Conduction in Rings With Internal Heat Generation

2021 ◽  
Vol 143 (5) ◽  
Author(s):  
C. Y. Wang

Abstract The basic problem of steady-state heat conduction in a ring with internal heat generation and convective boundary conditions is considered. An exact solution is found for the ring with a rectangular cross section and an efficient Ritz method is presented for general cross sections. The latter is applied to the torus or the ring with a circular cross section. Hot spots and cold spots are determined.

2021 ◽  
Vol 11 (5) ◽  
pp. 159-170
Author(s):  
Zsolt Hegyes ◽  
Máté Petrik ◽  
L. Gábor Szepesi

During the operation of the hydrocyclone the cut size diameter is the most important data. This is connected to feed rate, which is closely related to the feed cross section. Preliminary research has revealed that square cross-section is more effective than circular cross-section. The research compared 2 types of feed cross sections at 5 different feed rates. One is a standard rectangular cross-section and the other is a square cross-section that narrows with a baffle plate. Preliminary calculations for cut size diameter have shown that better particle separation at all speeds can be achieved with the baffle plate solution. In both types, the increased velocity created decreased cut size diameter. During the simulation, the baffle plate did not cause any abnormalities in the internal pressure and velocity distributions. The simulation revealed that the particles did not behave as previously calculated.


2009 ◽  
Vol 15 (1) ◽  
pp. 21-33 ◽  
Author(s):  
Artiomas Kuranovas ◽  
Douglas Goode ◽  
Audronis Kazimieras Kvedaras ◽  
Shantong Zhong

This paper represents the analysis of 1303 specimens of CFST experimental data. Test results are compared with EC4 provided method for determining the load‐bearing capacity of these composite elements. Several types of CFSTs were tested: both circular and rectangular cross‐sections with solid and hollow concrete core with axial load applied without and with moment, with sustained load and preloading. For circular cross‐section columns there is a good agreement between the test failure load and the EC4 calculation for both short and long columns with and without moment. For rectangular cross‐section columns the agreement is good except when the concrete cylinder strength was greater than 75 MPa, when many tests failed below the strength predicted by EC4. Preloading the steel tube before filling with concrete seems to have no effect on the strength. This paper also presents the stress distribution, confinement distribution and complete average longitudinal stress‐strain curves for concrete‐filled steel tubular elements. Based on the definition of the “Unified Theory”, the CFST is looked upon as an entity of a new composite material. In this paper, the research achievement of the strength and stability for centrifugal‐hollow and solid concrete filled steel tube are introduced. These behaviours relate to the hollowness ratio and the confining indexes of corresponding solid CFST. If the hollow ratio equals to 0,4–0,5 and over, the N‐ϵ relationship exists in steady descending stage. The critical stress of CFST elements stability is determined as an eccentric member with the initial eccentricity by use of finite element method. Santrauka Straipsnyje analizuojami 1303 betonšerdžių plieninių strypų bandinių eksperimentiniai duomenys. Duomenys lyginami su eurokode 4 pateiktais kompozitinių elementų laikomosios galios nustatymo metodais. Analizuojami šie betonšerdžių plieninių strypų bandinių tipai: pilnaviduriai ir tuščiaviduriai, apskrito ir stačiakampio skerspjūvio kolonos, kurių galuose veikia arba neveikia momentas, su iš anksto pridėta arba ilgalaike apkrova. Apskrito skerspjūvio kolonų laikomosios galios bandymų rezultatai atitinka skaičiavimų reikšmes, apskaičiuotas pagal eurokode 4 pateiktu metodu. Stačiakampio skerspjūvio elementų laikomosios galios reikšmių bandymo rezultatai puikiai atitinka teorines reikšmes, kai betono ritininis stipris nesiekia 75 MPa. Išankstinis elementų apkrovimas poveikio elementų laikomajai galiai beveik neturi. Taip pat nagrinėjami betonšerdžių elementų įtempių būvių pasiskirstymas, betono apspaudimo poveikis ir išilginių deformacijų ir įtempių kreivės. Pateikiama S. T. Zhong „Unifikuota teorija“, kuri nagrinėja kompozitinį elementą kaip visumą. Straipsnyje nagrinėjamos kompozitinio plieninio ir betoninio elemento stiprumo ir pastovumo sąlygos. Tokių elementų reikšmėmis. Jeigu tuštumos santykis lygus 0,4–0,5 ir daugiau, N-ε sąryšis yra kritimo stadijoje. Elgsenos stadijos keičiasi pagal tuštumos koeficientą.


2010 ◽  
Vol 638-642 ◽  
pp. 1579-1584 ◽  
Author(s):  
A.V. Nagasekhar ◽  
Carlos H. Cáceres ◽  
Mark Easton

Specimens of rectangular and circular cross section of a Mg-9Al binary alloy have been tensile tested and the cross section of undeformed specimens examined using scanning electron microscopy. The rectangular cross sections showed three scales in the cellular intermetallics network: coarse at the core, fine at the surface and very fine at the corners, whereas the circular ones showed only two, coarse at the core and fine at the surface. The specimens of rectangular cross section exhibited higher yield strength in comparison to the circular ones. Possible reasons for the observed increased strength of the rectangular sections are discussed.


2014 ◽  
Vol 621 ◽  
pp. 107-112 ◽  
Author(s):  
Bogdan Szybiński ◽  
Paweł Romanowicz

Cylindrical pressure vessels with circular cross section are commonly used in the construction of various pressure apparatus; however in certain cases other cross sections are applied. The vessels with rectangular and elliptical perpendicular cross section are of the main interest and certain formulas for their calculations are stated in the respective codes [1, 2]. In these appliances flat ends of various shapes are usually used as the vessels caps. Similarly, as for the cylindrical boilers, flat end plates with stress relieve grooves are recommended. Like in the flat ends for cylindrical pipes certain variation of the groove parameters is possible but again no clear suggestion is given how to choose the optimal groove parameters providing the minimum stress concentration [3]. In this paper the numerical analysis and optimization of the admitted by code [1] groove parameters is presented for the pipe with the rectangular cross section subjected to the internal pressure.


2013 ◽  
Vol 17 (3) ◽  
pp. 943-950 ◽  
Author(s):  
Haj El

Analysis of entropy generation in a rectangular slab with a nonuniform internal heat generation is presented. Dimensionless local and total entropy generation during steady state heat conduction through the slab are obtained. Two different boundary conditions have been considered in the analysis, the first with asymmetric convection and the second with constant slab surface temperature. Temperature distribution within the slab is obtained analytically. The study investigates the effect of some relevant dimensionless heat transfer parameters on entropy generation. The results show that there exists a minimum local entropy generation but there does not exist a minimum total entropy generation for certain combinations of the heat transfer parameters. The results of calculations are presented graphically.


2020 ◽  
pp. 235-235
Author(s):  
Zhipeng Duan ◽  
Hao Ma

A representative steady-state heat conduction problem in rectangular solids with uniformly distributed heat generation has been investigated analytically. An analytical solution is provided by solving a nonhomogeneous partial differential equation. A simple and accurate model is proposed to predict the dimensionless shape factor parameter for the first time. The dimensionless shape factor is obtained in the light of the solution of Poisson equation with constant wall temperature boundary conditions. The area-mean temperature is found by integration on the rectangular cross-section. The model is very concise and nice for quick real world approximations, and it provides acceptable accuracy for engineering practice.


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