Isosceles Triangular Research Articles

Lattice-Boltzmann Modeling of Natural Convection Between a Square Outer Cylinder and an Inner Isosceles Triangular Heating Body

The present study confirms the robustness and the computational effectiveness of the lattice-Boltzmann method in simulating natural convection between a triangular isosceles heating body and a square outer cylinder isothermally cooled/(insulated) from its vertical/(horizontal) walls. The heated body is symmetrically placed on the vertical centerline of the cavity with the summit opposite to its horizontal base pointing upwards. A detailed parametric study is conducted to investigate the effect of three positions (MB, MM, and MT) of the heating body on fluid flow and heat transfer characteristics for a wide range of Rayleigh number (103 ≤ Ra ≤ 107) and Pr = 7 (water). The method used is validated against previous works using classical numerical methods to solve Navier–Stokes and energy equations in similar geometries with a circular heating body. In the conductive and convective regimes, useful correlations for the total Nusselt number are deduced as for the three positions of the heating block.

The Ground Motion of Isosceles Triangular Hill in Right-Angle Plane Impacted by SH-Wave

The analytical solution to the problem of the scattering of SH-wave by isosceles triangular hill in right-angle plane is given by using the methods of complex function and multiple coordinate. Firstly, the solution region is divided into two domains, where domain I involves isosceles triangular hill and a semi-circular bottom, domain II involves a semi-circular hollow in right-angle plane. And a standing wave function is constructed which satisfies the zero-stress conditions at the triangular wedges. In domain II, the scattering wave functions which satisfy the stress free boundary conditions at the free surfaces for the right-angle plane are constructed. Secondly, based on the conditions of the displacement continuity and stress continuity at the “common border” in the domains, a series of infinite algebraic equations are given and solved by truncation. Finally, some examples for amplitude of displacement on the surface are given. Numerical results show that amplitude of displacement on the surface is influenced by isosceles triangular hill.

Laminar Natural Convection in Isosceles Triangular Roofs in Wintertime Conditions

In this work, numerical analysis of steady laminar natural convection in a roof with an isosceles triangular cross section has been performed for wintertime conditions. Base angles varying from 15° to 75°, that is, with corresponding aspect ratios between 0.13 and 1.87, have been used for Rayleigh numbers ranging from 103 to 105. The inclined and the base walls are maintained at cold and hot, respectively, representing the wintertime conditions. To perform the computational analysis, the finite-volume method is used for the discretization of the governing equations. The effects of the Rayleigh number and base angle on the flow field and heat transfer are analyzed. The detailed streamline patterns and temperature distributions are presented. The variation in the average convective Nusselt numbers versus Rayleigh numbers and base angles is given. The present study aims to help designers and builders to select the most suitable isosceles triangular roof base angle from an energy-saving point of view. It is found that roofs having low base angles are not suitable for wintertime conditions because of high heat transfer rates from the isosceles triangular attic space of the building.

Numerical Simulation of Buoyancy- Driven Laminar Flow Through An Air –Filled Isosceles Triangular Enclosure With A Differentially Heated Side Walls And An Adiabatic Bottom Wall

Numerical Simulation of Buoyancy- Driven Laminar Flow Through An Air –Filled Isosceles Triangular Enclosure With A Differentially Heated Side Walls And An Adiabatic Bottom Wall

Numerical Analysis of Natural Buoyancy-Induced Regimes in Isosceles Triangular Cavities

This article deals with a numerical simulation of natural-convection flows using the control-volume finite-element method in isosceles triangular cavities, submitted to a uniform heat flux from below when inclined sides are maintained isothermal, without symmetry assumptions for the flow structure. The aim of the study is to examine a pitchfork bifurcation occurrence. The study provides useful information on the thermal exchange sensitivity to two governing parameters, the Rayleigh number and the tilt angle in a basin still receiving a uniform heat flux. Results show that the heated wall is not isothermal and the flow structure is sensitive to the cover tilt angle. Three regimes with two vortices or more, symmetrical or asymmetrical, can be observed. Results can be constructive for design enhancements in energy systems such as solar water distillers and air conditioning processes.

