scholarly journals Internal Structure and Heat Conduction in Rigid Solids: A Two-Temperature Approach

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ruth Estephania Gonzalez-Narvaez ◽  
Mariano López de Haro ◽  
Federico Vázquez
Keyword(s):  
Heat Conduction ◽  
Internal Structure ◽  
Coupling Parameter ◽  
Thermal Response ◽  
Coupled Transport ◽  
Length Scales ◽  
The Matrix ◽  
Present Formalism ◽  
Fourier Type ◽  
Two Temperature

Abstract A non-Fourier thermal transport regime characterizes the heat conduction in solids with internal structure. Several thermodynamic theories attempt to explain the separation from the Fourier regime in such kind of systems. Here we develop a two-temperature model to describe the non-Fourier regime from the principles of non-equilibrium thermodynamics. The basic assumption is the existence of two well-separated length scales in the system, namely, one related with the matrix dimension (bulk) and the other with the characteristic length of the internal structure. Two Fourier type coupled transport equations are obtained for the temperatures which describe the heat conduction in each of the length scales. Recent experimental results from several groups on the thermal response of different structured materials are satisfactorily reproduced by using the coupling parameter as a fitting parameter. The similarities and differences of the present formalism with other theories are discussed.

Two-dimensional hybrid analytical approach for the investigation of thermal aspects in human tissue undergoing regional hyperthermia therapy

2020 ◽  
Vol 234 (20) ◽  
pp. 3951-3966
Author(s):  
Jaideep Dutta ◽  
Balaram Kundu
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Cancer Treatment ◽  
Thermal Response ◽  
Skin Tissue ◽  
Hyperbolic Heat Conduction ◽  
Two Dimensional ◽  
Regional Hyperthermia ◽  
Hyperthermia Therapy ◽  
The Impact

The formation of the present work is based on the development of the exact analytical solution of two-dimensional temperature response by employing the hyperbolic heat conduction bioheat model in a single-layered human skin tissue subjected to the regional hyperthermia therapy (RHT) for cancer treatment. The mathematical approach has been utilized as a hybrid form of ‘separation of variables’ and ‘finite integral transform’ method. Three kinds of surface heat fluxes (constant, sinusoidal and cosine) have been employed as an external heat source on the therapeutic surface of the square-shaped skin tissue of 100 mm × 100 mm. An innovative form of initial condition (spatially dependent) has been implemented in the present mathematical formulation as skin tissues are highly non-homogeneous and non-uniform in structure. The present research outcome indicates that cosine heat flux would be a suitable alternative for the sinusoidal heat flux. The impact of the relaxation time lag has been clearly noted in the thermal response with the waveform-like behaviour and it justifies the postulate of hyperbolic heat conduction. The two-dimensional temperature of the skin tissue has been observed in the range of 48.1 ℃–40 ℃ (in decreasing order). Estimated peak temperatures are in the proposed spectrum of hyperthermia therapy for an exposure time of 100 s, and this fact is true in an agreement with the medical protocol of the cancer treatment. The accuracy of the mathematical modelling and in-house computer codes are justified with the published numerical models and the maximum deviation of the thermal response has been noticed in order of 1.5–3%. The two-dimensional surface thermal contours have provided a glimpse of heat flow in the physical domain of skin tissue under different heating conditions and this research output may be beneficial to establish the theoretical standard of the regional hyperthermia treatment for cancer eradication.

COEXISTENCE OF LOW- AND HIGH-DIMENSIONAL SPATIOTEMPORAL CHAOS IN A CHAIN OF DISSIPATIVELY COUPLED CHUA’S CIRCUITS

1994 ◽  
Vol 04 (03) ◽  
pp. 639-674 ◽  
Author(s):  
A.L. ZHELEZNYAK ◽  
L.O. CHUA
Keyword(s):  
Phase Space ◽  
Initial Conditions ◽  
Coupling Parameter ◽  
Reaction Diffusion ◽  
Cellular Neural Network ◽  
Spatiotemporal Chaos ◽  
Matrix Phase ◽  
High Dimensional ◽  
The Matrix ◽  
A Chain

Spatiotemporal dynamics of a one-dimensional cellular neural network (CNN) made of Chua’s circuits which mimics a reaction-diffusion medium is considered. An approach is presented to analyse the properties of this reaction-diffusion CNN through the characteristics of the attractors of an associated infinite-dimensional dynamical system with a matrix phase space. Using this approach, the spatiotemporal correlation dimension of the CNN’s spatiotemporal patterns is computed over various ranges of the diffusion coupling parameter, length of the chain, and initial conditions. It is shown that in a finite-dimensional projection of the matrix phase space of the CNN, both low- and high-dimensional attractors corresponding to different initial conditions coexist.

scholarly journals Analysis of the possibility of determining the internal structure of composite material by estimating its thermal diffusivity

2014 ◽  
Vol 35 (1) ◽  
pp. 3-15
Author(s):  
Stanisław Kucypera
Keyword(s):  
Composite Material ◽  
Heat Conduction ◽  
Thermal Diffusivity ◽  
Internal Structure ◽  
Fibrous Composite ◽  
Electric Heater ◽  
Transient Temperature ◽  
Inverse Heat Conduction ◽  
Filtration Method ◽  
Fibrous Composite Material

