Analytical Expressions for View Factors with an Intervening Surface

2004 ◽  
Vol 18 (2) ◽  
pp. 273-277 ◽  
Author(s):  
M. Deiveegan ◽  
V. Ramamoorthy ◽  
Subrahmanya S. Katte
Keyword(s):  
View Factors ◽  
Analytical Expressions

View Factors to Grounds of Photovoltaic Collectors

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
J. Appelbaum
Keyword(s):  
Global Radiation ◽  
Appreciable Amount ◽  
View Factor ◽  
Solar Pv ◽  
Mathematical Expressions ◽  
Inclination Angles ◽  
View Factors ◽  
Solar Field ◽  
Analytical Expressions ◽  
General Configuration

Ground reflected radiation is one component of the global radiation on photovoltaic collectors in a solar field. This component depends on the view factor of the collector to ground, hence depends on the relative position of the collectors to each other. General analytical expressions and numerical values for the view factor to the ground were developed between flat-plate collectors positioned in a general configuration. Based on the general expression, the view factors to ground for particular collector configurations were derived. For deployment of photovoltaic collectors in multiple rows with common inclination angles, the view factor to ground is rather small, and hence, the reflected radiation from the ground on the collectors may be neglected compared to the direct beam and the diffuse components. However, in some cases the reflected radiation from the ground may constitute an appreciable amount as in snowy area. Bifacial photovoltaic (PV) panels can absorb solar radiation by both the front and the rear sides and are usually deployed vertically. In this case the reflected radiation from the ground on the panels may be appreciable depending on the ground albedo. The mathematical expressions of the different view factors may be used by the solar field designer to estimate the amount of reflected radiation from the ground reaching the collectors for different configurations of solar PV plants.

View Factors in Radiation Between Two Parallel Oriented Cylinders of Finite Lengths

1982 ◽  
Vol 104 (2) ◽  
pp. 384-388 ◽  
Author(s):  
N. H. Juul
Keyword(s):  
Line Source ◽  
Closed Form Solution ◽  
Diffuse Radiation ◽  
Form Solution ◽  
View Factor ◽  
Double Integral ◽  
Integral Expression ◽  
View Factors ◽  
Limiting Case ◽  
Analytical Expressions

A simple double-integral expression for the diffuse radiation view factor, F12, between two parallel cylinders of finite lengths is derived. No closed-form solution appears possible except for the limiting case of infinite long cylinders for which an analytical expression for the view factor F12∞ is derived by applying the crossed string method. The accuracies of the line source approximations are evaluated, and the regions for which they are accurate to one percentage or better are identified. The view factor F12 between two opposing cylinders of equal length is computed by numerical integration and normalized by F12∞. The results are presented. Analytical expressions, which approximate the view factors between two opposite cylinders of finite length, are derived and their accuracy is evaluated over a useful parameter range. The range of their applications corresponds approximately to that for the line source approximation. This result is expected, because the errors are caused in part by blockage of radiation which is similar.

Layered and ion implantation specimens as possible reference materials for the electron-probe microanalysis

1992 ◽  
Vol 50 (2) ◽  
pp. 1652-1653
Author(s):  
G. Remond ◽  
R.H. Packwood ◽  
C. Gilles ◽  
S. Chryssoulis
Keyword(s):  
Ion Implantation ◽  
Reference Materials ◽  
Analytical Techniques ◽  
Thin Film Deposition ◽  
Film Deposition ◽  
X Ray ◽  
Spatially Resolved ◽  
Analytical Expressions ◽  
Original Approach ◽  
Depth Concentration

Merits and limitations of layered and ion implanted specimens as possible reference materials to calibrate spatially resolved analytical techniques are discussed and illustrated for the case of gold analysis in minerals by means of x-ray spectrometry with the EPMA. To overcome the random heterogeneities of minerals, thin film deposition and ion implantation may offer an original approach to the manufacture of controlled concentration/ distribution reference materials for quantification of trace elements with the same matrix as the unknown.In order to evaluate the accuracy of data obtained by EPMA we have compared measured and calculated x-ray intensities for homogeneous and heterogeneous specimens. Au Lα and Au Mα x-ray intensities were recorded at various electron beam energies, and hence at various sampling depths, for gold coated and gold implanted specimens. X-ray intensity calculations are based on the use of analytical expressions for both the depth ionization Φ (ρz) and the depth concentration C (ρz) distributions respectively.

A Simple Real-Space Channelling Theory for Electron Diffraction and HREM

1990 ◽  
Vol 48 (1) ◽  
pp. 64-65
Author(s):  
D. Van Dyck
Keyword(s):  
High Resolution ◽  
Electron Diffraction ◽  
Direct Method ◽  
Real Space ◽  
Zone Axis ◽  
Phase Object ◽  
High Resolution Images ◽  
The Many ◽  
Analytical Expressions ◽  
Electron Wavefunction

The computation of the many beam dynamical electron diffraction amplitudes or high resolution images can only be done numerically by using rather sophisticated computer programs so that the physical insight in the diffraction progress is often lost. Furthermore, it is not likely that in this way the inverse problem can be solved exactly, i.e. to reconstruct the structure of the object from the knowledge of the wavefunction at its exit face, as is needed for a direct method [1]. For this purpose, analytical expressions for the electron wavefunction in real or reciprocal space are much more useful. However, the analytical expressions available at present are relatively poor approximations of the dynamical scattering which are only valid either for thin objects ((weak) phase object approximation, thick phase object approximation, kinematical theory) or when the number of beams is very limited (2 or 3). Both requirements are usually invalid for HREM of crystals. There is a need for an analytical expression of the dynamical electron wavefunction which applies for many beam diffraction in thicker crystals. It is well known that, when a crystal is viewed along a zone axis, i.e. parallel to the atom columns, the high resolution images often show a one-to-one correspondence with the configuration of columns provided the distance between the columns is large enough and the resolution of the instrument is sufficient. This is for instance the case in ordered alloys with a column structure [2,3]. From this, it can be suggested that, for a crystal viewed along a zone axis with sufficient separation between the columns, the wave function at the exit face does mainly depend on the projected structure, i.e. on the type of atom columns. Hence, the classical picture of electrons traversing the crystal as plane-like waves in the directions of the Bragg beams which historically stems from the X-ray diffraction picture, is in fact misleading.

