MATHEMATICAL MODELING OF FREEZING AND THAWING PROCESS IN TISSUES: A POROUS MEDIA APPROACH

2010 ◽  
Vol 02 (03) ◽  
pp. 617-633 ◽  
Author(s):  
SUSHIL KUMAR ◽  
V. K. KATIYAR
Keyword(s):  
Porous Media ◽  
Phase Change ◽  
Biological Tissues ◽  
Transient Temperature ◽  
Freezing And Thawing ◽  
Transient Temperature Distribution ◽  
Thawing Process ◽  
Phase Change Phenomena ◽  
Capacity Formulation ◽  
Change Problem

Biological tissues can be treated as porous media as it is composed of dispersed cell separated by connective voids which allow flow of nutrients, minerals, etc., to reach all cells within the tissue. In this present study, a mathematical model has been developed to study the phase change phenomena during the freezing and thawing process in biological tissues using porous media approach. Effective heat capacity formulation is used for the phase change problem. Numerical simulation is used to study the effect of porosity, on the motion of freezing and thawing front and transient temperature distribution in tissue. It is observed that porosity has significant effect on transient temp profile and phase change interfaces; further decrease in freezing and heating rate has been found with increased value of porosity.

Heat-Conduction Problems With Melting or Freezing

1969 ◽  
Vol 91 (3) ◽  
pp. 421-426 ◽  
Author(s):  
S. H. Cho ◽  
J. E. Sunderland
Keyword(s):  
Temperature Distribution ◽  
Phase Change ◽  
Closed Form Solution ◽  
Form Solution ◽  
Rate Of Change ◽  
Phase Changes ◽  
Transient Temperature ◽  
Infinite Body ◽  
Two Phase ◽  
Transient Temperature Distribution

An exact solution is presented for the temperature distribution and rate of change of phase for a semi-infinite body where the change of phase occurs over a range of temperatures. The surface temperature is instantaneously changed to and held at a temperature different from the phase-change temperature range and the initial temperature. The transient temperature distribution and rate of melting are also determined for a finite slab in which one or two phase changes take place. The slab is initially at a constant temperature and the temperature of one face is instantaneously changed so that a phase change takes place. The other surface of the slab is insulated. An exact closed form solution is presented for the temperature distribution in the newly formed phase and Goodman’s integral technique is used to find the temperature distribution in the initially existing phase.

scholarly journals LATTICE BOLTZMANN METHOD FOR NUMERICAL SIMULATION OF PHASE CHANGE PROBLEM

2019 ◽  
pp. 1-3
Author(s):  
Soumia Addakiri ◽  
El Alami Semma
Keyword(s):  
Phase Transition ◽  
Numerical Simulation ◽  
Liquid Phase ◽  
Phase Change ◽  
Lattice Boltzmann ◽  
Distribution Functions ◽  
Phase Change Phenomena ◽  
Boltzmann Method ◽  
Solid Liquid ◽  
Change Problem

In this work, a new numerical model for the treatment of phase change phenomena is developed. The LBM method is used to install this new model based on determining the image of distribution functions during the phase transition. The classical Stefan problem modeling the solid / liquid phase change is studied with this approach and validated by comparison with analytical results.

scholarly journals Theory of Effective Stress in Soil and Rock and Implications for Fracturing Processes: A Review

Geosciences ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 119
Author(s):  
Vincenzo Guerriero ◽  
Stefano Mazzoli
Keyword(s):  
Porous Media ◽  
Effective Stress ◽  
Biological Tissues ◽  
Theory Of Elasticity ◽  
Past Century ◽  
Metal Powders ◽  
Science Community ◽  
Experimental Approaches ◽  
Historical Remarks ◽  
Open Issues

The effective stress principle (ESP) plays a basic role in geology and engineering problems as it is involved in fundamental issues concerning strain and failure of rock and soil, as well as of other porous materials such as concrete, metal powders, biological tissues, etc. Although since its introduction in the 1920s the main ESP aspects have been unravelled and theoretically derived, these do not appear to have been always entirely perceived by many in the science community dealing with ESP-related topics but having little familiarity with the complex theories of porous media and poroelasticity. The purpose of this review is to provide a guidance for the reader who needs an updated overview of the different theoretical and experimental approaches to the ESP and related topics over the past century, with particular reference to geological fracturing processes. We begin by illustrating, after some introductive historical remarks, the basic theory underlying the ESP, based on theory of elasticity methods. Then the different ESP-related theories and experimental results, as well as main interpretations of rock jointing and fracturing phenomena, are discussed. Two main classical works are then revisited, and a rigorous ESP proof is derived. Such a proof is aimed at geologists, engineers and geophysicists to become more familiar with theories of porous media and poroelasticity, being based on the classical theory of elasticity. The final part of this review illustrates some still open issues about faulting and hydraulic fracturing in rocks.

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