Abstract The aim of this paper is analysis of the possibility of determining the internal structure of the fibrous composite material by estimating its thermal diffusivity. A thermal diffusivity of the composite material was determined by applying inverse heat conduction method and measurement data. The idea of the proposed method depends on measuring the timedependent temperature distribution at selected points of the sample and identification of the thermal diffusivity by solving a transient inverse heat conduction problem. The investigated system which was used for the identification of thermal parameters consists of two cylindrical samples, in which transient temperature field is forced by the electric heater located between them. The temperature response of the system is measured in the chosen point of sample. One dimensional discrete mathematical model of the transient heat conduction within the investigated sample has been formulated based on the control volume method. The optimal dynamic filtration method as solution of the inverse problem has been applied to identify unknown diffusivity of multi-layered fibrous composite material. Next using this thermal diffusivity of the composite material its internal structure was determined. The chosen results have been presented in the paper.

An Improved Specified Finite Particle Method and Its Application to Transient Heat Conduction

2016 ◽  
Vol 14 (05) ◽  
pp. 1750050 ◽  
Author(s):  
Lu Wang ◽  
Fei Xu ◽  
Yang Yang
Keyword(s):  
Heat Conduction ◽  
Matrix Theory ◽  
Taylor Series Expansion ◽  
Particle Method ◽  
Transient Heat Conduction ◽  
Boundary Region ◽  
The Matrix ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Finite Particle

Compared with the traditional Smoothed Particle Hydrodynamics (SPH), Finite Particle Method (FPM) has higher accuracy for boundary region. However, there are still two inherent defects which are the time consuming and the numerical instability in FPM. In this paper, a high-order algorithm based on the Taylor series expansion and the matrix theory is proposed and the corresponding particles selected mode is discussed. It is validated that the algorithm has higher-order accuracy than the previous low-order improvement algorithm for FPM. Further, transient heat conduction examples have been discussed to verify the feasibility and effectiveness of the new algorithm.

Analysis of the Thermal Response in Micromachine under the Thermal Shock

2011 ◽  
Vol 464 ◽  
pp. 583-587
Author(s):  
Ying Ze Wang ◽  
Xin Nan Song
Keyword(s):  
Heat Conduction ◽  
Relaxation Times ◽  
Boundary Surface ◽  
Thermal Relaxation ◽  
Thermal Response ◽  
Heat Propagation ◽  
Hyperbolic Heat Conduction ◽  
Thermal Relaxation Times ◽  
Fourier Heat Conduction ◽  
Sudden Temperature Change

The thermal response for given micromachine with the boundary surface exposed to sudden temperature change is studied by deriving an analytical solution of the hyperbolic heat conduction equation. Using the obtained analytical expression, the temperature profiles at the outer surface and interior of the micro beam are evaluated for various thermal relaxation times. The behaviors of hyperbolic heat propagation in micro beam are analyzed and possible anomalies are discussed by comparing the thermal behaviors of Fourier heat conduction.

scholarly journals Cooling Dynamics of a Gold Nanoparticle in a Host Medium Under Ultrafast Laser Pulse Excitation: A Ballistic-Diffusive Approach

2008 ◽  
Author(s):  
Majid Rashidi-Huyeh ◽  
Sebastian Volz ◽  
Bruno Palpant
Keyword(s):  
Heat Conduction ◽  
Laser Pulse ◽  
Gold Nanoparticle ◽  
Particle Temperature ◽  
Surrounding Medium ◽  
Pulse Excitation ◽  
Fourier’S Law ◽  
Host Medium ◽  
The Matrix ◽  
Fourier's Law

We present a numerical model allowing to determine the electron and lattice temperature dynamics in a gold nanoparticle under subpicosecond pulsed excitation, as well as that of the surrounding medium. For this, we have used the electron-phonon coupling equation in the particle with a source term linked with the laser pulse, and the ballistic-diffusive equations for heat conduction in the host medium. Our results show that the heat transfer rate from the particle to the matrix is significantly smaller than the prediction of Fourier’s law. Consequently, the particle temperature rise is much larger and its cooling dynamics is much slower than that obtained using Fourier’s law, which is attributed to the nonlocal and nonequilibrium heat conduction in the vicinity of the nanoparticle. These results are expected to be of great importance for interpreting pump-probe experiments performed on single nanoparticles or nanocomposite media.

Numerical Green’s Function for Steady-State Heat Conduction in Heterogeneous Media

1998 ◽  
Vol 120 (4) ◽  
pp. 284-286 ◽  
Author(s):  
Deok-Kee Choi ◽  
Seiichi Nomura
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Green’S Function ◽  
Green's Function ◽  
Heterogeneous Media ◽  
Homogeneous Boundary Condition ◽  
State Heat ◽  
The Matrix ◽  
Steady State Heat ◽  
The Galerkin Method

Numerical Green's function for steady-state heat conduction problems is derived in a finite-sized medium that may contain inclusions (fibers) in the matrix phase. Green's function is approximated by employing the Galerkin method that uses permissible functions which satisfy the homogeneous boundary condition for the given geometry. The present approach allows physical fields in a medium that contain multiple inclusions to be expressed through isolated integrals semi-analytically while retaining all the relevant material parameters.

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