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Highlights • A Li-ion battery pack cooled by CCFSS/paraffin composite PCMs was prepared. • The performance of CCFSS/paraffin was investigated by discharge experiments. • CCFSS/paraffin effectively cooled the battery and lowered temperature differences. • A two-equation non-thermal equilibrium numerical model was established and applied. • The effects of key parameters on the battery module temperature were predicted. Abstract The thermal safety of lithium-ion battery is a serious issue in its applications. A lithium-ion battery pack cooled by a cutting copper fiber sintered skeleton (CCFSS)/paraffin composite phase change material (PCM) is designed and fabricated. The effect of the CCFSS/paraffin composite PCM on the battery pack temperature is investigated by discharge experiments and compared with natural air cooling, pure paraffin, and copper foam/paraffin composite PCM. A two-equation non-thermal equilibrium model using the enthalpy method is established. The experimental results indicate that the battery temperature difference in the case with pure paraffin exceeds 5 °C, while the CCFSS/paraffin composite PCM effectively enhances the heat transfer performance and maintains the battery temperature differences within 5 °C. The numerical results show good agreement with the experimental data, validating the accuracy of the numerical model. Therefore, the effects of key parameters are investigated and predicted via the numerical model. The heating rate of the battery pack decreases with increases in the number of pores per linear inch (PPI) and the convective heat transfer coefficient. With the increase in the spacing between the cells, the heating rate of the battery pack decreases and the duration of the phase change increases. This work provided a reference for the application of CCFSS/paraffin composite PCM in the heat dissipation of lithium-ion batteries. [ABSTRACT FROM AUTHOR]

Abstract The approach to thermal equilibrium of each of three simple quantum systems in interaction with a reservoir is analyzed by calculating the time evolution of an observable appropriate for each system. Two types of interaction with the reservoir are considered: a single-phonon modulation of the interaction matrix element and a multiphonon interaction arising from a polaronic transformation for a given single-phonon, but strong, modulation of energy or frequency. The methodology employed is a recent formalism based on a coarse-grained generalized master equation. Interesting results are obtained for the multiphonon case including a nonmonotonic dependence of the time-dependent observables in the multiphonon system as the temperature is varied. Such a result does not appear in the single-phonon case, i.e. , for weak coupling. In addition to contributing towards the understanding of the detail in the approach to thermal equilibrium, the analysis has practical applications to the vibrational relaxation of molecules embedded in phonon baths and to the transport of charge in crystals subjected to electric fields strong enough to lead to the formation of Stark ladders. Highlights • Results include nonmonotonicity of relaxing observables, e.g. energy, when T is changed. • The effect appears only under strong interactions and is directly observable in principle. • Useful procedures developed: a half-Markoffian approximation and a relaxation memory/rate. [ABSTRACT FROM AUTHOR]

Both practices and experiments have shown that the thermal conductivity of icing has an obvious influence on ice-melting process, but it is ignored by most of the existing models which set the simulation parameter as a constant. In this paper, an experimental study is conducted to investigate the thermal conductivity for overhead transmission line icing. Based on the test data in artificial icing laboratory, a quadratic equation of thermal conductivity and icing density is presented. And then, the equation of icing thermal conductivity is employed to simulate the critical ice-melting current and ice-melting time. The results of the experiment and simulation show that the thermal conductivity can improve the prediction accuracy in thermal de-icing projects, with the mean error of 4% and 14%, respectively. [ABSTRACT FROM AUTHOR]

The Boltzmann–Gibbs thermodynamic equilibrium state of charged particles pitch-angle scattered by weak plasma waves is discussed. Degrees of freedom of these waves play a fundamental role in constructing the grand canonical ensemble. Via the gyro-resonance condition, fast particles have an inverse break power-law spectrum for ɛ − μ ≪ T , where ɛ is the particle energy, μ is the chemical potential, T is the temperature. The break energies are the rest energy and − μ. For ɛ ≪ − μ ≪ T , the energy spectral index α is δ / 2 + 1 and δ + 1 for non- and ultra-relativistic particles, respectively, with δ an effective fractal dimension of background magnetic field lines. The spectral index for − μ ≪ ɛ ≪ T is α + 1. This thermal equilibrium scenario, combined with the leaky-box model and cosmic-ray observations, seems to suggest that the Galactic magnetic field is super-diffusive with δ ≈ 1. 4. [ABSTRACT FROM AUTHOR]

