Despite its idealizations, thermodynamics has proven its power as a predictive theory for practical applications. In particular, the Curzon–Ahlborn efficiency provides a benchmark for any real engine operating at maximal power. Here we further develop the analysis of endoreversible Otto engines. For a generic class of working mediums, whose internal energy is proportional to some power of the temperature, we find that no engine can achieve the Carnot efficiency at finite power. However, we also find that for the specific example of photonic engines the efficiency at maximal power is higher than the Curzon–Ahlborn efficiency.
The fundamental issue in the energetic performance of power plants, working both as traditional fuel engines and as combined-cycle turbines (gas-steam), lies in quantifying the internal irreversibilities which are associated with the working substance operating in cycles. The purpose of several irreversible energy converter models is to find objective thermodynamic functions that determine operation modes for real thermal engines and at the same time study the trade-off between energy losses per cycle and the useful energy. As those objective functions, we focus our attention on a generalization of the so-called ecological function in terms of an ϵ parameter that depends on the particular heat transfer law used in the irreversible heat engine model. In this work, we mathematically describe the configuration space of an irreversible Curzon–Ahlborn type model. The above allows to determine the optimal relations between the model parameters so that a power plant operates in physically accessible regions, taking into account internal irreversibilities, introduced in two different ways (additively and multiplicatively). In addition, we establish the conditions that the ϵ parameter must fulfill for the energy converter to work in an optimal region between maximum power output and maximum efficiency points.
We use the Shannon (information) entropy to define an “entropic” temperature for 1D nonequilibrium system with heat flux. In contrast to the kinetic temperature, which is related to the average kinetic energy, the nonequilibrium entropic temperature is related to the changes in entropy and serves as a criterion for thermalization. However, the direction and value of the heat flux is controlled by the gradient of the kinetic temperature, whereas space-time evolution and the space-time evolution of the heat flux are governed by the hyperbolic heat conduction equation. The extended nonequilibrium variables, namely, entropy, entropic temperature, thermal conductivity, and heat capacity demonstrate a third-law-like behavior at high deviation from equilibrium when the heat flux tends to its maximum value, even at nonzero value of the kinetic temperature. The ratio of the heat flux to its maximum possible value plays a role of an order parameter – it varies from zero in the equilibrium (disordered) state to unity in the nonequilibrium (ordered) state.
In the kinetic rate laws of internal variables, it is usually assumed that the rates of internal variables depend on the conjugate forces of the internal variables and the state variables. The dependence on the conjugate force has been fully addressed around flow potential functions. The kinetic rate laws can be formulated with two potential functions, the free energy function and the flow potential function. The dependence on the state variables has not been well addressed. Motivated by the previous study on the asymptotic stability of the internal variable theory by J. R. Rice, the thermodynamic significance of the dependence on the state variables is addressed in this paper. It is shown in this paper that the kinetic rate laws can be formulated by one extended potential function defined in an extended state space if the rates of internal variables do not depend explicitly on the internal variables. The extended state space is spanned by the state variables and the rate of internal variables. Furthermore, if the rates of internal variables do not depend explicitly on state variables, an extended Gibbs equation can be established based on the extended potential function, from which all constitutive equations can be recovered. This work may be considered as a certain Lagrangian formulation of the internal variable theory.
The question of frame-indifference of the thermomechanical models has to be addressed to deal correctly with the behavior of matter undergoing finite transformations. In this work, we propose to test a spacetime formalism to investigate the benefits of the covariance principle for application to covariant modeling and numerical simulations for finite transformations. Several models especially for heat conduction are proposed following this framework and next compared to existing models. This article also investigates numerical simulations using the heat equation with two different thermal dissipative models for heat conduction, without thermomechanical couplings. The numerical comparison between the spacetime thermal models derived in this work and the corresponding Newtonian thermal models, which adds the time as a discretized variable, is also performed through an example to investigate their advantages and drawbacks.
The aim of this paper is to analyze the behavior of oxytactic microorganisms and thermo-bioconvection nanofluid flow through a Riga plate with a Darcy–Brinkman–Forchheimer porous medium. The Riga plate is composed of electrodes and magnets that are placed on a plane. The fluid is electrically conducting, and the Lorentz force evolves exponentially along the vertical direction. The governing equations are formulated with the help of dimensionless variables. With the aid of a shooting scheme, the numerical results are presented in graphs and tables. It is noted that the modified Hartmann number boosts the velocity profile when it is positive, but lowers these values when it is negative. The density-based Rayleigh number and the nanoparticle concentration enhance the fluid velocity. The thermal Rayleigh number and the Darcy–Forchheimer number decrease the velocity. An increase in Lewis number causes a remarkable decline in the oxytactic microorganism profile. Several useful results for these flows with oxytactic microorganisms through Darcy–Brinkman–Forchheimer porous media are presented in this paper.
Phonon hydrodynamics uses the fields of the total energy and the heat flux as state variables. We extend it by promoting the microscopic internal energy field into the status of an extra independent state variable. The governing equations of both the phonon and the extended (two temperature) phonon hydrodynamics are formulated as particular realizations of the abstract GENERIC equation. Such unified formulation makes both theories manifestly compatible with mechanics and thermodynamics. Also differences and similarities (in the physical content, in the mathematical structure, and in qualitative properties of solutions) between the two heat transfer theories, as well as their mutual compatibility, become manifestly displayed.
Momentum and thermal transport through open-celled metallic foams filled in a channel of small height is studied in the present technical brief. Fully developed momentum and thermal layers via the Brinkman–Darcy model enable us to obtain closed-form solutions regarding the fluid velocity and temperature distributions of metal and fluid, all depending upon a factor related to the wall slip velocity. A comparative study on the pertinent physical parameters helps us conclude that the wall slip cools the porous channel, enhancing the rate of heat transfer. In addition to this, increasing pore density leads to an effective reduction in the entropy generation number, followed by further reduction with the nonzero slip velocity, except the near-wall regions.