scholarly journals Stationary temperature field in multi-layered rods with discontinuous of cross section width

Vestnik MGSU ◽  
2019 ◽  
pp. 12-21
Author(s):  
Andrey V. Mishchenko
Keyword(s):  
Temperature Field ◽  
Heat Flow ◽  
Cross Section ◽  
Fourier Method ◽  
Temperature Fields ◽  
Correction Function ◽  
Two Dimensional ◽  
Stationary Temperature Field ◽  
Nonlinear Distortions ◽  
The Cross

Introduction. Presents a method for modeling a two-dimensional stationary temperature field in a layered rod. The peculiarity of the structure of the rod is the presence of discontinuity of the width of the cross section in the direction of heat flow and multilayer. Identification of the temperature field in such rods is a necessary step in solving the problem of thermoelasticity. The relevance of the problem lies in the development of analytical methods for analysis layered rods of complex geometric shape with thermal effects, with acceptable computational complexity and necessary accuracy. Materials and methods. For a multilayer rod, a method for constructing an approximate solution of the Dirichlet stationary heat conduction problem with a transverse heat flow direction is considered. Within each layer, the temperature distribution function is represented as a sum of two functions. The first function, linear in the direction of the heat flow, reflects the exact solution of the problem for a rectangular layered section. The second function is the correction nonlinear function of two variables. It describes the nonlinear distortions of the temperature field due to the presence of discontinuities in the width of the cross section. The correction function, according to the Fourier method, is represented as a product of a given coordinate function and the sum of the sought amplitudes caused by the width breaks. The functions of the effect of breaking the width on temperature fields in adjacent layers are introduced. An approximate formulation of the Dirichlet problem with integral conjugation conditions on interlayer boundaries is formulated. Results. The parameters of the stationary temperature field were calculated for a seven-layer section of a T-shaped form with alternating layers of carbon and steel. Testing the results of the Ansys program showed good qualitative and quantitative correspondence of two-dimensional temperature fields. Conclusions. The obtained solution satisfactorily describes the temperature field in the cross section of a layered rod in the vicinity of its geometric features. The method is characterized by acceptable laboriousness and accuracy suitable for solving the problem of thermoelasticity of a layered rod.

Temperature field evaluation of a two-dimensional partial heat flow problem through Green's Functions

2019 ◽  
Author(s):  
Guilherme Ramalho Costa ◽  
José Aguiar santos junior ◽  
José Ricardo Ferreira Oliveira ◽  
Jefferson Gomes do Nascimento ◽  
Gilmar Guimaraes
Keyword(s):  
Temperature Field ◽  
Heat Flow ◽  
Green's Functions ◽  
Flow Problem ◽  
Green’S Functions ◽  
Field Evaluation ◽  
Two Dimensional

scholarly journals Thermal conductivity of sandstones from Biot’s coefficient

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. D173-D185 ◽  
Author(s):  
Tobias Orlander ◽  
Eirini Adamopoulou ◽  
Janus Jerver Asmussen ◽  
Adam Andrzej Marczyński ◽  
Harald Milsch ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Flow ◽  
Cross Section ◽  
Geometric Mean ◽  
Well Log ◽  
Biot’S Coefficient ◽  
Model Predictions ◽  
The Cross ◽  
Rock Texture

Thermal conductivity of rocks is typically measured on core samples and cannot be directly measured from logs. We have developed a method to estimate thermal conductivity from logging data, where the key parameter is rock elasticity. This will be relevant for the subsurface industry. Present models for thermal conductivity are typically based primarily on porosity and are limited by inherent constraints and inadequate characterization of the rock texture and can therefore be inaccurate. Provided known or estimated mineralogy, we have developed a theoretical model for prediction of thermal conductivity with application to sandstones. Input parameters are derived from standard logging campaigns through conventional log interpretation. The model is formulated from a simplified rock cube enclosed in a unit volume, where a 1D heat flow passes through constituents in three parallel heat paths: solid, fluid, and solid-fluid in series. The cross section of each path perpendicular to the heat flow represents the rock texture: (1) The cross section with heat transfer through the solid alone is limited by grain contacts, and it is equal to the area governing the material stiffness and quantified through Biot’s coefficient. (2) The cross section with heat transfer through the fluid alone is equal to the area governing fluid flow in the same direction and quantified by a factor analogous to Kozeny’s factor for permeability. (3) The residual cross section involves the residual constituents in the solid-fluid heat path. By using laboratory data for outcrop sandstones and well-log data from a Triassic sandstone formation in Denmark, we compared measured thermal conductivity with our model predictions as well as to the more conventional porosity-based geometric mean. For outcrop material, we find good agreement with model predictions from our work and with the geometric mean, whereas when using well-log data, our model predictions indicate better agreement.