The melting process of phase change material (PCM) infiltrated in a finned metal foam was numerically investigated using two approaches: (a) pore-scale and (b) volume-averaged numerical simulations. The pore-scale simulation modeled the intricate geometry of the open-cell metal foam using sphere-centered tetrakaidecahedron and coupled the heat transfer in foam/fin solids with that in the PCM. The volume-averaged simulation used the Darcy–Brinkman–Forchheimer model to account for the motion of melt PCM as well as the one-temperature model based on local thermal equilibrium assumption. The volume-averaged simulation results were compared with the pore-scale simulation results which were used as the benchmark. Reasonable agreement between prediction results of the two approaches was observed. When using the volume-averaged method, the one-temperature model may be applicable without needing the more complicated two-temperature model. The thermal performance of the finned metal foam was compared with conventional plate-fin and metal foam structures, demonstrating its superiority as thermal conductivity enhancer of PCM. [ABSTRACT FROM AUTHOR]

Changes in the porosity and permeability of a porous medium due to melting are modeled. A frozen phase, which initially fills a part of the porous medium, melts and gets dissolved in the injected hot solvent. The amount of melted material, the rate of melting as well as the profiles of temperature, porosity, and concentration are analyzed to understand the nature of this naturally and industrially important phenomenon. Four reference scenarios corresponding to instantaneous thermal equilibrium, no heat transfer to the frozen phase, no-melting, and instantaneous melting conditions are solved analytically and the effects of different parameters are discussed. Numerical simulation results show that the profiles of the fluid temperature, porosity of the medium, and solvent concentration, form three fronts moving at different rates. It is found that for heat transfer coefficients above a certain value, the rate of melting is independent of this parameter and the system can be considered to have reached instantaneous thermal equilibrium. Moreover, slow heat transfer in the medium is shown to increase the rate of melting at long time periods by involving larger areas in the melting process. Heterogeneous scenarios are also analyzed by introducing frozen blocks of different geometries. The ability of the flow to bypass the frozen region involves a new heat transfer mechanism identified as outer-boundary convection. The effects of the geometry of the block along with the other parameters on the melting process are examined. Furthermore a generalizing scheme is proposed to predict the melt production for different block geometries and values of the saturation of the frozen phase. [ABSTRACT FROM AUTHOR]

Past Lagrangian/Eulerian modeling has served as a poor match for the mixing-limited physics present in many sprays. Though these Lagrangian/Eulerian methods are popular for their low cost, they are ill-suited for the physics of the dense spray core and suffer from limited predictive power. A new spray model, based on mixing-limited physics, has been constructed and implemented in a multi-dimensional CFD code. The spray model assumes local thermal and inertial equilibrium, with air entrainment being limited by the conical nature of the spray. The model experiences full two-way coupling of mass, momentum, species, and energy. An advantage of this approach is the use of relatively few modeling constants. The model is validated with three different sprays representing a range of conditions in diesel and gasoline engines. • A mixing-limited spray model with a two-way coupling with the gas phase. • ELMO is based on ideas of thermodynamic and inertial equilibrium in the dense spray core. • Minimal sensitivity to arbitrary input parameters. • Validated against ECN Spray A, Spray H, and Spray G. • ELMO can be applied to diesel and gasoline sprays without the need to adjust model constants. [ABSTRACT FROM AUTHOR]

