Removing Heat and Conceptual Loops from the Definition of Entropy

A rigorous and general logical scheme is presented, which provides an operative non-statistical definition of entropy valid also in the nonequilibrium domain and free of the usual conceptual loops and unnecessary assumptions that restrict the traditional definition of entropy to the equilibrium domain. The scheme is based on carefully worded operative definitions for all the fundamental concepts employed, including those of system, state of a system, isolated system, separable system, systems uncorrelated form each other, environment of a system, process and reversible process. The treatment considers also systems with movable internal walls and/or semipermeable walls, with chemical reactions and and/or external force fields, and with small numbers of particles. The definition of entropy involves neither the concept of heat nor that of quasistatic process; it applies to both equilibrium and nonequilibrium states. Simple and rigorous proofs of the additivity of entropy and of the principle of entropy nondecrease complete the logical framework

A new estimate of sand and grout thermal properties in the sandbox experiment for accurate validations of borehole simulation codes

Ground-coupled heat pumps usually employ fields of borehole heat exchangers (BHEs), which must be designed by suitable models. In order to validate a BHE model, it is advisable to compare the computation results with experimental data. A well-known data set was provided by Beier et al. (Geothermics 2011, 40) through a laboratory model usually called “sandbox”. Several authors proposed estimates of the thermal properties of the sandbox grout and sand. In this paper, we present a new estimate of those properties, obtained by means of 2D finite-element simulations that consider all the details of the experimental setup, including the thin aluminum pipe at the BHE boundary. Our results show that the measured temperatures in the fluid and in the sand can be reproduced very accurately by considering thermal conductivities 0.863 W/(mK) for the grout and 3.22 W/(mK) for the sand, volumetric heat capacities 4.6 MJ/(m3K) for the grout and 3.07 MJ/(m3K) for the sand, and a slightly enhanced heat capacity of the water contained in the BHE. The 2D simulations are validated by comparison with an analytical solution and by 3D simulations

Buoyant MHD flows in a vertical channel: the levitation regime

Buoyant magnetohydrodynamic (MHD) flows with Joulean and viscous heating effects are considered in a vertical parallel plate channel. The applied magnetic field is uniform and perpendicular to the plates which are subject to adiabatic and isothermal boundary conditions, respectively. The main issue of the paper is the levitation regime, i.e., the fully developed flow regime for large values of the Hartmann number M, when the hydrodynamic pressure gradient evaluated at the temperature of the adiabatic wall is vanishing. The problem is solved analytically by Taylor series method and the solution is validated numerically. It is found that the fluid velocity points everywhere and for all values of M downward. For small M's, the velocity field extends nearly symmetrically (with respect to the mid-plane) over the whole section of the channel between the adiabatic and the isothermal walls. For large values of M, by contrast, the fluid levitates over a broad transversal range of the channel, while the motion becomes concentrated in a narrow boundary layer in the neighborhood of the isothermal wall. Accordingly, the fluid temperature is nearly uniform in the levitation range and decreases rapidly within the boundary layer in front of the isothermal wall. It also turns out that not only the volumetric heat generation by the Joule effect, but also that by viscous friction increases rapidly with increasing values of M, the latter effect being even larger than the former one for all

Long-Term Performance of Borehole Heat Exchanger Fields with Groundwater Movement

Abstract: A numerical investigation of the longterm performance of double U-tube borehole heat exchanger (BHE) fields is performed by means of COMSOL Multiphysics, in the case of non-negligible effects of groundwater movement. Two time periodic heat loads, with a period of one year, are studied: Q 1 , with a partial compensation between winter heating (main load) and summer cooling; Q 2 , with no summer cooling. By assuming a distance of 6 m between adjacent BHEs, the following BHE field configurations are analyzed for a 50-year period: a single line of infinite BHEs; two staggered lines of infinite BHEs; four staggered lines of infinite BHEs. The BHE working fluid is a water-ethylene glycol 20% solution with a minimum allowed temperature equal to -5°C. The ground is modelled as a Darcian porous medium with an undisturbed temperature of 14°C. Three values of the groundwater velocity are investigated: W = 0, 10 -7 and 10 -6 m/s

