Injection of Fluid Into a Layer of Deformable Porous Medium

1995 ◽  
Vol 48 (10) ◽  
pp. 722-726 ◽  
Author(s):  
Steven Barry ◽  
Geoffrey Aldis ◽  
Geoffry Mercer
Keyword(s):  
Porous Material ◽  
Point Source ◽  
Elastic Solid ◽  
Hankel Transform ◽  
Solid Matrix ◽  
Governing Equations ◽  
Elastic Parameters ◽  
Subcutaneous Injections ◽  
Deformable Porous Medium ◽  
One Dimensional

The flow of fluid from a point source into a layer of deformable porous material is considered. The main applications of this work are to subcutaneous injections and subterranean soil flows. The porous material is assumed to be an isotropic, homogeneous, linearly elastic solid. The governing equations are derived for an axisymmetric geometry using linear poro-elasticity and are applied to the situation of a point source at some height z = z0 with a line sink at a distance r = ρ. These are solved analytically using Hankel transform techniques with the Hankel inversion integrals calculated numerically. Results are given for the pressure contours and the displacement of the solid matrix for a variety of source heights and elastic parameters. These indicate the swelling of the medium and subsequent deformation of the free surface. Results indicate regions where one dimensional models may be applicable.

Steady Flow in Porous, Elastically Deformable Materials

1987 ◽  
Vol 54 (4) ◽  
pp. 794-800 ◽  
Author(s):  
K. H. Parker ◽  
R. V. Mehta ◽  
C. G. Caro
Keyword(s):  
Fluid Flow ◽  
Theoretical Model ◽  
Porous Material ◽  
Applied Pressure ◽  
Local Strain ◽  
Governing Equations ◽  
Good Qualitative Agreement ◽  
One Dimensional ◽  
The Matrix ◽  
Deformable Materials

The steady, one-dimensional flow of an incompressible fluid through a deformable porous material is studied theoretically and experimentally. The theoretical model is essentially that of Biot. Assuming that the stiffness and permeability of the matrix are functions of the local strain gradient, the governing equations can be solved and analytical solutions are presented for several simple constitutive relationships. The stiffness and permeability properties of one particular foam are measured and then used to predict the rate of fluid flow and the distortion of the matrix as a function of the applied pressure difference across the material. Comparison of the predictions of the model with experimental observations indicates good qualitative agreement.

Wave Propagation in Inhomogeneous Elastic Media with (N + l)-Dimensional Spherical Symmetry

1974 ◽  
Vol 52 (14) ◽  
pp. 1246-1252 ◽  
Author(s):  
D. L. Clements ◽  
C. Rogers
Keyword(s):  
Wave Equation ◽  
Elastic Solid ◽  
Initial Boundary ◽  
Spherically Symmetric ◽  
Initial Boundary Value Problems ◽  
Governing Equations ◽  
Elastic Parameters ◽  
Uniform Loading ◽  
Inhomogeneous Elastic Media ◽  
Initial Boundary Value

Uniform loading of an (N + 1)-dimensional spherically symmetric inhomogeneous elastic solid is investigated. The governing equations are represented in a matrix form and reduction to the conventional wave equation is sought. Such reduction may be achieved for multiparameter forms of a certain function involving the density and elastic parameters of the material. The reduction to the wave equation allows certain initial/boundary value problems to be readily solved.

Design and Research of Flat Micro Heat Pipe with Glass Fiber Wick

2011 ◽  
Vol 483 ◽  
pp. 603-606
Author(s):  
Tian Han ◽  
Xiao Wei Liu ◽  
Chao Wang
Keyword(s):  
Glass Fiber ◽  
Heat Pipe ◽  
Experimental Testing ◽  
Governing Equations ◽  
Maximum Heat ◽  
One Dimensional ◽  
Micro Heat Pipe ◽  
Wick Structure

A kind of flat micro heat pipe with glass fiber wick structure is designed and fabricated. The structure of the wick is presented and also the excellence of the structure is described. For the glass fiber wick, the maximum heat transports is calculated by one-dimensional steady governing equations. Experimental testing is performed for the fabricated micro heat pipe in vacuum. The testing results is presented and analyzed.

scholarly journals A new method for solving a class of heat conduction equations

2015 ◽  
Vol 19 (4) ◽  
pp. 1205-1210
Author(s):  
Yi Tian ◽  
Zai-Zai Yan ◽  
Zhi-Min Hong
Keyword(s):  
Monte Carlo ◽  
Heat Conduction ◽  
Dimensional Space ◽  
Variable Coefficients ◽  
Algebraic Equations ◽  
Governing Equations ◽  
One Dimensional ◽  
Sparse System ◽  
Linear Algebraic Equations ◽  
Crank Nicolson