The unsteady, conjugate, forced convection heat transfer from a porous sphere embedded in another porous medium has been analysed. Both porous media are fluid saturated. Local thermal equilibrium between the two phases is assumed. The fluid flow inside and outside the sphere was considered axisymmetric, steady and incompressible (Darcy and Brinkman flows). The heat balance equations were solved numerically in spherical coordinates system by an implicit alternating direction finite difference method. The influence of the porous media permeability and sphere Peclet numbers on the heat transfer mechanism and rate was analysed for different values of the physical properties ratios (thermal conductivity ratio and heat capacity ratio). [ABSTRACT FROM AUTHOR]

Abstract: This paper outlines an analytical model to predict the temperature of fully-inflated balloon on float at high altitude in stratosphere. Simplified radiative and convective heat transfer models are developed to estimate absorption and emission heat of balloon film and lifting gas within balloon. Thermal equilibrium equations for the balloon system in the day time and night time are derived by incorporating radiative and convective heat transfer models. The new model is applied to calculate the day and night temperatures of the balloon system on float at a high-altitude in stratosphere and reasonable correlation is achieved between the predictions obtained from new models and from prior flight testing data, demonstrating the effective use of the proposed models. [Copyright &y& Elsevier]

Abstract: Heat transfer is one of the fundamental and veiled energy transfer processes. The complex characteristics of heat transfer in a thermal process are far from being understood entirely. We here propose a statistical thermodynamic transport theory which is applicable to the heat transfer mechanisms for non-equilibrium, quasi-equilibrium, and equilibrium to overcome limits on the heat diffusion equation. The heat transfer theory adopts a postulate that temperature, time, and displacement are independent and orthogonal variables in extended phase spaces. The solutions of the heat transfer theory are obtained for thermal non-equilibrium, quasi-equilibrium, and equilibrium and the heat fluxes are expressed as the functions of temperature, time, and displacement. The heat transfer theory demonstrates that there are heat flux gaps and broken discrete symmetries at the activation temperature, time, and displacement. The theory is consistent with statistical thermodynamics. The kinetic theory is the unification of conduction and internal convection heat transfer, a non-equilibrium generalization beyond quasi-equilibrium theories for isothermal and isentropic processes, and the integration of internal equilibrium and internal non-equilibrium. [Copyright &y& Elsevier]

Abstract: In this paper an analytical model was developed to minimize the thermal resistance of an air cooled porous matrix made up of solid spheres with internal heat generation. This was done under the assumption of local thermal equilibrium. The analytical solution of the optimum sphere diameter was found to be independent of the heat generation rate of the solid spheres, but was dependent on the applied pressure drop and fluid properties. The analytical model compared very well to a numerical model found in a computational fluid dynamics code when air and liquid water properties were used for the fluid phase and wood and silica/sand properties were used for the solid phase. [Copyright &y& Elsevier]

Abstract: The problem of diffusion and mass transfer in dual porous media is considered in a three-phase framework. The solid phase is assumed to contain two distinct cavities filled with fluid. The porous mixture is composed of two overlapping media: the porous blocks and the fissure network. The fluid can transfer between the cavities due to fluid pressure difference. In addition, hydraulic and thermal diffusions take place through the mixture. A global understanding of mass transfer, diffusion and deformation is provided. The governing equations associated with these phenomena are presented for a mixture in thermal equilibrium. The finite element approximation of the governing equations is formulated and applied to the stability analysis of a vertical borehole. A parametric analysis is carried out to evaluate the influence of mass transfer on the pressure profiles of the fluids around the borehole. Permeable and a semi-permeable boundary conditions are compared to predict the potential for failure of the wellbore under drained and partially undrained conditions. [Copyright &y& Elsevier]

Abstract: Porous media combustion (PMC) has interesting advantages compared with free flame combustion due to higher burning rates, increased power dynamic range, extension of the lean flammability limits, and low emissions of pollutants. Extensive experimental and numerical works were carried out and are still underway, to explore the feasibility of this interesting technology for practical applications. For this purpose, numerical modeling plays a crucial role in the design and development of promising PMC systems. This article provides an exhaustive review of the fundamental aspects and emerging trends in numerical modeling of gas combustion in porous media. The modeling works published to date are reviewed, classified according to their objectives and presented with general conclusions. Numerical modeling of liquid fuel combustion in porous media is excluded. [ABSTRACT FROM AUTHOR]

