Exact analytical expressions modelling effects of incident irradiance and temperature on physical parameters of photovoltaic solar module

2018 ◽  
Author(s):  
Hicham El Achouby ◽  
Mhammed Zaimi ◽  
Asmaa Ibral ◽  
El Mahdi Assaid
Keyword(s):  
Physical Parameters ◽  
Solar Module ◽  
Analytical Expressions

scholarly journals High-eccentricity migration of planetesimals around polluted white dwarfs

2020 ◽  
Vol 498 (3) ◽  
pp. 4005-4020
Author(s):  
Christopher E O’Connor ◽  
Dong Lai
Keyword(s):  
White Dwarfs ◽  
Physical Parameters ◽  
High Eccentricity ◽  
Tidal Friction ◽  
Pressure Drag ◽  
Ram Pressure ◽  
Tidal Heating ◽  
Analytical Expressions ◽  
Internal Viscosity ◽  
Orbital Migration

ABSTRACT Several white dwarfs (WDs) with atmospheric metal pollution have been found to host small planetary bodies (planetesimals) orbiting near the tidal disruption radius. We study the physical properties and dynamical origin of these bodies under the hypothesis that they underwent high-eccentricity migration from initial distances of several astronomical units. We examine two plausible mechanisms for orbital migration and circularization: tidal friction and ram-pressure drag in a compact disc. For each mechanism, we derive general analytical expressions for the evolution of the orbit that can be rescaled for various situations. We identify the physical parameters that determine whether a planetesimal’s orbit can circularize within the appropriate time-scale and constrain these parameters based on the properties of the observed systems. For tidal migration to work, an internal viscosity similar to that of molten rock is required, and this may be naturally produced by tidal heating. For disc migration to operate, a minimal column density of the disc is implied; the inferred total disc mass is consistent with estimates of the total mass of metals accreted by polluted WDs.

scholarly journals The influence of a thermal plasma on synchrotron radiation

1988 ◽  
Vol 6 (3) ◽  
pp. 421-436 ◽  
Author(s):  
A. Crusius
Keyword(s):  
Synchrotron Radiation ◽  
Energy Loss ◽  
Total Energy ◽  
Thermal Plasma ◽  
Large Scale ◽  
Lorentz Factor ◽  
Physical Parameters ◽  
Relativistic Electrons ◽  
Physical Conditions ◽  
Analytical Expressions

The synchrotron emission from relativistic electrons in a thermal plasma with large-scale random magnetic fields is considered. In this case, the spectral synchrotron power of a single electron can be given in closed form allowing exact analytical expressions for the synchrotron emissivity, absorption coefficient, intensity and total energy loss of particles to be derived. The influence of various physical parameters such as gas density, magnetic field strength, particle's Lorentz factor on the resulting emissivities, intensities and energy loss is discussed in detail. Below the Razin– Tsytovich frequency vR = 20 Hz (ne/l cm−3) (B/l Gauss)−1, the spectral appearance of synchrotron radiation both in the optically thin and thick case is quite different than the vacuum behaviour. Since in the quasar broad line regions, vR is of the order 1011 Hz the suppression of synchrotron radiation may explain why most quasars are radio quiet. Likewise, the necessary physical conditions for the occurrence of synchrotron masering in the optically thick case are given. We obtain optical depth |τ|>1 for compact nonthermal sources. The total energy loss of a single particle is shown to be exponentially reduced at Lorentz factors less than γR = 2·1. 10−3 (ne/1 cm−3)½ (B/1 Gauss)−1.

scholarly journals Calculation of Liquidus Temperature for Aluminum and Magnesium Alloys Applying Method of Equivalency

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Mile B. Djurdjević ◽  
Srećko Manasijević ◽  
Zoran Odanović ◽  
Natalija Dolić
Keyword(s):  
Magnesium Alloys ◽  
Liquidus Temperature ◽  
Physical Parameters ◽  
Chemical Compositions ◽  
Alloying Element ◽  
Reference Element ◽  
Cast Alloys ◽  
Aluminum And Magnesium Alloys ◽  
Analytical Expressions ◽  
Liquidus Temperatures

The purpose of this paper is to develop a mathematical equation, which will be able to accurately predict the liquidus temperature of various aluminum and magnesium cast alloys on the basis of their known chemical compositions. An accurate knowledge of liquidus temperature permits a researcher to predict a variety of physical parameters pertaining to a given alloy. The analytical expressions presented in this paper are based on the “method of equivalency.” According to this concept, the influence of any alloying element on the liquidus temperature of an aluminum and/or magnesium alloy can be translated into the equivalent influence of a reference element. Silicon as a reference element has been chosen for aluminum alloys and aluminum for magnesium alloys. The sum of the equivalent concentrations for other elements, when added to the influence of the actual reference element is used to calculate the liquidus temperature of the alloy. The calculated liquidus temperatures for wide ranges of alloy chemical compositions show a good correlation with corresponding measured liquidus temperatures.

