in a finite time and in equipment of finite dimension. These processes include heat and separation operations and are found in heat and mass exchangers, thermal networks, energy convertors, energy recovery units, storage systems, chemical reactors, and chemical plants. Our analysis is based on the condition that in order to make the results of thermodynamic analyses usable in engineering it is a thermodynamic limit (e.g. a lower bound for consumption or work or heat or an upper bound for work or heat production) which must be ensured for prescribed process requirements. The goal of this paper is not only to review and classify all main methods and results obtained in the field but also to consider common objections caused by misunderstanding of these methods and results. In fact, the paper contains a critical comparison of various methods applied in the field of energy generation, such as second law analyses, entropy generation minimization, approaches coming from ecology, and finite-time thermodynamics. A creative part of this paper outlines a general approach to the construction of ‘Carnot variables’ as suitable controls. Finite-rate models include minimal irreducible losses caused by thermal resistances to the classical exergy potential. Functions of extremum work, which incorporate residual minimum entropy production, are formulated in terms of initial and final states, total duration and (in discrete processes) number of stages.
This paper derives and discusses variational formulations for heat flows subject to physical constraints that involve the (generally) non-conserved balance of internal energy and the entropy ...representation kinetics in the form of the Cattaneo equation of heat. Another approach is also outlined which uses the (generally) non-conserved balance of the entropy and the energy-representation counterpart of the Cattaneo equation called Kaliski’s equation. Results of nonequilibrium statistical mechanics (Grad’s theory) lead to nonequilibrium corrections to entropy and energy of the fluid in terms of the nonequilibrium density distribution function,
f. These results also yield coefficients of the wave model of heat such as: relaxation time, propagation speed and thermal inertia. With these data a quadratic Lagrangian and a variational principle of Hamilton’s type follows for a fluid with heat flux in the field representation of fluid motion. For an irreversible heat transfer we show that despite of generally non-canonical form of the matter tensor the coefficients in source terms of the variational conservation laws can be suitably adjusted, so that physical (source-less and canonical) conservation laws are obtained for the energy and momentum. We discuss canonical and generalized conservation laws and show the satisfaction of the second law under the constraint of canonical conservation laws.
Two competing directions in elementary chemical or transport steps are analyzed from the viewpoint of their contribution to the overall rates. Systems with nonlinear transport phenomena and chemical ...reactions are described by the equations of nonlinear kinetics of the Marcelin-Kohnstamm–de Donder type that contain terms exponential with respect to the Planck potentials and temperature reciprocal. Simultaneously these equations are analytical expressions characterizing the transport of the substance or energy through the energy barrier. They constitute potential representations of a generalized law of mass action that includes the effect of transfer phenomena and external fields. Important are the physical consequences of these kinetics near and far from equilibrium. In these developments nonlinear symmetries and generalized affinity are important. The affinity picture - new for transport phenomena - and the traditional Onsagerian picture are shown to constitute two equivalent representations for kinetics of chemical reactions and transfer processes. Correspondence with the Onsager’s theory is shown closely to the thermodynamic equilibrium. Yet, it can be shown that rates of transport processes and chemical reactions far-from-equilibrium cannot be determined uniquely in terms of their affinities since these rates depend on all state coordinates of the system.
The study estimates minimal entropy production, the corresponding distribution of heat exchange surfaces and contact temperatures for heat exchange systems with fixed total heat load and constant ...heat transfer coefficients for the whole system. Mathematical conditions to reach this minimal entropy production are found. For a typical heat exchange system entropy production can be expressed through flow’s temperatures. Comparison of the actual entropy production with its minimal value leads to estimates of thermodynamic feasibility and efficiency of the system.
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