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This paper presents a new discretization technique of the hydrodynamic energy balance model based on a finite‐element formulation. The concept of heat source lumping is introduced, and the thermal conductivity model includes the effect of varying both carrier concentrations and temperatures. The energy balance equation is formulated to account for kinetic energy as a convective flow. The new discretization method has the advantage that it allows for assembling the functions out of elementary variables available over elements instead of along element links. Therefore, theoretically, calculation of the Jacobian should be three times faster than by the classic method. Results are given for three examples. The method suffers from mathematical instabilities, but provides a good basis for future work to solve these problems.

An energy balance equation model coupled with drift‐diffusion transport equations are solved in heterojunction p‐i‐n diodes with embedded single quantum well to model hot electron effects. A detailed formulation of hot electron transport is presented. In the well, the carrier energy levels are estimated from the analytical expressions applied to a quantum well with finite height. Both bound and free carriers are modeled by Fermi‐Dirac statistics. Both size quantization and the two dimensional density of states in the well are considered. Thermionic emission is applied to the heterojunctions and quantum wells boundary. Energy transfer among the charge carriers and crystal lattice is modeled by an energy relaxation lifetime. Two sets of devices are simulated. First, the simulated kinetic energy and carrier density profiles were compared with published Monte Carlo results on an GaAs n⁺/n/n⁺ diode. Second, the current‐voltage characteristics of an embedded single quantum well AlGaAs/GaAs p‐i‐n structure was compared with measured data. Both comparisons are satisfactory and demonstrate the usefulness of the model for studying quantum well structures.

Presents numerical aspects of the program CODE_BRIGHT, which is a simulator for COupled DEformation, BRIne, Gas and Heat transport problems. It solves the equations of mass and energy balance and stress equilibrium and, originally, it was developed for saline media. The governing equations also include a set of constitutive laws and equilibrium conditions. The main peculiarities of saline media are in the dissolution/precipitation phenomena, presence of brine inclusions in the solid salt and creep deformation of the solid matrix.

The objective of this study is to highlight the questions arising in the design of district heating and cooling systems (DHCSs) in a distributed generation context and to present a model to help find cost‐effective solutions.

Literature on energy systems optimisation is reviewed and a mixed integer programming model for decentralized DHCSs design is developed and applied to two real case studies.

Distributed cooling generation partly coupled with distributed cogeneration and DH is the preferred solution in the examined areas. The optimal configurations, with special reference to network sizing and layout, significantly depend on heating demand profiles and energy prices.

Interdependencies between energy units sizing and network layout definition should be considered. Obtaining more robust and reliable network configurations should be the objective of future modelling efforts.

Despite the growth of distributed energy conversion, designers often rely on centralized concepts in order to reap economies of scale. The presented model helps in discovering less usual solutions representing the most profitable option.

Combining and comparing central and distributed production of heat and cooling under consideration of network costs.

The purpose of this paper is to reply to the following question: do there exist piecewise smooth solutions to the 2D MEP hydrodynamical model of charge transport in semiconductors with smooth parts separated by a surface of strong discontinuity?

A standard approach is used to obtain jump conditions for the balance equations under consideration.

For the balance equations of charge transport in semiconductors based on the maximum entropy principle Rankine‐Hugoniot jump conditions were derived and studied. Considering the important case of planar discontinuity, the authors discuss the legitimacy of the introduction of surface charge and surface current in the Rankine‐Hugoniot jump conditions.

The jump conditions are derived for the balance equations written for the case of the parabolic approximation of energy bands. However, it is possible also to perform the analysis of corresponding jump conditions for the case of Kane dispersion relation approximation.

The paper presents derivation and study of Rankine‐Hugoniot jump conditions for the 2D MEP hydrodynamical model of charge transport in semiconductors.

The aim of this paper is to revisit the albedo for uncertainty. The albedo is considered as a fuzzy value due to some realistic reasons which they will be discussed in details. After defining an appropriate uncertain albedo by using fuzzy set theory, the related energy balance model is also redefined as a fuzzy differential equation by using the concept of fuzzy derivative.

