Macroscopic Heat Conduction Research Articles

MACROSCALE AND MICROSCALE THERMAL TRANSPORT AND THERMO-MECHANICAL INTERACTIONS: SOME NOTEWORTHY PERSPECTIVES

Some noteworthy and historical perspectives and an overview of macroscale and microscale heat transport behavior in materials and structures are presented. The topic of heat waves is also discussed. The significance of constitutive models for both macroscale and microscale heat conduction are described in conjunction with generalizations drawn concerning the physical relevance and the role of relaxation and retardation times emanating from the Jeffreys type heat flux constitutive model, with consequences to the Cattaneo heat flux model and subsequently to the Fourier heat flux model. Both macroscopic model formulations for applications to macroscopic heat conduction problems and two-step models for use in specialized applications to account for microscale heat transport mechanisms are overviewed with emphasis on the proposition of a Generalized Two-Step relaxation / retardation time-based heating model. So as to bring forth a variety of issues in a single forum, illustrative numerical applications are overviewed including some relevance to thermo-mechanical interactions

MOLECULAR DYNAMICS SIMULATION OF HEAT CONDUCTION AND THERMAL STRESS IN RELATION WITH CONTINUUM MECHANICS

Heat conduction phenomena and induced thermal stresses are simulated from a microscopic viewpoint by using a molecular dynamics method. Three dimensional rectangular parallelepiped model composed of 2000 atoms surrounded by periodic boundary is imposed for the simulations. Thermo-physical properties such as melting temperature, specific heat, heat conductivity and latent heat are evaluated at the first step to obtain the fundamental data for the following heat conduction simulation. The central part of the model is heated for two cases with and without melting, and the variation of temperature, potential energy and thermal stresses are simulated. These simulations are carried out with two different potential functions, Lennard-Jones and Morse type, in order to clarify the effects of the interatomic potential, which follows to qualitatively demonstrate similar tendency in spite of remarkable quantitative differences. Then the variation of temperature is compared with the numerical solution of macroscopic heat conduction equation. It is clarified that the results show good agreement with each other if they are plotted against non-dimensional time, or Fourier number. Stresses calculated by molecular dynamics method are also compared with macroscopic thermal stresses.

Molecular Dynamics Study of Heat Conduction in Solid Materials.

Using the molecular dynamics method, the process of heat conduction in solid materials has been numerically studied for the configuration of lattice particles having the Lennard-Jones (12-6) potential. Under the condition of constant heat flux, the temperature distributions through the conduction layer are calculated with changing the amount of heat flux, layer temperature and layer thickness of the lattice particles, and the lattice configuration including defects. If averaged over sufficiently long time intervals, the molecular process of heat conduction exhibits the same features of Fourier's law as the macroscopic heat conduction. For less than four particle layers, the boundary conditions take part in the process of heat conduction, changing the relationships of the heat flux to the temperature gradient

Modelling of heat transfer by conduction in a transition region between a porous medium and an external fluid

We study the modelling of purely conductive heat transfer between a porous medium and an external fluid within the framework of the volume averaging method. When the temperature field for such a system is classically determined by coupling the macroscopic heat conduction equation in the porous medium domain to the heat conduction equation in the external fluid domain, it is shown that the phase average temperature cannot be predicted without a generally negligible error due to the fact that the boundary conditions at the interface between the two media are specified at the macroscopic level. Afterwards, it is presented an alternative modelling by means of a single equation involving an effective thermal conductivity which is a function of point inside the interfacial region. The theoretical results are illustrated by means of some numerical simulations for a model porous medium. In particular, temperature fields at the microscopic level are presented.

Homogenized equations for steady heat conduction in composite materials with dilutely-distributed impurities

In this paper, by using the two-space method, homogenized equations for steady heat conduction in the composite material cylinders with dilutely-distributed elliptic cylinders of impurities are derived, and the explicit expressions for the corresponding effective heat conductivity of those which are concerned are obtained. It is also shown that the macroscopic heat conduction is anisotropic when the cross-sections of the impurity cylinders are unidirectionally oriented and isotropic when the angular distribution of the cross-sections is uniform.

The applicability of Fourier's theory of heat conduction on laser produced plasmas

Thermal conduction in laser produced plasmas is usually treated by the macroscopic heat conduction equation. It is shown that this treatment can be incorrect in the case of a laser ablative implosion.