Nonlocal electron heat relaxation in a plasma shock at arbitrary ionization number

A recently obtained nonlocal expression for the electron heat flux valid for arbitrary ionization numbers Z is used to study the structure of a plane shock wave in a fully ionized plasma. Nonlocal effects are only important in the foot of the electronic preheating region, where the electron temperature gradient is the steepest. The results are quantified as a function of a characteristic Knudsen number of that region. This work also generalizes to arbitrary values of Z previous results on plasma shock wave structure.

Radiation heat savings in polysilicon production: validation of results through a CVD laboratory prototype

This work aims at a deeper understanding of the energy loss phenomenon in polysilicon production reactors by the so-called Siemens process. Contributions to the energy consumption of the polysilicon deposition step are studied in this paper, focusing on the radiation heat loss phenomenon. A theoretical model for radiation heat loss calculations is experimentally validated with the help of a laboratory CVD prototype. Following the results of the model, relevant parameters that directly affect the amount of radiation heat losses are put forward. Numerical results of the model applied to a state-of-the-art industrial reactor show the influence of these parameters on energy consumption due to radiation per kilogram of silicon produced; the radiation heat loss can be reduced by 3.8% when the reactor inner wall radius is reduced from 0.78 to 0.70 m, by 25% when the wall emissivity is reduced from 0.5 to 0.3, and by 12% when the final rod diameter is increased from 12 to 15 cm.

Thermographic imaging: assessment of drought and heat tolerance in Spanish germplasm of Brachypodium distachyon.

The annual grass Brachypodium distachyon has been recently recognized as the model plant for functional genomics of temperate grasses, including cereals of economic relevance like wheat and barley. Sixty-two lines of B. distachyon were assessed for response to drought stress and heat tolerance. All these lines, except the reference genotype BD21, derive from specimens collected in 32 distinct locations of the Iberian Peninsula, covering a wide range of geo- climatic conditions. Sixteen lines of Brachypodium hybridum, an allotetraploid closely related to B. distachyon were used as reference of abiotic-stress well-adapted genotypes. Drought tolerance was assessed in a green-house trial. At the rosette-stage, no irrigation was applied to treated plants whereas their replicates at the control were maintained well watered during all the experiment. Thermographic images of treated and control plants were taken after 2 and 3 weeks of drought treatment, when stressed plants showed medium and extreme wilting symptoms. The mean leaf temperature of stressed (LTs) and control (LTc) plants was estimated based upon thermographic records from selected pixels (183 per image) that strictly correspond to leaf tissue. The response to drought was based on the analysis of two parameters: LTs and the thermal difference (TD) between stressed and control plants (LTs – LTc). The response to heat stress was based on LTc. Comparison of the mean values of these parameters showed that: 1) Genotypes better adapted to drought (B. hybridum lines) presented a higher LTs and TD than B. distachyon lines. 2) Under high temperature conditions, watered plants of B. hybridum lines maintained lower LTc than those of B. distachyon. Those results suggest that in these species adaptation to drought is linked to a more efficient stomata regulation: under water stress stomata are closed, increasing foliar temperature but also water use efficiency by reducing transpiration. With high temperature and water availability the results are less definite, but still seems that opening stomata allow plants to increase transpiration and therefore to diminish foliar temperature.

Heat losses in a CVD reactor for polysilicon: comprehensive model and experimental validation

This work addresses heat losses in a CVD reactor for polysilicon production. Contributions to the energy consumption of the so-called Siemens process are evaluated, and a comprehensive model for heat loss is presented. A previously-developed model for radiative heat loss is combined with conductive heat loss theory and a new model for convective heat loss. Theoretical calculations are developed and theoretical energy consumption of the polysilicon deposition process is obtained. The model is validated by comparison with experimental results obtained using a laboratory-scale CVD reactor. Finally, the model is used to calculate heat consumption in a 36-rod industrial reactor; the energy consumption due to convective heat loss per kilogram of polysilicon produced is calculated to be 22-30 kWh/kg along a deposition process.