The well-known Earth energy balance model is redefined as a fuzzy differential equation by using the concept of fuzzy derivative. Thus, instead of an ordinary differential equation, a fuzzy differential equation arises which it's solution procedure will be discussed in details.

Results indicate that the fuzzy uncertainty for albedo causes more real results after solving the fuzzy energy balance equation. Considering albedo as a fuzzy number is more realistic than considering a single certain number for albedo of a surface. This is due to this fact that the Earth's surface coverage is not crisp and the boundaries of different types of lands are not consistent. The proposed approach of this paper can help us to provide more realistic climate models and construct dynamical models which can model the albedo based on its variability.

In this paper, we defined fuzzy energy balance model as a fuzzy differential equation for the first time. We also, considered albedo as a fuzzy number which is another novel approach.

The use of energy balance and simplified hydrodynamic models for simulating GaAs devices is investigated. The simplified hydrodynamic model predicts velocity spikes that are not present in more detailed Monte Carlo simulation results. These velocity spikes are associated with overestimation of thermal diffusion. The simplified hydrodynamic model can predict terminal currents that are significantly lower than those predicted by the energy balance model. The differences between the models are significantly greater than those observed previously for silicon devices. The main conclusion of this study is that the energy balance model is preferable to the simplified hydrodynamic model as the basis for GaAs device simulation, but the energy balance model still needs refinement to improve the agreement with more general simulation and experimental results.

Transient climate sensitivity relates total climate forcings from anthropogenic and other sources to surface temperature. Global transient climate sensitivity is well studied, as are the related concepts of equilibrium climate sensitivity (ECS) and transient climate response (TCR), but spatially disaggregated local climate sensitivity (LCS) is less so. An energy balance model (EBM) and an easily implemented semiparametric statistical approach are proposed to estimate LCS using the historical record and to assess its contribution to global transient climate sensitivity. Results suggest that areas dominated by ocean tend to import energy, they are relatively more sensitive to forcings, but they warm more slowly than areas dominated by land. Economic implications are discussed.

This paper is aimed to study natural convection in enclosures with curved (concave and convex) side walls for porous media via the heatline-based heat flow visualization approach.

The numerical scheme involving the Galerkin finite element method is used to solve the governing equations for several Prandtl numbers (Pr_m) and Darcy numbers (Da_m) at Rayleigh number, Ra_m = 10⁶, involving various wall curvatures. Finite element method is advantageous for curved domain, as the biquadratic basis functions can be used for adaptive automated mesh generation.

Smooth end-to-end heatlines are seen at the low Da_m involving all the cases. At the high Da_m, the intense heatline cells are seen for the Cases 1-2 (concave) and Cases 1-3 (convex). Overall, the Case 1 (concave) offers the largest average Nusselt number ( Nur¯) at the low Da_m for all Pr_m. At the high Da_m, Nur¯ for the Case 1 (concave) is the largest involving the low Pr_m, whereas Nur¯ is the largest for Case 1 (convex) involving the high Pr_m.

Thermal management for flow systems involving curved surfaces which are encountered in various practical applications may be complicated. The results of the current work may be useful for the material processing, thermal storage and solar heating applications

The heatline approach accompanied by energy flux vectors is used for the first time for the efficient heat flow visualization during natural convection involving porous media in the curved walled enclosures involving various wall curvatures.

Proposes a new quasi‐static vector hysteresis model based on an energy approach, where dissipation is represented by a friction‐like force.

The start point is the local energy balance of the ferromagnetic material. Dissipation is represented by a friction‐like force, which derives from a non‐differentiable convex functional. Several elementary hysteresis cells can be combined, in order to increase the number of free parameters in the model, and therefore improve the accuracy.

A friction‐like force is a good way to represent magnetic dissipation at the macroscopic level. The proposed method is easy to implement and non‐differentiability amounts in this case to a simple “if” statement.

The next steps are the extension to dynamic hysteresis and the in‐depth analysis of the identification process, which is only sketched in this paper.

This vector model, which is based on a reasonable phenomenological description of local magnetic dissipation, enables the numerical analysis of rotational hysteresis losses on a sound theoretical basis.

It proposes a simple, general purpose macroscopic model of hysteresis that is intrinsically a vector one, and not the vectorization of a scalar model.