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.

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 of Flat Solar Collectors Array in Flat, Inclined, and Step-Like Solar Fields

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Nassar Yasser Fathi ◽  
Alsadi Samer
Keyword(s):  
Solar Radiation ◽  
Diffuse Radiation ◽  
Dynamic Parameter ◽  
Incident Radiation ◽  
Appreciable Amount ◽  
Design Parameters ◽  
View Factor ◽  
Solar Radiation Incident ◽  
View Factors ◽  
Reflecting Surfaces

Solar radiation consists of direct beam, sky diffuse, and reflected radiations from the ground and adjacent surfaces. The amount of diffuse radiation falling on solar collector depends on the view factor of the collector to sky. The reflected radiation striking the collector's surface depends on the reflectivity of the surface, as well as on view factors and the amount of solar radiation reaching the reflecting surfaces. The amount of reflected radiation coming from the ground can be of an appreciable amount, and can be amplified using special reflector surfaces. This study develops general analytical expressions for the sky's view factors as well as factors related to the ground and those between collectors for the deployment of collectors in multiple rows, in three types of solar fields: flat, inclined, and steplike solar fields. All parameters presented in these expressions are measurable (edge-to-edge dimension). The effects of the design parameters such as the tilt of the angle of the collector, the distance between the collectors, the height of the collector, the position of the collector above the ground (as in the case of step-like field), and the inclination of the land of the field (as in the case of an inclined field) on the view factors are numerically demonstrated. The current study also specifies new terms such as the sunny zone and the shadow zone; these zones control the amount of solar radiation reflected onto the collector. As a result, the ground-view factor that depends on the altitude of the solar angle is considered to be a dynamic parameter. The results obtained may be used to estimate the solar radiation incident on all types of solar fields, with the possibility of increasing the incident radiation on a collector by using planar reflectors.

Horizontal Tubular Microalgae Photobioreactor Plant View Factors and Diffuse Radiation

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
T. Maor ◽  
J. Appelbaum
Keyword(s):  
Solar Radiation ◽  
Present Article ◽  
Diffuse Radiation ◽  
Design Parameters ◽  
View Factor ◽  
Diffuse Solar Radiation ◽  
Horizontal Tubes ◽  
Vertical Walls ◽  
View Factors

Different view factors and different components of the diffuse solar radiation impinging on a photobioreactor plant for cultivating microalgae products are formulated and calculated in the present article. The outdoor plant consists of multiple horizontal tubes arranged in multiple vertical walls. The diffuse radiation on a tube may come from three directions of the sky: from the aperture between the walls (from the sky above), from the penetration of the diffuse radiation between the tubes, and from the plant edges. Each component of the diffuse radiation is associated with a different view factor. For design parameters of a practical plant, the largest component of the diffuse radiation comes from the sky above the plant.

scholarly journals Solutions for Downslope Pipeline Walking on a Seabed With a Peaky Trilinear Soil Resistance Model

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Adriano Castelo ◽  
David White ◽  
Yinghui Tian
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Soil Resistance ◽  
Finite Element Analyses ◽  
Soil Behavior ◽  
Rigid Plastic ◽  
Offshore Pipelines ◽  
Soil Response ◽  
Resistance Model ◽  
Analytical Expressions

Abstract Offshore pipelines used for transporting hydrocarbons are cyclically loaded by great variations of pressure and temperature. These variations can induce axial instability in such pipelines. This instability may cause the pipelines to migrate globally along their length; an effect known as pipeline walking. Traditional models of pipeline walking have considered the axial soil response as rigid-plastic (RP); however, such behavior does not match observations from physical soil tests. It leads to inaccurate estimates of walking rate (WR) per cycle and over design. In this paper, a trilinear (3L) soil resistance model is used to represent seabed resistance to investigate the behavior of pipeline walking. Different parameters, i.e., shapes and properties of trilinearity (within the peaky soil model type), have been considered leading to a closed-form solution. This solution improves the understanding of the main properties involved in the peaky trilinear soil behavior by providing a set of analytical expressions for pipe walking, which were benchmarked and validated against a set of finite element analyses.

scholarly journals Anisotropic Scattering Characteristics of a Radially Multilayered Gyrotropic Sphere