A numerical method for solving a class of heat conduction equations with variable coefficients in one dimensional space is demonstrated. This method combines the Crank-Nicolson and Monte Carlo methods. Using Crank-Nicolson method, the governing equations are discretized into a large sparse system of linear algebraic equations, which are solved by Monte Carlo method. To illustrate the usefulness of this technique, we apply it to two problems. Numerical results show the performance of the present work.

scholarly journals Mathematical analysis of hydrodynamics and tissue deformation inside an isolated solid tumor

2018 ◽  
Vol 45 (2) ◽  
pp. 253-278 ◽  
Author(s):  
Meraj Alam ◽  
Bibaswan Dey ◽  
Sekhar Raja
Keyword(s):  
Solid Tumor ◽  
Solid Phase ◽  
Fluid Motion ◽  
Extracellular Fluid ◽  
Mixture Theory ◽  
Coupled System ◽  
Weak Sense ◽  
Governing Equations ◽  
One Dimensional ◽  
2D And 3D

In this article, we present a biphasic mixture theory based mathematical model for the hydrodynamics of interstitial fluid motion and mechanical behavior of the solid phase inside a solid tumor. The tumor tissue considered here is an isolated deformable biological medium. The solid phase of the tumor is constituted by vasculature, tumor cells, and extracellular matrix, which are wet by a physiological extracellular fluid. Since the tumor is deformable in nature, the mass and momentum equations for both the phases are presented. The momentum equations are coupled due to the interaction (or drag) force term. These governing equations reduce to a one-way coupled system under the assumption of infinitesimal deformation of the solid phase. The well-posedness of this model is shown in the weak sense by using the inf-sup (Babuska?Brezzi) condition and Lax?Milgram theorem in 2D and 3D. Further, we discuss a one-dimensional spherical symmetry model and present some results on the stress fields and energy of the system based on ??2 and Sobolev norms. We discuss the so-called phenomena of ?necrosis? inside a solid tumor using the energy of the system.

scholarly journals A new class of discontinuous solar wind solutions

2020 ◽  
Vol 496 (2) ◽  
pp. 1023-1034
Author(s):  
Bidzina M Shergelashvili ◽  
Velentin N Melnik ◽  
Grigol Dididze ◽  
Horst Fichtner ◽  
Günter Brenn ◽  
...  
Keyword(s):  
Solar Wind ◽  
External Source ◽  
Analytic Solutions ◽  
Governing Equations ◽  
Discontinuous Solutions ◽  
One Dimensional ◽  
Heating Source ◽  
New Class ◽  
Localized Heating ◽  
Physical Quantities

ABSTRACT A new class of one-dimensional solar wind models is developed within the general polytropic, single-fluid hydrodynamic framework. The particular case of quasi-adiabatic radial expansion with a localized heating source is considered. We consider analytical solutions with continuous Mach number over the entire radial domain while allowing for jumps in the flow velocity, density, and temperature, provided that there exists an external source of energy in the vicinity of the critical point that supports such jumps in physical quantities. This is substantially distinct from both the standard Parker solar wind model and the original nozzle solutions, where such discontinuous solutions are not permissible. We obtain novel sample analytic solutions of the governing equations corresponding to both slow and fast winds.

scholarly journals A Fast-Converging Scheme for the Electromagnetic Scattering from a Thin Dielectric Disk

Electronics ◽  
2020 ◽  
Vol 9 (9) ◽  
pp. 1451
Author(s):  
Mario Lucido ◽  
Mykhaylo V. Balaban ◽  
Sergii Dukhopelnykov ◽  
Alexander I. Nosich
Keyword(s):  
Integral Equations ◽  
Electromagnetic Scattering ◽  
Disk Surface ◽  
Hankel Transform ◽  
Transform Domain ◽  
One Dimensional ◽  
Analytical Technique ◽  
Generalized Boundary Conditions ◽  
Dielectric Disk ◽  
Dimensional Integral

In this paper, the analysis of the electromagnetic scattering from a thin dielectric disk is formulated as two sets of one-dimensional integral equations in the vector Hankel transform domain by taking advantage of the revolution symmetry of the problem and by imposing the generalized boundary conditions on the disk surface. The problem is further simplified by means of Helmholtz decomposition, which allows to introduce new scalar unknows in the spectral domain. Galerkin method with complete sets of orthogonal eigenfunctions of the static parts of the integral operators, reconstructing the physical behavior of the fields, as expansion bases, is applied to discretize the integral equations. The obtained matrix equations are Fredholm second-kind equations whose coefficients are efficiently numerically evaluated by means of a suitable analytical technique. Numerical results and comparisons with the commercial software CST Microwave Studio are provided showing the accuracy and efficiency of the proposed technique.

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