Novel Multi-frequency and Broad-band Designs of Isosceles Triangular Microstrip Antennas with Five Stubs

This paper presents a novel microstrip patch antenna for three-frequency and broad-band application, consisting of a 120 degree isosceles triangle with five stubs which are loaded at the bottom edge of the triangle. By adjusting lengths of these stubs, the antenna's operating frequency ratios can be tuned, and the three frequencies have the similar broadside radiation characteristics. Moreover, it is found that two separate resonate frequencies can be connected to increase bandwidth of the proposed antenna.

Backscattering from Isosceles Triangular Metallic Plates

The Geometrical Theory of Diffraction is used to describe backscattering from a triangular plate illuminated with vertical polarization. RCS predictions based upon single diffraction are compared with numerical results from the Method of Moments for conducting plates between 2 and 14 wavelengths in dimension. Results are presented for plates having form factor (ratio of height-to-width) of two or greater. The asymptotic theory provides an excellent match at all aspects except approaching grazing incidence on the rear, where multiple diffraction plays an important role.

Free Convective Mass Transfer at Isosceles Triangular Surfaces of Varying Inclination

The limiting diffusion current technique was used for investigation of free convective mass transfer at down-pointing up-facing isosceles triangular surfaces of varying length and inclination. As the mass transfer process, copper deposition from acidified copper(II) sulfate solution was used. It was found that the mass transfer rate increases with inclination from the vertical to the horizontal position and decreases with length of inclined surface. Correlation equations for 7 angles from 0 to 90° were found. The exponent in the ShL-RaL correlation ranged from 0.247 for the vertical case, indicating laminar flow, to 0.32 for inclinations of 60 to 90°, indicating mixed or turbulent flow. The general correlation ShL = 0.358(RaL sin θ)0.30 for the RaL sin θ range from 7 × 106 to 2 × 1011 and inclination range from 15 to 90° was obtained.

Fully Developed Laminar Fluid Flow in a Rotating Isothermal Isosceles Triangular Channel

Fully Developed Laminar Fluid Flow in a Rotating Isothermal Isosceles Triangular Channel

Fully Developed Laminar Fluid Flow in a Rotating Isothermal Isosceles Triangular Channel

This article has no abstract.

Laminar Natural Convection in Isosceles Triangular Enclosures Heated From Below and Symmetrically Cooled From Above

A numerical study of natural convection in an isosceles triangular enclosure with a heated horizontal base and cooled upper walls is presented. Nearly every previous study conducted on this subject to date has assumed that the geometric plane of symmetry is also a plane of symmetry for the flow. This problem is re-examined over aspect ratios ranging from 0.2 to 1.0 and Grashof numbers from 103 to 105. It is found that a pitchfork bifurcation occurs at a critical Grashof number for each of the aspect ratios considered, above which the symmetric solutions are unstable to finite perturbations and asymmetric solutions are instead obtained. Results are presented detailing the occurrence of the pitchfork bifurcation in each of the aspect ratios considered, and the resulting flow patterns are described. A flow visualization study is used to validate the numerical observations. Computed local and mean heat transfer coefficients are also presented and compared with results obtained when flow symmetry is assumed. Differences in local values of the Nusselt number between asymmetric and symmetric solutions are found to be more than 500 percent due to the shifting of the buoyancy-driven cells. [S0022-1481(00)02503-2]

Laminar Fully Developed Momentum and Heat Transfer of Air With Variable Physical Properties in Isosceles Triangular Ducts

Article Laminar Fully Developed Momentum and Heat Transfer of Air With Variable Physical Properties in Isosceles Triangular Ducts was published on September 1, 1993 in the journal International Journal of Turbo & Jet-Engines (volume 10, issue 3).

Analysis of The Gravity Effect of A Two-dimensional Inverted Isosceles Triangular Prism Using Fourier Transforms

The gravity effect of an infinite horizontal inverted isosceles triangular prism has been derived. The Fourier Transform of its gravity effect has been obtained and the Fourier spectrum has been analysed to yield the following parameters: depth to the top of the body, depth to the bottom, width of the body, inclination of the sides and the density contrast between the body and the surrounding rocks. The method has been tested on synthetic models and the validity of the procedure has been thus established.