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Lei Cao ◽  
Yongpin Chen ◽  
Kai Kang
Keyword(s):  
Plane Wave ◽  
Spherical Wave ◽  
Fem Simulation ◽  
Closed Form Solution ◽  
Anisotropic Scattering ◽  
Form Solution ◽  
Scattering Coefficients ◽  
Full Wave ◽  
Spherical Scatterer ◽  
Analytical Expressions

We present a new closed-form solution to the scattering of a monochromatic plane wave by a radially multilayered gyrotropic sphere using the T-matrix method. This approach can be utilized to investigate the interactions of a plane wave and a gyrotropic spherical scatterer of multiple layers with each layer characterized by both permittivity and permeability tensors. Based on the completeness and noncoplanar properties of vector spherical wave functions (VSWFs), analytical expressions of the electromagnetic fields in each gyrotropic layer are first derived. The boundary conditions are then applied on each discontinuous interface to obtain the scattering coefficients. Validations are made by first comparing the radar cross section (RCS) values of a 2-layered gyrotropic sphere with that computed from the full-wave finite element method (FEM) simulation and then reducing the general case to uniaxial case to compare the RCS values with the published results computed by Fourier transform combined with VSWFs method; in both cases good agreements are observed. Several specific cases are fully explored to investigate how the RCS are influenced by the parameters of the multilayered spherical structure. The results show that when both electric and magnetic gyrotropy tensors are considered, the RCS of the multilayered spherical scatterer can be suppressed or enhanced, depending on proper configurations of the material parameters.

Motion of a Bored Sphere in a Spinning Spherical Cavity

1981 ◽  
Vol 103 (4) ◽  
pp. 389-394 ◽  
Author(s):  
R. H. Nunn ◽  
J. W. Bloomer
Keyword(s):  
Numerical Methods ◽  
Closed Form ◽  
Predictive Model ◽  
Spherical Cavity ◽  
Equations Of Motion ◽  
Closed Form Solution ◽  
Form Solution ◽  
Analytical Expressions ◽  
Theory And Experiment

Theory and experiment are combined to develop a predictive model for the motion of a bored sphere within a spinning spherical cavity. The motion is gyroscopic in nature with the sphere eventually aligning its hole with the axis of spin of the cavity. Analytical expressions are derived for the applied moments on the sphere due to its motion relative to that of the cavity, and the resulting equations of motion are solved by numerical methods. An approximate closed-form solution is also obtained. Experiments are described in which the measured nutation of the sphere substantiates the analytical predictions.

Dynamical Compliance of Rectangular Foundations on an Elastic Half-Space

1963 ◽  
Vol 30 (4) ◽  
pp. 579-584 ◽  
Author(s):  
William T. Thomson ◽  
Takuji Kobori
Keyword(s):  
Half Space ◽  
Closed Form Solution ◽  
Static Problem ◽  
Elastic Half Space ◽  
Form Solution ◽  
Ground Displacement ◽  
Foundation Slab ◽  
Limiting Case ◽  
Rectangular Foundation ◽  
Zero Frequency

Equation for the compliance of the ground, considered as an elastic half-space under a rectangular foundation slab, is developed for harmonic forces normal to the ground. Displacement of the center of the slab for several rectangular shapes is evaluated numerically and plotted as a function of the frequency. A closed-form solution for the limiting case of zero frequency is shown to agree exactly with the static problem of Love [7].

Frictional Contact Between the Surface Wave and a Rigid Strip

1996 ◽  
Vol 63 (1) ◽  
pp. 15-20 ◽  
Author(s):  
O. Y. Zharii
Keyword(s):  
Surface Wave ◽  
Frictional Contact ◽  
Mixed Boundary ◽  
Closed Form Solution ◽  
Tangential Velocity ◽  
Form Solution ◽  
Load Force ◽  
Tangential Load ◽  
Normal Stress Distribution ◽  
Limiting Case

A problem of frictional contact between a running surface wave and a motionless rigid strip is considered. The corresponding mixed boundary value problem of elastodynamics is reduced to a singular integral equation for the normal stress distribution and a closed-form solution of it has been found. Boundaries of the contact zone are determined from a system of transcendental equations involving trigonometric functions. Also, simple formulae obtained for kinematic characteristics of solution (tangential velocity inside the contact area, velocity and slope of the free surface outside it). The problem considered represents a limiting case of operating ultrasonic motor when it is completely braked by an external tangential load force.

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