Smooth Entropy in Axiomatic Thermodynamics

Thermodynamics can be formulated in either of two approaches, the phenomenological approach, which refers to the macroscopic properties of systems, and the statistical approach, which describes systems in terms of their microscopic constituents. We establish a connection between these two approaches by means of a new axiomatic framework that can take errors and imprecisions into account. This link extends to systems of arbitrary sizes including very small systems, for which the treatment of imprecisions is pertinent to any realistic situation. Based on this, we identify the quantities that characterise whether certain thermodynamic processes are possible with entropy measures from information theory. In the error-tolerant case, these entropies are so-called smooth min and max entropies. Our considerations further show that in an appropriate macroscopic limit there is a single entropy measure that characterises which state transformations are possible. In the case of many independent copies of a system (the so-called i.i.d. regime), the relevant quantity is the von Neumann entropy. Transformations among microcanonical states are characterised by the Boltzmann entropy

A re-interpretation of the concept of mass and of the relativistic mass-energy relation

For over a century the definitions of mass and derivations of its relation with energy continue to be elaborated, demonstrating that the concept of mass is still not satisfactorily understood. The aim of this study is to show that, starting from the properties of Minkowski spacetime and from the principle of least action, energy expresses the property of inertia of a body. This implies that inertial mass can only be the object of a definition - the so called mass-energy relation - aimed at measuring energy in different units, more suitable to describe the huge amount of it enclosed in what we call the "rest-energy" of a body. Likewise, the concept of gravitational mass becomes unnecessary, being replaceable by energy, thus making the weak equivalence principle intrinsically verified. In dealing with mass, a new unit of measurement is foretold for it, which relies on the de Broglie frequency of atoms, the value of which can today be measured with an accuracy of a few parts in 10^9

Perturbation and numerical study of double-diffusive dissipative reactive convective flow in an open vertical duct containing a non-darcy porous medium with robin boundary conditions

A mathematical model for thermosolutal convection flow in an open two-dimensional vertical channel containing a porous medium saturated with reactive Newtonian fluid is developed and studied. Robin boundary conditions are prescribed, and a first-order homogenous chemical reaction is considered. The Darcy–Forchheimer model is used to simulate both the first- and second-order porous mediums’ drag effects. For the general non-Darcy-case, a numerical solution is presented using the Runge–Kutta quadrature and a shooting method. The influences of thermal (0≤λ1≤15) and solute Grashof numbers (0≤λ2≤20) , Biot numbers (1≤Bi1≤10,Bi2=10) , Brinkman number (0≤Br≤0.5) , first-order chemical reaction parameter (2≤α≤8) , porous medium parameter (2≤σ≤8) and Forchheimer (inertial drag) parameter (0≤I≤12) on the evolutions of velocity, temperature and concentration (species) distributions are visualized graphically. Nusselt number and skin friction at the walls are also computed for specific values of selected parameters. The study is relevant to the analysis of geothermal energy systems with chemical reaction

Il sistema energetico italiano nel quadro globale ed europeo: motivi per il rilancio del nucleare

Il lavoro presenta una analisi del problema energetico ed ambientale mondiale e, in tale contesto, delle criticit\ue0 del sistema energetico nazionale, mostrando che, allo stato attuale delle conoscenze e della tecnologia, sussistono forti motivazioni per il rilancio del nucleare del nostro Paese. Dapprima, viene presentata una analisi delle cause del riscaldamento globale del pianeta e si evidenzia che la causa principale \ue8 l\u2019incremento della concentrazione di gas serra causato dall\u2019attivit\ue0 dell\u2019uomo. Vengono quindi esposte le stime sulle riserve di combustibili fossili, da cui si evince che i combustibili pi\uf9 pregiati, petrolio e gas naturale, potranno assicurare gli attuali fabbisogni energetici solo per pochi decenni. In questo scenario generale, viene analizzata la situazione del sistema energetico nazionale, illustrando le principali anomalie e criticit\ue0. Si esaminano quindi le prospettive offerte nel nostro Paese dalle fonti rinnovabili, evidenziando l\u2019impossibilit\ue0 di un forte sviluppo dell\u2019idroelettrico, le condizioni climatiche non favorevoli per lo sviluppo della fonte eolica, gli altissimi costi del fotovoltaico, i problemi causati dalla distribuzione irregolare nel tempo dell\u2019energia elettrica prodotta mediante le fonti eolica e fotovoltaica. Si conclude che, pur essendo opportuno uno sviluppo delle fonti rinnovabili, specialmente per aumentare l\u2019efficienza energetica del patrimonio edilizio, l\u2019integrazione del nostro sistema energetico mediante produzione di energia elettrica da fonte nucleare \ue8 una scelta fortemente raccomandabile