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We discuss three models describing the carrier densities in highly doped silicon, which have been used for process and device simulation. We calculate nie for each of the models for various doping concentrations within temperature ranges interesting for the device and process simulation. We try to explain the behaviour of nie for high compensation and compare our calculated results to measured values of nie. We offer simple formulae for the calculated nie and show how far the relations between the carrier densities and the Fermi levels can be described by the simple formulae of Boltzmann statistics when we use a doping dependent effective intrinsic number.

The purpose of this paper is to describe two‐ and three‐dimensional numerical modelling of solid oxide fuel cells (SOFCs) by employing an accurate and stable fully matrix inversion free finite element algorithm.

A general and detailed mathematical model has been developed for the description of the coupled complex phenomena occurring in fuel cells. A fully matrix inversion free algorithm, based on the artificial compressibility (AC) version of the characteristic‐based split (CBS) scheme and single domain approach have been successfully employed for the accurate and efficient simulation of high temperature SOFCs.

For the first time, a stable fully explicit algorithm has been applied to detailed multi‐dimensional simulation transport phenomena, coupled to chemical and electrochemical reactions, in fluid, porous and solid parts of a SOFC. The accuracy of the present results has been verified via comparison with experimental and numerical data available in the literature.

For the first time, thanks to a stabilization analysis conducted, the AC‐CBS algorithm has been successfully used to numerically solve the generalized model, applied in this paper to describe transport phenomena through free fluid channels and porous electrodes of SOFCs, without the need of further conditions at the fluid‐electrode interface.

Knowledge of the dependence structure between financial assets is crucial to improve the performance in financial risk management. It is known that the copula completely summarizes the dependence structure among multiple variables. We propose a multivariate exponential series estimator (ESE) to estimate copula densities nonparametrically. The ESE has an appealing information-theoretic interpretation and attains the optimal rate of convergence for nonparametric density estimations in Stone (1982). More importantly, it overcomes the boundary bias of conventional nonparametric copula estimators. Our extensive Monte Carlo studies show the proposed estimator outperforms the kernel and the log-spline estimators in copula estimation. It also demonstrates that two-step density estimation through an ESE copula often outperforms direct estimation of joint densities. Finally, the ESE copula provides superior estimates of tail dependence compared to the empirical tail index coefficient. An empirical examination of the Asian financial markets using the proposed method is provided.

The purpose of this paper is to first present the key features of hybrid numerical methods that enable cost-effective simulations of complex thermofluid systems, and then demonstrate the formulation and application of such a method.

A hybrid numerical method is formulated for simulations of a closed-loop thermosyphon operating with slurries of a micro-encapsulated phase-change material suspended in distilled water. The slurries are modeled as homogeneous mixtures, with inputs of effective properties and overall heat-loss coefficients. Combinations of an axisymmetric two-dimensional (2D) control-volume finite-element method and a segmented-quasi-one-dimensional (1D) model are used to achieve cost-effective simulations. Proper matching of the solutions at the interfaces between adjacent axisymmetric 2D and quasi-1D zones is ensured by incorporating and heuristically determining suitable lengths of pre- and post-heating (and also pre- and post-cooling) sections.

In the demonstration problem, which would strictly require full three-dimensional simulations of the fluid flow and heat transfer phenomena, the proposed hybrid 1D/2D numerical method produces results that are in very good agreement with those obtained in a complementary experimental investigation.

The hybrid numerical methods discussed in this paper allow cost-effective computer simulations of complex thermofluid systems. These methods can therefore serve as very useful tools for the design, parametric studies, and optimization of such systems.

The purpose of this paper is to electrically examine the quality of thin thermally grown SiO₂ with thickness variation, on Si‐face of 4H‐SiC <0001> (having 50 μm epitaxial layer) by current‐voltage (I‐V) and capacitance‐voltage (C‐V) methods.

Metal‐oxide‐silicon carbide (MOSiC) structures with varying oxide thickness have been fabricated on device grade 4H‐SiC substrate. Ni has been used for gate metal on thermally oxidized Si‐face and a composite layer of Ti‐Au has been used for Ohmic contact on the highly doped C‐face of the substrate. Each structure was diced and bonded on a TO‐8 header with a suitable wire bonding for further testing using in‐house developed LabVIEW‐based computer aided measurement setup.

The leakage current of fabricated structures shows an asymmetric behavior with the polarity of gate bias ( + V or −V at the anode). A strong relation of oxide thickness and temperature on effective barrier height at SiO₂/4H‐SiC interface as well as on oxide charges have been established and reported in this paper.

The paper focuses on the development of 4H‐SiC based device technology in the fabrication of MOSiC‐based integrated structures.

