Comparison of bio-heat transfer numerical models based on the Pennes and Cattaneo-Vernotte equations

Ciesielski, Mariusz; Duda, Mateusz; Mochnacki, B.

doi:10.17512/jamcm.2016.4.04

Cited by 10 publications

(4 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As part of the project, the research concerning the non-Fourier models in the scope of bio-heat transfer are also carried out. The examples of the problems considered can be found in [14][15][16][17].…”

Section: Discussionmentioning

confidence: 99%

Application of numerical methods for solving the non-fourier equations. A review of our own and collaborators’ works

Majchrzak¹,

Mochnacki²

2018

J. Appl. Math. Comput. Mech.

Self Cite

View full text Add to dashboard Cite

Abstract. Thermal processes occuring in the solid bodies are, as a rule, described by the well-known Fourier equation (or the system of these equations) supplemented by the appropriate boundary and initial conditions. Such a mathematical model is sufficiently exact to describe the heat transfer processes in the macro scale for the typical materials. It turned out that the energy equation based on the Fourier law has the limitations and it should not be used in the case of the microscale heat transfer and also in the case of materials with a special inner structure (e.g. biological tissue). The better approximation of the real thermal processes assure the modifications of the energy equation, in particular the models in which the so-called lag times are introduced. The article presented is devoted to the numerical aspects of solving these types of equations (in the scope of the microscale heat transfer). The results published by the other authors can be found in the references posted in the works cited below. MSC 2010: 35L10, 65M06Keywords: heat transfer, non-Fourier heat diffusion models, numerical methods, computational mechanics Governing equationsIn the well-known Fourier law, the relationship between the heat flux and the temperature gradient for the heat conduction process is of the formwhere q is a heat flux vector, λ is a thermal conductivity, T, X, t denote the temperature, spatial co-ordinates and time.

show abstract

Section: Discussionmentioning

confidence: 99%

Application of numerical methods for solving the non-fourier equations. A review of our own and collaborators’ works

Majchrzak¹,

Mochnacki²

2018

J. Appl. Math. Comput. Mech.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The model discussed often finds application in the case of bioheat transfer problems, e,g. (Ciesielski et al, 2016). In fact, according to literature, e.g.…”

Section: Introductionmentioning

confidence: 99%

Application of the Alternating Direction Implicit Method for numerical solution of the dual-phase lag equation

Ciesielski

2017

jtam

Self Cite

View full text Add to dashboard Cite

The problem discussed in the paper concerns the numerical modeling of thermal processes proceeding in micro-scale described using the Dual Phase Lag Model (DPLM) in which the relaxation and thermalization time appear. The cylindrical domain of a thin metal film subjected to a strong laser pulse beam is considered. The laser action is taken into account by the introduction of an internal heat source in the energy equation. At the stage of numerical modeling, the Control Volume Method is used and adapted to resolve the hyperbolic partial differential equation. In particular, the Alternating Direction Implicit (ADI) method for DPLM is presented and discussed. The examples of computations are also presented.

show abstract

“…A large variety of generalizations of the constitutive equation for the heat transfer and their applications are presented in the literature [13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

A Fractional Single-Phase-Lag Model of Heat Conduction for Describing Propagation of the Maximum Temperature in a Finite Medium

Kukla

Siedlecka

2018

Entropy

View full text Add to dashboard Cite

In this paper, an investigation of the maximum temperature propagation in a finite medium is presented. The heat conduction in the medium was modelled by using a single-phase-lag equation with fractional Caputo derivatives. The formulation and solution of the problem concern the heat conduction in a slab, a hollow cylinder, and a hollow sphere, which are subjected to a heat source represented by the Robotnov function and a harmonically varying ambient temperature. The problem with time-dependent Robin and homogenous Neumann boundary conditions has been solved by using an eigenfunction expansion method and the Laplace transform technique. The solution of the heat conduction problem was used for determination of the maximum temperature trajectories. The trajectories and propagation speeds of the temperature maxima in the medium depend on the order of fractional derivatives occurring in the heat conduction model. These dependencies for the heat conduction in the hollow cylinder have been numerically investigated.

show abstract

Comparison of bio-heat transfer numerical models based on the Pennes and Cattaneo-Vernotte equations

Cited by 10 publications

References 10 publications

Application of numerical methods for solving the non-fourier equations. A review of our own and collaborators’ works

Application of numerical methods for solving the non-fourier equations. A review of our own and collaborators’ works

Application of the Alternating Direction Implicit Method for numerical solution of the dual-phase lag equation

A Fractional Single-Phase-Lag Model of Heat Conduction for Describing Propagation of the Maximum Temperature in a Finite Medium

Contact Info

Product

Resources

About