Application of Transparent Enclosure Theory to Solar Energy Absorption by Cylindrical Tubes in Sunspaces

1985 ◽  
Vol 107 (1) ◽  
pp. 5-9 ◽  
Author(s):  
M. E. McCabe ◽  
M. Van Migom
Keyword(s):  
Solar Energy ◽  
Cylindrical Tube ◽  
Solar Flux ◽  
Dimensional Model ◽  
Matrix Formulation ◽  
General Matrix ◽  
Solar Absorbers ◽  
Cylindrical Tubes ◽  
The Matrix ◽  
Tube Space

A general matrix formulation for beam and diffuse radiative solar transfer is presented for an enclosure containing partially transparent walls. The general theory is used to study the absorption of radiant solar energy in a building sunspace having a south-facing window and a row of opaque vertical cylindrical-tube solar absorbers. A two-dimensional model is formulated for the sunspace in which a typical cylindrical absorber tube is subdivided into a number of uniform elements and the window and sunspace surfaces are each represented as single elements. The matrix expressions are evaluated for incident solar flux conditions typical for a south vertical window on a clear winter day. The results are presented as dimensionless ratios of absorbed-to-incident solar flux as a function of the tube spacing to radius ratio. The spatial distribution of absorbed solar flux is presented at discrete time interals for the cylindrical tube. Space and time-averaged values of absorbed solar flux are also presented for the cylinder, the window, and the room. The potential application of these results for thermal modeling in passive solar applications is discussed.

The Convex Polytopes and Homogeneous Coordinate Rings of Bivariate Polynomials

2019 ◽  
Vol 16 (2) ◽  
pp. 1
Author(s):  
Shamsatun Nahar Ahmad ◽  
Nor’Aini Aris ◽  
Azlina Jumadi
Keyword(s):  
Convex Polytopes ◽  
Polynomial Systems ◽  
Matrix Formulation ◽  
Bivariate Polynomials ◽  
Homogeneous Coordinates ◽  
The Matrix ◽  
Projective Vector ◽  
Coordinate Rings ◽  
Resultant Matrix ◽  
The Given

Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated with the entries of the resultant matrix of the system under consideration. This paper presents some conditions for the homogeneous coordinates of a certain system of bivariate polynomials through the construction and implementation of the Sylvester-Bèzout hybrid resultant matrix formulation. This basis of the implementation of the Bèzout block applies a combinatorial approach on a set of linear inequalities, named 5-rule. The inequalities involved the set of exponent vectors of the monomials of the system and the entries of the matrix are determined from the coefficients of facets variable known as brackets. The approach can determine the homogeneous coordinates of the given system and the entries of the Bèzout block. Conditions for determining the homogeneous coordinates are also given and proven.

Performance Enhancement of Solar Parabolic Trough Collector Using Intensified Ray Convergence System

2017 ◽  
Vol 867 ◽  
pp. 191-194
Author(s):  
Anbu Manimaran Sukanta ◽  
M. Niranjan Sakthivel ◽  
Gopalsamy Manoranjith ◽  
Loganathan Naveen Kumar
Keyword(s):  
Renewable Energy ◽  
Solar Energy ◽  
Performance Enhancement ◽  
Solar Flux ◽  
Parabolic Trough ◽  
Parabolic Trough Collector ◽  
Chrome Coating ◽  
Convergence System ◽  
And Performance

Solar Energy is one of the forms of Renewable Energy that is available abundantly. This work is executed on the enhancement of the performance of solar parabolic trough collector using Intensified Ray Convergence System (IRCS). This paper distinguishes between the performance of solar parabolic trough collector with continuous dual axis tracking and a fixed solar parabolic trough collector (PTC) facing south (single axis tracking). The simulation and performance of the solar radiations are visualized and analyzed using TRACEPRO 6.0.2 software. The improvement in absorption of solar flux was found to be enhanced by 39.06% in PTC using dual axis tracking, absorption of solar flux increases by 52% to 200% in PTC receiver using perfect mirror than PTC using black chrome coating.

scholarly journals Homogenization of very rough three-dimensional interfaces for the poroelasticity theory with Biot's model

2019 ◽  
Author(s):  
Nguyen Thi Kieu ◽  
Pham Chi Vinh ◽  
Do Xuan Tung
Keyword(s):  
Incident Angle ◽  
Three Dimensional ◽  
Homogenization Method ◽  
Reflection And Transmission Coefficients ◽  
Biot Theory ◽  
Rough Interface ◽  
Matrix Formulation ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
The Matrix

In this paper, we carry out the homogenization of a very rough three-dimensional interface separating  two dissimilar generally anisotropic poroelastic solids modeled by the Biot theory. The very rough interface is assumed to be a cylindrical surface that rapidly oscillates between two parallel planes, and the motion is time-harmonic. Using the homogenization method with the matrix formulation of the poroelasicity theory, the explicit  homogenized equations have been derived. Since the obtained  homogenized equations are totally explicit, they are very convenient for solving various practical problems. As an example proving this, the reflection and transmission of SH waves at a very rough interface of tooth-comb type is considered. The closed-form analytical expressions of the reflection and transmission coefficients have been  derived. Based on them, the effect of the incident angle and some material parameters  on the reflection and transmission coefficients are examined numerically.

scholarly journals The matrix formulation of type IIB five-branes

1998 ◽  
Vol 523 (1-2) ◽  
pp. 158-170 ◽  
Author(s):  
Savdeep Sethi
Keyword(s):  
Matrix Formulation ◽  
The Matrix

Closed Shell Hartree Theory with Orthonormal Orbitals

1980 ◽  
Vol 35 (4) ◽  
pp. 408-411 ◽  
Author(s):  
Yasuyuki Ishikawa
Keyword(s):  
Closed Shell ◽  
Natural Orbital ◽  
Matrix Formulation ◽  
The Matrix ◽  
Polyatomic Systems

Abstract A natural orbital multiconfigurational SCF formalism has been applied to the closed shell Hartree theory with orthonormal orbitals. A prescription is given for constructing a single, one-electron Hamiltonian with which one can determine all the occupied orbitals. The formalism is suited to the matrix formulation of the orthogonalized Hartree theory for polyatomic systems.

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