scholarly journals An Eigenvalues Approach for a Two-Dimensional Porous Medium Based Upon Weak, Normal and Strong Thermal Conductivities

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 848
Author(s):  
Faris Alzahrani ◽  
Aatef Hobiny ◽  
Ibrahim Abbas ◽  
Marin Marin
Keyword(s):  
Porous Medium ◽  
Porous Material ◽  
Volume Fraction ◽  
Numerical Results ◽  
Two Dimensional ◽  
Temperature Stresses ◽  
Symmetric Geometry ◽  
Thermal Conductivities

This work is devoted to the investigation of a two-dimensional porous material under weak, strong and normal conductivity, using the eigenvalues method. By using Laplace–Fourier transformations with the eigenvalues technique, the variables are analytically obtained. The derived technique is assessed with numerical results that are obtained from the porous mediums using simplified symmetric geometry. The results, including the displacements, temperature, stresses and the change in the volume fraction field, are offered graphically. Comparisons are made among the outcomes obtained under weak, normal and strong conductivity.

Generalized thermoelastic interaction in a two-dimensional porous medium under dual phase lag model

2020 ◽  
Vol 30 (11) ◽  
pp. 4865-4881 ◽  
Author(s):  
Aatef Hobiny ◽  
Ibrahim Abbas
Keyword(s):  
Porous Medium ◽  
Volume Fraction ◽  
Phase Lag ◽  
Dual Phase ◽  
Two Dimensional ◽  
Thermoelastic Wave ◽  
Content Type ◽  
Lag Model ◽  
The Difference ◽  
Laplace Transformations

Purpose The purpose of this study is to use the generalized model for thermoelastic wave under the dual phase lag (DPL) model to compute the increment of temperature, the components of displacement, the changes in volume fraction field and the stress components in a two-dimensional (2D) porous medium. Design/methodology/approach Using Fourier and Laplace transformations with the eigenvalue technique, the exact solutions of all physical quantities are obtained. Findings The derived method is evaluated with numerical results, which are applied to the porous medium in a simplified geometry. Originality/value Finally, the outcomes are graphically represented to show the difference among the models of classical dynamical coupled, the Lord and Shulman and DPL.

Experimental Study of Turbulent Flow in Two-Dimensional Porous Media

2009 ◽  
Author(s):  
Sintia Bejatovic ◽  
Martin Agelinchaab ◽  
Mark F. Tachie
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Turbulent Flow ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Channel Height ◽  
Two Dimensional ◽  
Clear Fluid ◽  
Test Channel ◽  
Flow Through

The paper reports on an experimental investigation of turbulent flow through model two-dimensional porous media. The porous media was bounded on one side by a solid plane wall and on the other side by a zone of clear fluid. The model porous media comprised of square arrays of circular acrylic rods that were inserted into precision holes drilled onto pairs of removable plates. The removable plates were then inserted into groves made in the side walls of the test channel. The rods fill about 59% of the channel height. Different combinations of rod diameter and center-to-center spacing were used to produce solid volume fractions that ranged from 0.11 to 0.44. The Reynolds number based on the bulk velocity of the approach flow and channel height was 16800. A high resolution particle image velocimetry (PIV) system was used to conduct detailed velocity measurements within the porous media and the adjacent clear fluid. The results demonstrate that permeability of the porous medium is more useful in correlating the flow characteristics than the porosity or solid volume fraction. Irrespective of rod diameter or spacing, a decrease in permeability of the porous medium produced a lower value of the dimensionless slip velocity. A decrease in permeability also produced higher resistance to the fluid flow through the porous medium. As a result, a larger fraction of the approach flow is channeled through the clear zone adjacent to a porous medium with lower permeability than those with relatively higher permeability. It was also observed that spatially averaged profiles of the mean velocities and turbulent quantities depend strongly on permeability.

