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.

Microwave heating of materials with low conductivity

1991 ◽  
Vol 433 (1889) ◽  
pp. 479-498 ◽  
Keyword(s):  
Wave Equation ◽  
Microwave Heating ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Coupled System ◽  
Damped Wave Equation ◽  
Governing Equations ◽  
One Dimensional ◽  
Approximate Analytical Solutions ◽  
Very High

The microwave heating of a one-dimensional, semi-infinite material with low conductivity is considered. Starting from Maxwell’s equations, it is shown that this heating is governed by a coupled system consisting of the damped wave equation and a forced heat equation with forcing depending on the amplitude squared of the electric field. For simplicity, the conductivity of the material and the speed of microwave radiation in the material are assumed to have power law dependencies on temperature. Approximate analytical solutions of the governing equations are found as a slowly varying wave. These solutions and the slow equations from which they are derived are found to give criteria for when ‘hotspots' (regions of very high temperature relative to their surroundings) can form. The approximate analytical solutions are compared with numerical solutions of the governing equations.

Nonlinear singular one dimensional thermo-elasticity coupled system and double Laplace decomposition methods

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6269-6280
Author(s):  
Hassan Gadain
Keyword(s):  
Laplace Transform ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Coupled System ◽  
Decomposition Methods ◽  
One Dimensional ◽  
Convergence Proof ◽  
Double Laplace Transform ◽  
Adomian Decomposition

In this work, combined double Laplace transform and Adomian decomposition method is presented to solve nonlinear singular one dimensional thermo-elasticity coupled system. Moreover, the convergence proof of the double Laplace transform decomposition method applied to our problem. By using one example, our proposed method is illustrated and the obtained results are confirmed.

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 Flexible parallel implicit modelling of coupled thermal–hydraulic–mechanical processes in fractured rocks

Solid Earth ◽  
2017 ◽  
Vol 8 (5) ◽  
pp. 921-941 ◽  
Author(s):  
Mauro Cacace ◽  
Antoine B. Jacquey
Keyword(s):  
Groundwater Flow ◽  
Fractured Rocks ◽  
Object Oriented ◽  
Coupled System ◽  
Weak Sense ◽  
Rock Properties ◽  
Solid Matrix ◽  
Scaling Parameters ◽  
Active Processes ◽  
Element Technique

Abstract. Theory and numerical implementation describing groundwater flow and the transport of heat and solute mass in fully saturated fractured rocks with elasto-plastic mechanical feedbacks are developed. In our formulation, fractures are considered as being of lower dimension than the hosting deformable porous rock and we consider their hydraulic and mechanical apertures as scaling parameters to ensure continuous exchange of fluid mass and energy within the fracture–solid matrix system. The coupled system of equations is implemented in a new simulator code that makes use of a Galerkin finite-element technique. The code builds on a flexible, object-oriented numerical framework (MOOSE, Multiphysics Object Oriented Simulation Environment) which provides an extensive scalable parallel and implicit coupling to solve for the multiphysics problem. The governing equations of groundwater flow, heat and mass transport, and rock deformation are solved in a weak sense (either by classical Newton–Raphson or by free Jacobian inexact Newton–Krylow schemes) on an underlying unstructured mesh. Nonlinear feedbacks among the active processes are enforced by considering evolving fluid and rock properties depending on the thermo-hydro-mechanical state of the system and the local structure, i.e. degree of connectivity, of the fracture system. A suite of applications is presented to illustrate the flexibility and capability of the new simulator to address problems of increasing complexity and occurring at different spatial (from centimetres to tens of kilometres) and temporal scales (from minutes to hundreds of years).

Pulsatile Waterhammer Subject to Laminar Friction

1972 ◽  
Vol 94 (2) ◽  
pp. 467-472 ◽  
Author(s):  
D. A. P. Jayasinghe ◽  
H. J. Leutheusser
Keyword(s):  
Stokes Equations ◽  
Fluid Motion ◽  
Present Theory ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Arbitrary Velocity ◽  
Velocity Input ◽  
Special Case ◽  
Signalling Problem

This paper deals with elastic waves which may be generated in a fluid by the sudden movement of a flow boundary. In particular, an analysis of the classical piston, or signalling problem is presented for the special case of arbitrary velocity input into a stationary fluid contained in a circular, semi-infinite waveguide. The decay of the pulse, as well as the resulting flow development in the inlet region of the pipe are analyzed by means of an asymptotic expansion of the suitably nondimensionalized Navier-Stokes equations for a compressible, nonheat-conducting Newtonian fluid. The results differ significantly from those of the more conventional one-dimensional approach based on the so-called telegrapher’s equation of mathematical physics. The present theory realistically predicts the growth of a boundary layer both in time and position and, hence, it appears to represent the transient fluid motion in a manner which is physically more appealing.

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.

Floating Membrane Breakwater

1996 ◽  
Vol 118 (1) ◽  
pp. 46-52 ◽  
Author(s):  
A. N. Williams
Keyword(s):  
Wave Reflection ◽  
Structural Parameters ◽  
Unit Length ◽  
Fluid Motion ◽  
Integral Equation Method ◽  
Equation Of Motion ◽  
Boundary Integral ◽  
Mooring Line ◽  
Hydrodynamic Properties ◽  
One Dimensional

The hydrodynamic properties of a flexible floating breakwater consisting of a membrane structure attached to a small float restrained by moorings are investigated theoretically. The tension in the membrane is achieved by hanging a clump weight from its lower end. The fluid motion is idealized as linearized, two-dimensional potential flow and the equation of motion of the breakwater is taken to be that of a one-dimensional membrane of uniform mass per unit length subjected to a constant axial force. The boundary integral equation method is applied to the fluid domain, and the dynamic behavior of the breakwater is also described through an appropriate Green function. Numerical results are presented which illustrate the effects of the various wave and structural parameters on the efficiency of the breakwater as a barrier to wave action. It is found that the wave reflection properties of the structure depend strongly on the membrane length, the magnitude of the clump weight, and the mooring line stiffness, while the membrane weight and excess buoyancy of the system are of lesser importance.

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.

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