Heat Conduction In Systems Research Articles

Heat transfer at nanometric scales described by extended irreversible thermodynamics

Abstract The purpose of this work is to present a study on heat conduction in systems that are composed out of spherical and cylindrical micro- and nanoparticles dispersed in a bulk matrix. Special emphasis is put on the dependence of the effective heat conductivity on various selected parameters as particle size and also its shape, surface specularity and density, including particle-matrix interaction. The heat transfer at nanometric scales is modelled using extended irreversible thermodynamics, whose main feature is to elevate the heat flux vector to the status of independent variable. The model is illustrated by a Copper-Silicium (Cu-Si) system. It is shown that all the investigated parameters have a considerable influence, the particle size being especially useful to either increase or decrease the effective thermal conductivity.

Effective Thermal Conductivity of Spherical Particulate Nanocomposites: Comparison with Theoretical Models, Monte Carlo Simulations and Experiments

The purpose of this work is to study heat conduction in systems that are composed out of spherical micro-and nanoparticles dispersed in a bulk matrix. Special emphasis will be put on the dependence of the effective heat conductivity on various selected parameters as dimension and density of particles, interface interaction with the matrix. This is achieved by combining the effective medium approximation and extended irreversible thermodynamics, whose main feature is to elevate the heat flux vector to the status of independent variable. The model is illustrated by three examples: Silicium-Germanium, Silica-epoxy-resin and Copper-Silicium systems. Predictions of our model are in good agreement with other theoretical models, Monte-Carlo simulations and experimental data.

Mathematical modeling of heat transfer in closed two-phase thermosyphon

There was conducted numerical analysis of heat-transfer in close two-phase thermosyphon of cylindrical form in the condition of admission of warmth on lower lid and taking from the high bound of lid. For description of the researched process was offered the simplified mathematical model, which describes only processes of heat conductivity in system a corps of thermosyphon - steam channel - condensate membrane. This formulated task with boundary conditions was decided by the method of eventual differences using an implicit difference scheme. As result have got fields of temperatures in thermosyphon for typical thermal loads and methods of working. Was conducted comparative analysis of fields of temperature in thermosyphon at different thermal streams on lower lid. Was studied an Influence of coefficient of heat emission and basic geometrical descriptions on forming of the field of temperature in the crossrunner of thermosyphon.

Heat conduction in systems with Kolmogorov-Arnold-Moser phase space structure

We study heat conduction in a billiard channel formed by two sinusoidal walls and the diffusion of particles in the corresponding channel of infinite length; the latter system has an infinite horizon, i.e., a particle can travel an arbitrary distance without colliding with the rippled walls. For small ripple amplitudes, the dynamics of the heat carriers is regular and analytical results for the temperature profile and heat flux are obtained using an effective potential. The study also proposes a formula for the temperature profile that is valid for any ripple amplitude. When the dynamics is regular, ballistic conductance and ballistic diffusion are present. The Poincaré plots of the associated dynamical system (the infinitely long channel) exhibit the generic transition to chaos as ripple amplitude is increased. When no Kolmogorov-Arnold-Moser (KAM) curves are present to forbid the connection of all chaotic regions, the mean square displacement grows asymptotically with time t as tln(t).

Experimental validation of a frequency domain BEM model to study 2D and 3D heat transfer by conduction

Abstract This article presents an experimental validation of 2D and 2.5D boundary element method (BEM) solutions for transient heat conduction in systems containing heterogeneities. The problem is formulated in the frequency domain. The responses in the time domain are obtained by means of an inverse Fourier transform. Complex frequencies with a small imaginary part are introduced to cope with aliasing. Their effect is taken into account by rescaling the results in the time domain.For validation purposes, the solutions provided by the proposed BEM formulation were first verified against analytical solutions and then compared with experimental results. In the laboratory tests a steel inclusion was embedded in a confined host medium and unsteady temperatures were applied to its boundary. Two host media were tested: molded expanded polystyrene and medium-density fiberboard. The systems were subjected to plane and point heat sources. The thermal properties of these materials have been previously defined experimentally. The results show that the BEM solutions agree well with the experimental results.

Discrete thermal element modelling of heat conduction in particle systems: Pipe-network model and transient analysis

In our recent work [Y.T. Feng, K. Han, C.F. Li, D.R.J. Owen. Discrete thermal element modelling of heat conduction in particle systems: basic formulations. Journal of Computational Physics. 227: 5072–5089, 2008], a novel numerical methodology, termed the discrete thermal element method (DTEM), is proposed for the modelling of heat conduction in systems involving a large number of circular particles in 2D cases. The method cannot be easily extended to transient analysis, which causes difficulties in combining the DTEM with the conventional discrete element method for modelling thermal/mechanical coupling problems in particle systems. This paper presents a simplified version of the DTEM, termed the pipe-network model, in which each particle is replaced by a simple thermal pipe-network connecting the particle centre with each contact zone associated with the particle. The model essentially neglects the direct heat transfer between the contact zones and thus significantly simplifies the solution procedure of the original DTEM. With this feature, transient heat conduction analysis can now be performed in a straightforward manner. In addition, the entire algorithmic structure of the pipe-network model is compatible with the discrete element method, leading to an effective scheme for simulating thermal–mechanical coupling problems. Numerical experiments are conducted to establish the solution accuracy of the proposed model.

Discrete thermal element modelling of heat conduction in particle systems: Basic formulations

This paper proposes a novel numerical methodology, termed the discrete thermal element method (DTEM), for the effective modelling of heat conduction in systems comprising a large number of circular particles in 2D cases. Based on an existing analytical integral solution for the temperature distribution over a circular domain subjected to the Neumann boundary condition, a linear algebraic system of thermal conductivity equations for each particle is derived in terms of the average temperatures and the resultant fluxes at the contact zones with its neighboring particles. Thus, each particle is treated as an individual element with the number of (temperature) unknowns equal to the number of particles that it is in contact with. The element thermal conductivity matrix can be very effectively evaluated and is entirely dependent on the characteristics of the contact zones, including the contact positions and contact angles. This new element shares the same form and properties with its conventional thermal finite element counterpart. In particular, the whole solution procedure can follow exactly the same steps as those involved in the finite element analysis. Unlike finite elements or other modern numerical techniques, however, no discretization errors are involved in the discrete thermal elements. The modelling error mainly stems from the assumption made about the heat flux distribution within the contact zones. Based on some theoretical work, an enhanced version is suggested to improve the approximation. The numerical assessment against finite element results indicates that the basic version of DTEM can achieve a very reasonable solution accuracy, while the enhanced version further improves the accuracy to a high level. In addition, thermal resistance phenomena between the contact zones can be readily incorporated into the current modelling framework.

Entropy production rate in the one-dimensional heat conduction for systems whose thermal conductivity or its derivative are piecewise continuous with respect to temperature

In a previous paper the author considered, according to the methods and the purposes of the generalized thermodynamics, the one-dimensional heat conduction in systems, whose conductivity is a function of both temperature and the coordinate in the heat flux direction and is piecewise continuous with respect to the latter. The aim of this paper is to study in a similar way the cases when thermal conductivity or its derivative are piecewise continuous with respect to temperature.

Thermodynamic analysis of the one-dimensional heat conduction with inhomogeneities in the heat flux direction

Starting from the results of Li, Prigogine and others about the one-dimensional heat conduction with constant temperature boundary conditions, the aim of this paper is to study, according to the methods and the purposes of the generalized thermodynamics, the more general case of one-dimensional heat conduction in systems, whose conductivity is function of both temperature and the coordinate in the heat flux direction and presents a finite number of discontinuities.