Analytical Expressions for Shear and Axial Joint Deformations in Area-Array Assemblies Due to Global CTE Mismatch

2002 ◽  
Author(s):  
S. M. Heinrich ◽  
S. Shakya ◽  
P. S. Lee ◽  
J. Liang
Keyword(s):  
Shear Deformation ◽  
Correction Factor ◽  
Material Properties ◽  
Practical Interest ◽  
Physical Parameters ◽  
Axial Deformation ◽  
Deformation Problem ◽  
Area Array ◽  
Cte Mismatch ◽  
Analytical Expressions

In a previous study the authors derived an analytical expression for calculating the maximum shear deformation, (Δu)max, in an area array of solder joints under global CTE mismatch loading. The result was expressed in the form (Δu)max = βsh(Δu)0, where βsh fish is the “shear correction factor” and (Δu)0 is the commonly used and easily calculated estimate of shear deformation, which is based on the free thermal expansion of component and substrate. A key assumption in the previous model was that warping of the assembly was neglected. In the present work the companion problem of assembly warpage is treated, the results of which are analytical expressions for the maximum axial deformation in the array, (Δw)max. The present results are cast in the form of an “axial correction factor,” βax, to be applied to the same convenient reference deformation: (Δw)max = βax(Δu)0. Exact solutions are presented for several cases of practical interest: (1) an assembly in which the component and substrate have the same plan dimensions, (2) a rigid-substrate assembly, and (3) a rigid-component assembly. In addition, approximate expressions are presented in simple analytical form for the case in which the array is relatively flexible in comparison with the component and substrate. When combined with the previous solution for array shear deformation, the present results may be viewed as furnishing the complete solution to the thermal deformation problem for area-array assemblies of the types considered. The analytical results clearly indicate the relationship between the correction factors and the physical parameters of the problem: (a) the dimensions and material properties (elastic and thermal) of the component and substrate; (b) the material properties of the interconnect material (effective Young’s modulus and Poisson’s ratio); (c) the array size and population; and (d) the geometric parameters of the individual joints. An interesting and potentially useful conclusion is that the sign of the maximum axial deformation (tension or compression) in the corner joints can be related to the sign of a very simple expression that depends on the assembly dimensions and the material properties of the component and substrate. This result could be used to design more reliable assemblies, as it enables one to minimize the amount of axial deformation in the corner joints or, for a given thermal loading condition, to create a desirable compression in the corner joints to inhibit shear-driven fatigue cracking. The solution is based on a theoretical model of two circular elastic disks connected by an elastic layer whose distributed axial and shear stiffnesses are related to the joint/array characteristics by means of the authors’ previously derived stiffnesses for a single joint.

scholarly journals Modeling of thermometric characteristics of thermodiode sensors by using the dimensionless sensitivity

2020 ◽  
Vol 23 (04) ◽  
pp. 437-441
Author(s):  
P.S. Smertenko ◽  
Keyword(s):  
Numerical Differentiation ◽  
Analytical Approximation ◽  
High Accuracy ◽  
Physical Parameters ◽  
Differential Analysis ◽  
Temperature Ranges ◽  
Analytical Expressions ◽  
Silicon Sensor

Dimensionless sensitivity and slope of its characteristic in the forms α=d(log V)/d(log T) and γ=d(log α)/d(log T) have been proposed as a base for modeling of thermometric characteristics V(T). The differential analysis of V(T) curves within the range from 4.2 up to 400 K by numerical differentiation has allowed obtaining the analytical approximation in the form V(T)=ATαexp[-BTγ1(1+CTγ1)], where A, B and C are the constants depending on physical parameters of thermodiode silicon sensor. This approach is useful both for the analysis of these characteristics as well as for modeling and determining an approximating function by finding out the regions where power-like or exponential dependences are the adequate expressions to describe the thermometric characteristic sections. By contrast to the known methods, one should not know beforehand the function that describes the process or the characteristic. It permits to elucidate fine peculiarities of thermometric characteristics and to achieve high accuracy of modeling by using the analytical expressions. In view of the practical purposes, the thermometric characteristics are approximated within the three temperature ranges. The errors of approximation do not exceed ±0.02%, ±0.2% and ±0.4% within the temperature ranges 4.2…40 K, 40…170 K and 170…400 K, respectively.

Kinetic Simulation of Heat Transfer in Microflow

2009 ◽  
Author(s):  
Irina A. Graur ◽  
Alexey Ph. Polikarpov
Keyword(s):  
Heat Transfer ◽  
Transfer Problem ◽  
Physical Parameters ◽  
Kinetic Simulation ◽  
Parallel Plates ◽  
Discrete Velocity Method ◽  
Steady State Heat ◽  
Steady State Heat Transfer ◽  
S Model ◽  
Analytical Expressions

The steady-state heat transfer problem between two parallel plates is investigated using kinetic models of the Boltzmann equation: BGK, S-model and ES-model. The discrete velocity method is used to determine the values of physical parameters: density, bulk velocity, temperature and heat flux. The obtained results are compared with the analytical expressions and some experimental data.

scholarly journals Prediction of Axial Variation of Plasma Potential in Helicon Plasma Source Using Linear Regression Techniques

2020 ◽  
Vol 5 (6) ◽  
pp. 1284-1299
Author(s):  
Vipin Shukla ◽  
Mainak Bandyopadhyay ◽  
Vivek Pandya ◽  
Arun Pandey
Keyword(s):  
Plasma Source ◽  
Plasma Potential ◽  
Ion Source ◽  
Training Data ◽  
Negative Ion ◽  
Physical Parameters ◽  
Plasma Parameters ◽  
Data Set ◽  
Regression Techniques ◽  
Analytical Expressions

Analytical expressions are used frequently for the determination and analysis of plasma parameters. Instead of relying on analytical expressions, the proposed method uses regression techniques supplemented with experimental data for the selected parameters (plasma potential). In the machine learning domain, this is equivalent to the creation of the training data set, building and training the model, and authenticating the result over a range of desired physical parameters. An experimental dataset is built using two axially movable Triple Langmuir Probe (TLPs) which measure the electron temperature, electron density, and electric potential of a plasma. The presented work is a first step towards developing an inclusive model with detailed kinetic simulations capable of characterizing the HELicon Experiment for Negative ion source (HELEN-I) with a single driver. Plasma potential is measured at different axial locations (z) by keeping pressure fixed at 6 mTorr.

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