FTCS finite difference scheme GPGPU parallel computing for the heat conduction equation = Programación en paralelo GPGPU del método en diferencias finitas FTCS para la ecuación del calor

En el presente artículo se muestran las ventajas de la programación en paralelo resolviendo numéricamente la ecuación del calor en dos dimensiones a través del método de diferencias finitas explícito centrado en el espacio FTCS. De las conclusiones de este trabajo se pone de manifiesto la importancia de la programación en paralelo para tratar problemas grandes, en los que se requiere un elevado número de cálculos, para los cuales la programación secuencial resulta impracticable por el elevado tiempo de ejecución. En la primera sección se describe brevemente los conceptos básicos de programación en paralelo. Seguidamente se resume el método de diferencias finitas explícito centrado en el espacio FTCS aplicado a la ecuación parabólica del calor. Seguidamente se describe el problema de condiciones de contorno y valores iniciales específico al que se va a aplicar el método de diferencias finitas FTCS, proporcionando pseudocódigos de una implementación secuencial y dos implementaciones en paralelo. Finalmente tras la discusión de los resultados se presentan algunas conclusiones. In this paper the advantages of parallel computing are shown by solving the heat conduction equation in two dimensions with the forward in time central in space (FTCS) finite difference method. Two different levels of parallelization are consider and compared with traditional serial procedures. We show in this work the importance of parallel computing when dealing with large problems that are impractical or impossible to solve them with a serial computing procedure. In the first section a summary of parallel computing approach is presented. Subsequently, the forward in time central in space (FTCS) finite difference method for the heat conduction equation is outline, describing how the heat flow equation is derived in two dimensions and the particularities of the finite difference numerical technique considered. Then, a specific initial boundary value problem is solved by the FTCS finite difference method and serial and parallel pseudo codes are provided. Finally after results are discussed some conclusions are presented.

Modelling of chloride transport in non-saturated concrete : from microscale to macroscale

Corrosion of steel bars embedded in concrete has a great influence on structural performance and durability of reinforced concrete. Chloride penetration is considered to be a primary cause of concrete deterioration in a vast majority of structures. Therefore, modelling of chloride penetration into concrete has become an area of great interest. The present work focuses on modelling of chloride transport in concrete. The differential macroscopic equations which govern the problem were derived from the equations at the microscopic scale by comparing the porous network with a single equivalent pore whose properties are the same as the average properties of the real porous network. The resulting transport model, which accounts for diffusion, migration, advection, chloride binding and chloride precipitation, consists of three coupled differential equations. The first equation models the transport of chloride ions, while the other two model the flow of the pore water and the heat transfer. In order to calibrate the model, the material parameters to determine experimentally were identified. The differential equations were solved by means of the finite element method. The classical Galerkin method was employed for the pore solution flow and the heat transfer equations, while the streamline upwind Petrov Galerkin method was adopted for the transport equation in order to avoid spatial instabilities for advection dominated problems. The finite element codes are implemented in Matlab® . To retrieve a good understanding of the influence of each variable and parameter, a detailed sensitivity analysis of the model was carried out. In order to determine the diffusive and hygroscopic properties of the studied concretes, as well as their chloride binding capacity, an experimental analysis was performed. The model was successfully compared with experimental data obtained from an offshore oil platform located in Brazil. Moreover, apart from the main objectives, numerous results were obtained throughout this work. For instance, several diffusion coefficients and the relation between them are discussed. It is shown how the electric field set up between the ionic species depends on the gradient of the species’ concentrations. Furthermore, the capillary hysteresis effects are illustrated by a proposed model, which leads to the determination of several microstructure properties, such as the pore size distribution and the tortuosity-connectivity of the porous network. El fenómeno de corrosión del acero de refuerzo embebido en el hormigón ha tenido gran influencia en estructuras de hormigón armado, tanto en su funcionalidad estructural como en aspectos de durabilidad. La penetración de cloruros en el interior del hormigón esta considerada como el factor principal en el deterioro de la gran mayoría de estructuras. Por lo tanto, la modelización numérica de dicho fenómeno ha generado gran interés. El presente trabajo de investigación se centra en la modelización del transporte de cloruros en el interior del hormigón. Las ecuaciones diferenciales que gobiernan los fenómenos a nivel macroscópico se deducen de ecuaciones planteadas a nivel microscópico. Esto se obtiene comparando la red porosa con un poro equivalente, el cual mantiene las mismas propiedades de la red porosa real. El modelo está constituido por tres ecuaciones diferenciales acopladas que consideran el transporte de cloruros, el flujo de la solución de poro y la transferencia de calor. Con estas ecuaciones se tienen en cuenta los fenómenos de difusión, migración, advección, combinación y precipitación de cloruros. El análisis llevado a cabo en este trabajo ha definido los parámetros necesarios para calibrar el modelo. De acuerdo con ellas, se seleccionaron los ensayos experimentales a realizar. Las ecuaciones diferenciales se resolvieron mediante el método de elementos finitos. El método clásico de Galerkin se empleó para solucionar las ecuaciones de flujo de la solución de poro y de la transferencia de calor, mientras que el método streamline upwind Petrov-Galerkin se utilizó para resolver la ecuación de transporte de cloruros con la finalidad de evitar inestabilidades espaciales en problemas con advección dominante. El código de elementos finitos está implementado en Matlab® . Con el objetivo de facilitar la comprensión del grado de influencia de cada variable y parámetro, se realizó un análisis de sensibilidad detallado del modelo. Se llevó a cabo una campaña experimental sobre los hormigones estudiados, con el objeto de obtener sus propiedades difusivas, químicas e higroscópicas. El modelo se contrastó con datos experimentales obtenidos en una plataforma petrolera localizada en Brasil. Las simulaciones numéricas corroboraron los datos experimentales. Además, durante el desarrollo de la investigación se obtuvieron resultados paralelos a los planteados inicialmente. Por ejemplo, el análisis de diferentes coeficientes de difusión y la relación entre ellos. Así como también se observó que el campo eléctrico establecido entre las especies iónicas disueltas en la solución de poro depende del gradiente de concentración de las mismas. Los efectos de histéresis capilar son expresados por el modelo propuesto, el cual conduce a la determinación de una serie de propiedades microscópicas, tales como la distribución del tamaño de poro, además de la tortuosidad y conectividad de la red porosa.