Instrumentation For Quantitative Microscopy

1977 ◽  
Vol 35 ◽  
pp. 206-209
Author(s):  
B. Ralph ◽  
A.R. Jones
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Automatic Data ◽  
Phase Volume Fraction ◽  
Statistical Confidence ◽  
Resultant Data ◽  
Automatic Data Collection ◽  
Third Dimension ◽  
Evolution Of Microstructure

In all fields of microscopy there is an increasing interest in the quantification of microstructure. This interest may stem from a desire to establish quality control parameters or may have a more fundamental requirement involving the derivation of parameters which partially or completely define the three dimensional nature of the microstructure. This latter categorey of study may arise from an interest in the evolution of microstructure or from a desire to generate detailed property/microstructure relationships. In the more fundamental studies some convolution of two-dimensional data into the third dimension (stereological analysis) will be necessary.In some cases the two-dimensional data may be acquired relatively easily without recourse to automatic data collection and further, it may prove possible to perform the data reduction and analysis relatively easily. In such cases the only recourse to machines may well be in establishing the statistical confidence of the resultant data. Such relatively straightforward studies tend to result from acquiring data on the whole assemblage of features making up the microstructure. In this field data mode, when parameters such as phase volume fraction, mean size etc. are sought, the main case for resorting to automation is in order to perform repetitive analyses since each analysis is relatively easily performed.

Analysis of two-dimensional solute transport through heterogeneous porous medium

2018 ◽  
Vol 2 (3) ◽  
Author(s):  
Atul Kumar ◽  
◽  
Lav Kush Kumar ◽  
Shireen Shireen ◽  
◽  
...  
Keyword(s):  
Porous Medium ◽  
Solute Transport ◽  
Two Dimensional ◽  
Heterogeneous Porous Medium

scholarly journals Onset of Convection in Two-Dimensional Porous Cavities with Open and Conducting Boundaries

2021 ◽  
Vol 136 (3) ◽  
pp. 791-812
Author(s):  
Peder A. Tyvand ◽  
Jonas Kristiansen Nøland
Keyword(s):  
Critical Rayleigh Number ◽  
Numerical Results ◽  
Temperature Perturbation ◽  
Two Dimensional ◽  
Onset Of Convection ◽  
Order Problem ◽  
Fourth Order Problem ◽  
Thermally Conducting ◽  
Perturbation Pressure ◽  
Special Case

AbstractThe onset of thermal convection in two-dimensional porous cavities heated from below is studied theoretically. An open (constant-pressure) boundary is assumed, with zero perturbation temperature (thermally conducting). The resulting eigenvalue problem is a full fourth-order problem without degeneracies. Numerical results are presented for rectangular and elliptical cavities, with the circle as a special case. The analytical solution for an upright rectangle confirms the numerical results. Streamlines penetrating the open cavities are plotted, together with the isotherms for the associated closed thermal cells. Isobars forming pressure cells are depicted for the perturbation pressure. The critical Rayleigh number is calculated as a function of geometric parameters, including the tilt angle of the rectangle and ellipse. An improved physical scaling of the Darcy–Bénard problem is suggested. Its significance is indicated by the ratio of maximal vertical velocity to maximal temperature perturbation.

Numerical Analysis of Two-Phase Pipe Flow of Liquid Helium Using Multi-Fluid Model

2001 ◽  
Vol 123 (4) ◽  
pp. 811-818 ◽  
Author(s):  
Jun Ishimoto ◽  
Mamoru Oike ◽  
Kenjiro Kamijo
Keyword(s):  
Phase Transition ◽  
Gas Phase ◽  
Liquid Helium ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Numerical Results ◽  
Phase Flow ◽  
Two Dimensional ◽  
Two Phase ◽  
Normal Fluid

The two-dimensional characteristics of the vapor-liquid two-phase flow of liquid helium in a pipe are numerically investigated to realize the further development and high performance of new cryogenic engineering applications. First, the governing equations of the two-phase flow of liquid helium based on the unsteady thermal nonequilibrium multi-fluid model are presented and several flow characteristics are numerically calculated, taking into account the effect of superfluidity. Based on the numerical results, the two-dimensional structure of the two-phase flow of liquid helium is shown in detail, and it is also found that the phase transition of the normal fluid to the superfluid and the generation of superfluid counterflow against normal fluid flow are conspicuous in the large gas phase volume fraction region where the liquid to gas phase change actively occurs. Furthermore, it is clarified that the mechanism of the He I to He II phase transition caused by the temperature decrease is due to the deprivation of latent heat for vaporization from the liquid phase. According to these theoretical results, the fundamental characteristics of the cryogenic two-phase flow are predicted. The numerical results obtained should contribute to the realization of advanced cryogenic industrial applications.