A compound emitter heterojunction bipolar transistor (HBT) structure that incorporates an additional heterojunction within the emitter for minority carrier confinement has been proposed. In this new device configuration, the single wide band‐gap emitter layer in a conventional HBT is replaced by two sub‐layers of wide band‐gap material, with the sub‐layer nearer the base having a narrower band‐gap. By means of numerical simulations, the compound emitter HBT was found to perform better than comparable conventional HBTs. With the AlGaAs(n) / GaAs heterostructure system, the optimum compound emitter HBT structure was found to be Al0.3Ga0.7As(n) ‐ Al0. 2Ga0.8As(n) / GaAs with grading at the two hetero‐interfaces. It has a low turn‐on voltage that is almost identical to that of a homojunction GaAs bipolar transistor with similar doping conditions. Compared with a conventional single emitter layer Al0.3Ga0.7As/GaAs HBT, the optimum compound emitter HBT has an enhancement in the current gain by approximately 2 folds, an improvement in the uniform current gain region from 2 to 4 decades of collector current density, and a slight increase in the unity‐gain cut‐off frequency fT by about 7 %.

A new approach called the “variational theory of complex rays” (VTCR) is developed for calculating the vibrations of weakly damped elastic structures in the medium‐frequency range. Here, the emphasis is put on the most fundamental aspects. The effective quantities (elastic energy, vibration intensity, etc.) are evaluated after solving a small system of equations which does not derive from a finite element discretization of the structure. Numerical examples related to plates show the appeal and the possibilities of the VTCR.

The purpose of this paper is to investigate the momentum, heat and mass transfer characteristics of magnetic-nanofluid flow past a vertical plate embedded in a porous medium filled with ferrous nanoparticles. The analysis is carried out in the presence of pertinent physical parameters such as aligned magnetic field, thermal radiation, chemical reaction, radiation absorption, heat source/sink.

The flow governing PDEs are transformed into ODEs using appropriate conversions. Further, the set of ODEs is solved analytically using the perturbation technique. The flow quantities such as velocity, thermal and concentration fields are discussed under the influence of above-mentioned pertinent physical parameters with the assistance of graphical depictions. Moreover, the friction factor, local Nusselt and Sherwood number are discussed in tabular form.

The results indicate that flow and thermal transport phenomenon is more effective in the case of the aligned magnetic field as compared with the transverse magnetic field. Also, the nanoparticle volume fraction plays a vital role in controlling the wall friction and heat transfer performance. The validation of the obtained results is done by comparing them with the results of various numerical techniques, and hence found them in excellent agreement.

In present days, the external magnetic fields are very effective to set the thermal and physical properties of magnetic-nanofluids and regulate the flow and heat transfer characteristics. The strength of the applied magnetic field affects the thermal conductivity of magnetic-nanofluids and makes it aeolotropic. With this incentive, the authors investigated the flow and heat transfer characteristics of electrically conducting magnetic-nanofluids over a vertical surface embedded in a porous medium. The authors discussed the dual nature of ferrous-water nanofluid in the presence of aligned magnetic field and transverse magnetic field cases. The influence of several physical parameters on velocity, thermal and concentration field converses with the succour of graphs.

The purpose of this paper is to theoretically investigate the steady two‐dimensional boundary‐layer flow past a moving semi‐infinite flat plate in a water‐based nanofluid containing three different types of nanoparticles: copper (cuprum) Cu, alumina (aluminium oxide) Al₂O₃, and titania (titanium dioxide) TiO₂. The effects of moving parameter λ as well as solid volume fraction parameter φ on the flow and heat transfer characteristics are studied. Taking into account the rising demands of modern technology, including chemical production, power stations and microelectronics, there is a need to develop new types of fluids that will be more effective in terms of heat exchange performance.

A similarity transformation is used to reduce the governing partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using Keller‐box method.

There is a region of unique solutions for λ>0, however, multiple (dual) solutions exist for λ_c<λ≤0 and no solutions for λ<λ_c<0. A reverse flow is formed when λ<0.

The solutions can be obtained up to a certain value of the moving parameter (critical value or turning point). The boundary layer separates from the plate beyond the turning point hence it is not possible to get the solution based on the boundary‐layer approximations after this point. To obtain further solutions, the full Navier‐Stokes equations have to be solved.

The present results are original and new for the boundary‐layer flow and heat transfer of a moving flat plate in a nanofluid. Therefore, this study would be important for the scientists and engineers in order to become familiar with the flow behaviour and properties of such nanofluids, and the way to predict the properties of this flow for the process equipments.

This paper aims to study forced convection in a double tube heat exchanger using nanofluids with constant and variable thermophysical properties.

The cold fluid was distilled water flowing in the annulus and the hot fluid was aluminum oxide/water nanofluid which flows in the inner tube. Thermal conductivity and viscosity were taken as variable thermophysical properties, and the results were compared against runs with constant values. Finite volume method was used for solving the governing equations. For distilled water, Re = 500 was used, while for nanofluid, nanoparticles volume fraction equal to 2.5-10 per cent and Re = 100-1,500 were used.

Heat transfer rate can be enhanced by increasing the volume fraction of nanoparticles and Reynolds number. Thermal efficiency is better with constant thermophysical characteristics and the average Nusselt number is better for variable characteristics.

Heat exchanger efficiency is evaluated by using distilled water and nanofluid bulk temperature, thermal efficiency and average and local Nusselt numbers for both variable and constant thermophysical characteristics.