A modified mixture theory for one-dimensional melting of pure PCM and PCM/metal foam composite: Numerical analysis and experiment validation

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.

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Numerical analysis of one dimensional nonlinear theory in relativistic klystron amplifier

High Power Laser and Particle Beams ◽

10.3788/hplpb20142606.63005 ◽

2014 ◽

Vol 26 (6) ◽

pp. 63005

Author(s):

何琥 He Hu ◽

黄华 Huang Hua ◽

雷禄容 Lei Lurong

Keyword(s):

Numerical Analysis ◽

Nonlinear Theory ◽

One Dimensional ◽

Relativistic Klystron

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Analytical considerations of thermal storage and interface evolution of a PCM with/without porous media

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-02-2019-0094 ◽

2019 ◽

Vol 30 (1) ◽

pp. 373-400 ◽

Cited By ~ 8

Author(s):

Huijin Xu ◽

Yan Wang ◽

Xingchao Han

Keyword(s):

Porous Medium ◽

Metal Foam ◽

Thermal Storage ◽

Liquid Interface ◽

Storage Device ◽

Content Type ◽

Foam Composite ◽

Storage Rate ◽

Solid Liquid Interface ◽

Solid Liquid

Purpose Phase change energy storage is an important solution for overcoming human energy crisis. This study aims to present an evaluation for the thermal performances of a phase change material (PCM) and a PCM–metal foam composite. Effects of pore size, pore density, thermal conductivity of solid structure and mushy region on the thermal storage process are examined. Design/methodology/approach In this paper, temperature, flow field and solid–liquid interface of a PCM with or without porous media were theoretically assessed. The influences of basic parameters on the melting process were analyzed. A PCM thermal storage device with a metal foam composite is designed and a thermodynamic analysis for it is conducted. The optimal PCM temperature and the optimal HTF temperature in the metal foam-enhanced thermal storage device are derived. Findings The results show that the solid–liquid interface of pure PCM is a line area and that of the mixture PCM is a mushy area. The natural convection in the melting liquid is intensive for a PCM without porous medium. The porous medium weakens the natural convection and makes the temperature field, flow field and solid–liquid interface distribution more homogeneous. The metal foam can greatly improve the heat storage rate of a PCM. Originality/value Thermal storage rate of a PCM is compared with that of a PCM–metal foam composite. A thermal analysis is performed on the multi-layered parallel-plate thermal storage device with a PCM embedded in a highly conductive porous medium, and an optimal melting temperature is obtained with the exergy optimization. The heat transfer enhancement with metal foams proved to be necessary for the thermal storage application.

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