The Unrestricted Hartree-Fock Theory of Chemical Reactions. V: The Reaction of Three Hydrogens in Isosceles Triangular Conformations

A UHF theoretical analysis is carried out for the reaction of three hydrogens in iso­ sceles triangular conformations. It is shown that the UHF ground state of the H 8 system consists of· three different phases; an RHF configuration in a region of acute triangles, an ASDW configuration in a region of flat triangles and a TSDW configuration iri a region near equilateral triangles. The potentials of the UHF states are calculated and their interconnection relation is studied. A configurational analysis in terms of the RHF orbitals is carried out for the UHF states at equilateral triangles. It is shown that the TSDW state is a good approximation to ·the full CI ground state. The reason for the missing of the Jahn-Teller cusp in the UHF ground state potential is discussed. Importance of spin flipping instabilities in mechanistic characterization of radical reactions is pointed out. In previous papers,n-5> we have carried out unrestricted Hartree-Fock (UHF) theoretical analyses of the chemical reactions in singlet ground state. We consider, in this paper, the three hydrogen system with isosceles triangular conformations as one of the simplest model system for insertion reactions of free radicals. We show from an analysis of the H 3 system that instability of a ground state configu­ ration and appearance of a new ground state of broken symmetry character are phenomena which may occur not only in the reacting systems with a singlet ground state but also in the systems with a doublet ground state, i.e., in free radical reactions. The UHF ground state of the H 3 system undergoes phase transitions between a restricted Hartree-Fock (RHF), an axial spin density wave (ASDW) and a torsional spin density wave (TSDW) configurations, indicating the presence of a hierarchy of doublet radicals with electronic structures of increas­ ing complexities as in singlet radicals discussed previously.5> A configurational analysis is carried out for the ASDW and the TSDW states at equilateral triangles in order to clarify the nature of the electronic correlation effects incorporated into the UHF states. The reason for the missing of the Jahn-Teller cusp6> in the UHF ground state

Transitional Flow in Isosceles Triangular Ducts

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTTransitional Flow in Isosceles Triangular DuctsRichard C. Cope and Richard W. HanksCite this: Ind. Eng. Chem. Fundamen. 1972, 11, 1, 106–117Publication Date (Print):February 1, 1972Publication History Published online1 May 2002Published inissue 1 February 1972https://doi.org/10.1021/i160041a016RIGHTS & PERMISSIONSArticle Views301Altmetric-Citations5LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (5 MB) Get e-Alerts

Laminar Heat Transfer and Pressure Drop in Isosceles Triangular, Right Triangular, and Circular Sector Ducts

Laminar Heat Transfer and Pressure Drop in Isosceles Triangular, Right Triangular, and Circular Sector Ducts

Torsion of Bars With Isosceles Triangular and Diamond Sections

Torsional problems of prismatical bars with cross sections in the shape of isosceles triangles and diamonds are solved by means of a stress function used previously by Saint-Venant for a circular sector. Complete information on the magnitude and location of the maximum shearing stress and on the twisting moment is presented.

Vibration of Isosceles Triangular Plates having the Base Clamped and Other Edges Simply-Supported

SummaryApproximate solutions are given for the lowest natural frequency of flexural vibration of isosceles triangular plates which have the equal edges simply-supported and the base clamped. The results are presented graphically to allow rapid determination of a desired fundamental frequency.

Buckling and Vibration of Isosceles Triangular Plates having the Two Equal Edges Clamped and the Other Edge Simply–Supported

Approximate Solutions obtained by the method of collocation are presented for the lowest critical buckling load of an isosceles triangular plate loaded as shown in Fig. 1. Also, the fundamental frequency is given. The base of the triangle is simply supported and the other equal edges are clamped. The usual assumptions regarding the bending of thin plates are made. The governing differential equation for the plate loaded as shown in Fig. 1 is1whereDis the plate stiffness,Nis axial load per unit length,wis deflection, positive downward, and the quantitiesaandhare dimensions shown in Fig.1.