Calculation of two-dimensional dispersion in a gas in unsteady flow in a porous medium

1983 ◽  
Vol 17 (5) ◽  
pp. 704-710
Author(s):  
E. G. Basanskii ◽  
V. M. Kolobashkin ◽  
N. A. Kudryashov
Keyword(s):  
Porous Medium ◽  
Unsteady Flow ◽  
Two Dimensional

scholarly journals An effective thermal conductivity and thermomechanical homogenization scheme for a multiscale Nb3Sn filaments

2021 ◽  
Vol 10 (1) ◽  
pp. 187-200
Author(s):  
Xiaoyu Zhao ◽  
Guannan Wang ◽  
Qiang Chen ◽  
Libin Duan ◽  
Wenqiong Tu
Keyword(s):  
Volume Fraction ◽  
Material Design ◽  
Axial Direction ◽  
High Heat ◽  
Thermomechanical Properties ◽  
Homogenization Theory ◽  
High Heat Flux ◽  
Element Analysis ◽  
Hierarchical Microstructure ◽  
Thermal Conductivities

Abstract A comprehensive study of the multiscale homogenized thermal conductivities and thermomechanical properties is conducted towards the filament groups of European Advanced Superconductors (EAS) strand via the recently proposed Multiphysics Locally Exact Homogenization Theory (LEHT). The filament groups have a distinctive two-level hierarchical microstructure with a repeating pattern perpendicular to the axial direction of Nb3Sn filament. The Nb3Sn filaments are processed in a very high temperature between 600 and 700°C, while its operation temperature is extremely low, −269°C. Meanwhile, Nb3Sn may experience high heat flux due to low resistivity of Nb3Sn in the normal state. The intrinsic hierarchical microstructure of Nb3Sn filament groups and Multiphysics loading conditions make LEHT an ideal candidate to conduct the homogenized thermal conductivities and thermomechanical analysis. First, a comparison with a finite element analysis is conducted to validate effectiveness of Multiphysics LEHT and good agreement is obtained for the homogenized thermal conductivities and mechanical and thermal expansion properties. Then, the Multiphysics LEHT is applied to systematically investigate the effects of volume fraction and temperature on homogenized thermal conductivities and thermomechanical properties of Nb3Sn filaments at the microscale and mesoscale. Those homogenized properties provide a full picture for researchers or engineers to understand the Nb3Sn homogenized properties and will further facilitate the material design and application.

Free vibration analysis of three-layer thin cylindrical shell with variable thickness two-dimensional FGM middle layer under arbitrary boundary conditions

2021 ◽  
pp. 109963622110204
Author(s):  
Xue-Yang Miao ◽  
Chao-Feng Li ◽  
Yu-Lin Jiang ◽  
Zi-Xuan Zhang
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Volume Fraction ◽  
Ritz Method ◽  
Admissible Function ◽  
Free Vibration Analysis ◽  
Middle Layer ◽  
Two Dimensional ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions

In this paper, a unified method is developed to analyze free vibrations of the three-layer functionally graded cylindrical shell with non-uniform thickness. The middle layer is composed of two-dimensional functionally gradient materials (2D-FGMs), whose thickness is set as a function of smooth continuity. Four sets of artificial springs are assigned at the ends of the shells to satisfy the arbitrary boundary conditions. The Sanders’ shell theory is used to obtain the strain and curvature-displacement relations. Furthermore, the Chebyshev polynomials are selected as the admissible function to improve computational efficiency, and the equation of motion is derived by the Rayleigh–Ritz method. The effects of spring stiffness, volume fraction indexes, configuration on of shell, and the change in thickness of the middle layer on the modal characteristics of the new structural shell are also analyzed.

Sign in / Sign up

Export Citation Format

Share Document