Abstract: The large-scale impacts of sub-mesoscale physics are addressed by comparing mean characteristics of basin-scale, seasonally varying, subtropical and subpolar gyres in a suite of numerical experiments varying in horizontal resolution (1°, 1/9° and 1/54°) and accordingly, in sub-grid scale mixing. After 100years of simulation, and as suggested from earlier studies, the mean circulation and the mean structure of the ventilated thermocline strongly differ when switching from 1° to 1/9° resolution. Our results emphasize that increasing the resolution from 1/9° to 1/54° leads to major further changes. These changes ensue from the emergence of a denser and more energetic vortex population at 1/54°, occupying most of the basin and sustained by sub-mesoscale physics. Non-linear effects of this turbulence strongly intensify the jet that separates the two gyres, thus steepening the isopycnals and counter-balancing the strong eddy-driven heat transport that tends to flatten them. The jet is more zonal, penetrates further to the east, and is shifted southward by a few degrees, which significantly alters the shape and position of the gyres. The strengthening of the main jet comes together with the emergence of a regime of energetic secondary zonal jets, associated with complex recirculations. In parallel, sub-mesoscales restratify both the seasonal and the main thermocline, inducing in particular a reduction of deep convection and the modification of the water masses involved in the meridional overturing circulation. Although the results presented here are presumably highly constrained by the idealized geometry of our basin, they suggest that sub-mesoscale processes play an important role on the mean circulation and mean transports at the scale of oceanic basins. At the highest resolution presented here (1/54°), momentum effects are becoming important so that eddies do not simply cause the slumping of isopycnals but can arrange the flow to form jet-like structures with steeper isopycnals in places. [Copyright &y& Elsevier]

The demand of high speed and miniaturization of electronic components results in increased power dissipation requirement for thermal management. In this work, the effects of porosity (ε), pore density (PPI) and air velocity on the heat-transfer characteristics of aluminum-foam heat sinks are investigated experimentally. The phenomenon of non-local thermal equilibrium (NLTE) is also observed and reported. Results show that the Nu increases as the pore density increases, due to the fact that aluminum foam with a larger pore density has a larger heat-transfer area. The Nusselt number also increases with the increase of porosity due to the same reason. It is noted that temperatures of the solid and gas phases of the aluminum foam decrease as Reynolds number increases, caused by the increased convective heat-transfer rate at higher Reynolds number. The deduced temperature difference between the solid and gas phases clearly indicates the existence of non-local thermal equilibrium condition within the aluminum-foam heat sink. The increase of the porosity and the pore density enhances the phenomenon of non-local thermal equilibrium. The temperature difference increases with the decrease of Reynolds number and the distance away from the heat source. [Copyright &y& Elsevier]

We consider the evolution of a system composed of N non-interacting point particles of mass m in a container divided into two regions by a movable adiabatic wall (adiabatic piston). In this talk we discuss the thermodynamic limit where the area A of the container, the number N of particles, and the mass M of the piston go to infinity keeping A/M and N/M fixed. We show that in this limit the motion of the piston is deterministic. Introducing simplifying assumptions we discuss the approach to equilibrium and we illustrate the results with numerical simulations. The comparison with the case of a system with finite (A,N,M) will be presented. [Copyright &y& Elsevier]

The concept of the Wigner function is used to construct a semi-classical kinetic theory describing the evolution of the axial current phase-space density of spin- 1 2 particles in the relaxation time approximation. The resulting approach can be used to study spin polarization effects in relativistic matter, in particular, in heavy-ion collisions. An expression for the axial current based on the classical treatment of spin is also introduced and we show that it is consistent with earlier calculations using Wigner functions. Finally, we derive non-equilibrium corrections to the spin tensor, which are used to define, for the first time, the structure of spin transport coefficients in relativistic matter. [ABSTRACT FROM AUTHOR]