Self-consistent, nonlocal electron heat flux at arbitrary ion charge number

A single, nonlocal expression for the electron heat flux, which closely reproduces known results at high and low ion charge number 2, and “exact” results for the local limit at all 2, is derived by solving the kinetic equation in a narrow, tail-energy range. The solution involves asymptotic expansions of Bessel functions of large argument, and (Z-dependent)order above or below it, corresponding to the possible parabolic or hyperbolic character of the kinetic equation; velocity space diffusion in self-scattering is treated similarly to isotropic thermalization of tail energies in large Z analyses. The scale length H characterizing nonlocal effects varies with Z, suggesting an equal dependence of any ad hoc flux limiter. The model is valid for all H above the mean-free path for thermal electrons.

Thermal shields for heat loss reduction in Siemens-type CVD reactors

The use of thermal shields to reduce radiation heat loss in Siemens-type CVD reactors is analyzed, both theoretically and experimentally. The potential savings from the use of the thermal shields is first explored using a radiation heat model that takes emissivity variations with wavelength into account, which is important for materials that do not behave as grey bodies. The theoretical calculations confirm that materials with lower surface emissivity lead to higher radiation savings. Assuming that radiation heat loss is responsible for around 50% of the total power consumption, a reduction of 32.9% and 15.5% is obtained if thermal shields with constant emissivities of 0.3 and 0.7 are considered, respectively. Experiments considering different thermal shields are conducted in a laboratory CVD reactor, confirming that the real materials do not behave as grey bodies, and proving that significant energy savings in the polysilicon deposition process are obtained. Using silicon as a thermal shield leads to energy savings of between 26.5-28.5%. For wavelength-dependent emissivities, the model shows that there are significant differences in radiation heat loss, of around 25%, when compared to that of constant emissivity. The results of the model highlight the importance of having reliable data on the emissivities within the relevant range of wavelengths, and at deposition temperatures, which remains a pending issue.