ACOUSTIC BAND GAPS TUNED BY TRANSLATION GROUP SYMMETRY IN TWO-DIMENSIONAL PERIODIC COMPOSITES

2009 ◽  
Vol 23 (13) ◽  
pp. 1687-1694 ◽  
Author(s):  
ZHONGFEI MU ◽  
FUGEN WU
Keyword(s):  
Cross Section ◽  
Band Gaps ◽  
Group Symmetry ◽  
Two Dimensional ◽  
Translation Group ◽  
Plane Wave Expansion ◽  
Periodic Arrays ◽  
Periodic Composites ◽  
Super Cell ◽  
The Cross

The acoustic band structures of two kinds of acoustic crystals (two-dimensional periodic arrays of rigid solid rods embedded in air with two different configurations) have been studied by the plane-wave expansion (PWE) method based on super cell calculation. The translation group symmetry of the acoustic crystal is changed by changing the area of the cross section of adjacent rods. We found that by changing the translation group symmetry, one can effectively adjust the acoustic band gaps (ABGs). In the case that the cross section of scattering rods is square without any rotation, the decrease of translation group symmetry is advantaged to form ABGs. But when the cross section of scattering rods is square with a rotation of 45°, the decrease of translation group symmetry is disadvantaged to form ABGs.

Numerical Simulation on Temperature Field of CFST Member under Solar Radiation

2011 ◽  
Vol 354-355 ◽  
pp. 1241-1244
Author(s):  
Yan He ◽  
Man Ding ◽  
Qian Zhang
Keyword(s):  
Numerical Simulation ◽  
Temperature Field ◽  
Temperature Distribution ◽  
Solar Radiation ◽  
Cross Section ◽  
Temperature Difference ◽  
Steel Tube ◽  
Concrete Filled Steel Tube ◽  
Nonlinear Temperature ◽  
The Cross

In this paper the temperature field of Concrete Filled Steel Tube (CFST) member under solar radiation is simulated. The results show that temperature distribution caused by solar radiation is nonlinear over the cross-section of CFST member, and it is significantly varied with time and sections, the largest nonlinear temperature difference is over 26.3°C.

scholarly journals Diffusive skin effect and topological heat funneling

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Pei-Chao Cao ◽  
Ying Li ◽  
Yu-Gui Peng ◽  
Minghong Qi ◽  
Wen-Xi Huang ◽  
...  
Keyword(s):  
Temperature Field ◽  
Robust Control ◽  
Heat Flow ◽  
Skin Effect ◽  
Temperature Fields ◽  
Wave System ◽  
The Past ◽  
Gain Loss ◽  
Diffusive System ◽  
Diffusive Systems

AbstractNon-Hermitian wave system has attracted intense attentions in the past decade since it reveals interesting physics and generates various counterintuitive effects. However, in the diffusive system that is inherently non-Hermitian with natural dissipation, the robust control of heat flow is hitherto still a challenge. Here we introduce the skin effect into diffusive systems. Different from the skin effect in wave systems, where asymmetric couplings were enabled by dynamic modulations or judicious gain/loss engineering, asymmetric couplings of the temperature fields in diffusive systems can be realized by directly contacted metamaterial channels. Topological heat funneling is further presented, where the temperature field automatically concentrates towards a designated position and shows a strong immunity against the defects. Our work indicates that the diffusive system can provide a distinctive platform for exploring non-Hermitian physics as well as thermal topology.

New Pseudo Functions To Control Numerical Dispersion

1975 ◽  
Vol 15 (04) ◽  
pp. 269-276 ◽  
Author(s):  
J.R. Kyte ◽  
D.W. Berry
Keyword(s):  
Capillary Pressure ◽  
Cross Section ◽  
Three Dimensional ◽  
Vertical Cross Section ◽  
Numerical Dispersion ◽  
Two Dimensional ◽  
Cross Sectional ◽  
One Dimensional ◽  
Sectional Model ◽  
The Cross