KINEMATIC FEATURES OF THE LAPPING PROCESS AND DETERMINATION OF ITS BASIC PARAMETERS

2020 ◽  
Vol 7 (3) ◽  
pp. 23-28
Author(s):  
EZIZ SARVAN SHIRVAN ◽  
Keyword(s):  
Dynamic Properties ◽  
Cutting Speed ◽  
Equilibrium System ◽  
Technological Parameters ◽  
Kinematic Characteristics ◽  
Angular Velocities ◽  
Basic Parameters ◽  
Grinding Tool ◽  
Mathematical Relationships ◽  
Analytical Expressions

This paper discusses the kinematic characteristics of lapping process and the main parameters of the process. It was determined that the influencing degree of technological parameters to the forming surface and processes. It was projected the construction of the lapping head for processing of internal cylindrical surfaces, scheme of the lapping operation and graphic description of the forces influencing. The relationships between the axial, radial and tangential cutting forces and the effect of the combined force thereof are determined in order to ensure the necessary surface pressure. During the analysis geometric and mathematical relationships were obtained. The extracted analytical expressions can be realized by further experimental researches and can be used in engineering calculations of technological parameters of processing by lapping. Angular velocity, friction force, linear velocity, also the length of the tactile curve and the radius of the part can be considered the main kinematic and dynamic parameters of the process that the formation of the surface, also the course of the process depends on these parameters. Depending on the kinematic parameters, the wear nature of the tool changes and this changes the linear and angular velocities, which have a significant impact on the accuracy, quality and productivity of processing. When examining the technological capabilities of the process, the nature of the movement between the part and the grinding tool, also changes in cutting speed are often considered as a main factor. Analytical expressions were obtained to determine the main parameters of the process, taking into account the kinematic characteristics of the friction process. These expressions can be used in engineering calculations and allow to determine the optimal values of the processing mode. In order to obtain the required micrometric surface cleanliness and measurement accuracy, correlation relationships were established between the main parameters of the process, equations of the equilibrium system of shear forces were compiled and analytical expressions were obtained based on the analysis of kinematic and dynamic properties of the system.

Evaluation of the Power Transformer Magnetizing Inrush Currents

2020 ◽  
Vol 10 (10) ◽  
pp. 20-32
Author(s):  
Aleksey A. KUVSHINOV ◽  
◽  
Vera V. VAKHNINA ◽  
Aleksey N. CHERNENKO ◽  
◽  
...  
Keyword(s):  
Power Transformer ◽  
Geomagnetic Disturbance ◽  
Inrush Current ◽  
Geomagnetic Disturbances ◽  
Disturbance Intensity ◽  
Magnetizing Inrush Current ◽  
Inrush Currents ◽  
Instantaneous Values ◽  
The Mathematical Model ◽  
Analytical Expressions

The mathematical model of a shell-core power transformer’s magnetization branch is substantiated. By using the model, analytical expressions for the magnetizing current instantaneous values under the conditions of geomagnetic disturbances can be obtained. Quantitative assessments of the magnetizing inrush current amplitudes and durations versus the geomagnetic disturbance intensity are obtained. The dynamics of the power transformer magnetic system saturation transient and changes in the magnetization inrush current amplitudes and durations after a sudden occurrence of geomagnetic disturbances are shown. The error of estimating the magnetizing inrush current amplitudes under geomagnetic disturbances is determined based on comparison with experimental data.

Extended electric power sources

2018 ◽  
Author(s):  
T.A. Konev ◽  
V.A. Kuzmin ◽  
E. Yu. Mutovina ◽  
R.D. Puzhaykin ◽  
Vladimir Salomatov
Keyword(s):  
Electric Power ◽  
Electric Current ◽  
Load Resistance ◽  
Active Power ◽  
Operating Voltage ◽  
Power Sources ◽  
Distributed Parameters ◽  
Analytical Expressions ◽  
Characteristic Resistance ◽  
Length Effects

Chemical sources of current are investigated as lines with distributed parameters. Analytical expressions are obtained for the voltage and active power values of the source at different distances from the beginning of the cell as well as dependences of the working voltage and active power on the source length. Effects of a reduction in the operating voltage and active power are due to the flow of electric current along the source during operation. The magnitude of these effects depends not only on the length of the source, but also on the ratio of characteristic resistance to the load resistance.<br>

Henderson Hasselbalch Relationship and Weak Acid Titration

2019 ◽  
Author(s):  
Marc Blétry
Keyword(s):  
Theoretical Framework ◽  
Weak Acid ◽  
Acid Base ◽  
Sensitive Technique ◽  
Chemistry Students ◽  
Advanced Students ◽  
Acid Titration ◽  
Acid Base Titration ◽  
Analytical Expressions

Henderson-Hasselbalch relation is generally the simplified theoretical framework used to introduce students to acid-base titration. However, it is not always valid and its limitations should be made clear to chemistry students. The appropriate parameter to evaluate its validity is K a /C 0 , in connection with Ostwald dilution law. For more advanced students, it is possible to deduce analytical expressions that always fit accurately acid-base titrations and allow an evaluation of Henderson Hasselbalch relation. Gran plot appears as a particularly sensitive technique to the breakdown of Henderson Hasselbalch relation.

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