Abstract This paper presents an improved procedure for calculating dynamic pseudo junctions that may be used in two-dimensional, areal reservoir simulations to approximate three-dimensional reservoir behavior. Comparison of one-dimensional areal and two-dimensional vertical cross-sectional results for two example problems shows that the new pseudos accurately transfer problems shows that the new pseudos accurately transfer the effects of vertical variations in reservoir properties, fluid pressures, and saturations from the properties, fluid pressures, and saturations from the cross-sectional model to the areal model. The procedure for calculating dynamic pseudo-relative permeability accounts for differences in computing block lengths between the areal and cross-sectional models. Dynamic pseudo-capillary pressure transfers the effects of pseudo-capillary pressure transfers the effects of different pressure gradients in different layers of the cross-sectional model to the areal model. Introduction Jacks et al. have published procedures for calculating dynamic pseudo-relative permeabilities fro m vertical cross-section model runs. Their procedures for calculating pseudo functions are procedures for calculating pseudo functions are more widely applicable than other published approaches. They demonstrated that, in some cases, the derived pseudo functions could be used to simulate three-dimensional reservoir behavior using two-dimensional areal simulators. For our purposes, an areal simulator is characterized by purposes, an areal simulator is characterized by having only one computing block in the vertical dimension. The objectives of this paper are to present an improved procedure for calculating dynamic pseudo functions, including a dynamic pseudo-capillary pressure, and to demonstrate that the new procedure pressure, and to demonstrate that the new procedure generally is more applicable than any of the previously published approaches. The new pseudos previously published approaches. The new pseudos are similar to those derived by jacks et al. in that they are calculated from two-dimensional, vertical cross-section runs. They differ because (1) they account for differences in computing block lengths between the cross-sectional and areal models, and (2) they transfer the effects of different flow potentials in different layers of the cross-sectional potentials in different layers of the cross-sectional model to the areal model. Differences between cross-sectional and areal model block lengths are sometimes desirable to reduce data handling and computing costs for two-dimensional, areal model runs. For very large reservoirs, even when vertical calculations are eliminated by using pseudo functions, as many as 50,000 computing blocks might be required in the two-dimensional areal model to minimize important errors caused by numerical dispersion. The new pseudos, of course, cannot control numerical pseudos, of course, cannot control numerical dispersion in the cross-sectional runs. This is done by using a sufficiently large number of computing blocks along die length of the cross-section. The new pseudos then insure that no additional dispersion will occur in the areal model, regardless of the areal computing block lengths. Using this approach, the number of computing blocks in the two-dimensional areal model is reduced by a factor equal to the square of the ratio of the block lengths for the cross-sectional and areal models. The new pseudos do not prevent some loss in areal flow-pattern definition when the number of computing blocks in the two-dimensional areal model is reduced. A study of this problem and associated errors is beyond the scope of this paper. Our experience suggests that, for very large reservoirs with flank water injection, 1,000 or 2,000 blocks provide satisfactory definition. Many more blocks provide satisfactory definition. Many more blocks might be required for large reservoirs with much more intricate areal flow patterns. The next section presents comparative results for cross-sectional and one-dimensional areal models. These results demonstrate the reliability of the new pseudo functions and illustrate their advantages pseudo functions and illustrate their advantages over previously derived pseudos for certain situations. The relationship between two-dimensional, vertical cross-sectional and one-dimensional areal reservoir simulators has been published previously and will not be repeated here in any detail. Ideally, the pseudo functions should reproduce two-dimensional, vertical cross-sectional results when they are used in the corresponding one-dimensional areal model. SPEJ P. 269

scholarly journals Two-dimensional strain fields on the cross-section of the bovine humeral head under contact loading

2008 ◽  
Vol 41 (15) ◽  
pp. 3145-3151 ◽  
Author(s):  
Clare E. Canal ◽  
Clark T. Hung ◽  
Gerard A. Ateshian
Keyword(s):  
Cross Section ◽  
Humeral Head ◽  
Two Dimensional ◽  
Strain Fields ◽  
Contact Loading ◽  
The Cross

An Experimental Investigation of the Permeability in Porous Chip Formed by Micropost Arrays Based on Microparticle Image Velocimetry and Micromanometer Measurements

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Haoli Wang ◽  
Pengwei Wang
Keyword(s):  
Cross Section ◽  
Particle Image ◽  
Brinkman Equation ◽  
Two Dimensional ◽  
Micro Particle Image Velocimetry ◽  
Micro Piv ◽  
Image Velocimetry ◽  
Measurement Results ◽  
Microparticle Image Velocimetry ◽  
The Cross

Measurements of velocity and pressure differences for flows in porous chip fabricated with micropost arrays arranged in square pattern were implemented by using micro-particle image velocimetry (micro-PIV) and high precision micromanometer. Based on the measurement results, the permeability was solved by Brinkman equation under the averaged velocities over the cross section, two-dimensional velocities on the center plane of the microchannels, and the averaged velocities on the center plane considering the effect of depth of correlation (DOC), respectively. The experimental results indicate that the nondimensional permeability based on different velocities satisfies the Kozeny–Carman (KC) equation. The Kozeny factor is taken as 40 for the averaged velocity over the cross section and 15 for two kinds of center velocities based on the micropost array of this study, respectively. The permeability calculated by the velocities on the center plane is greater than that by the averaged velocity over the cross section.

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