The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but neither temperature nor heat flux is prescribed there. Instead, the physical assumptions of their continuity at the interfaces are the only conditions imposed. T...

CURRENT THEORIES OF DISSIPATION IN THE RELATIVISTIC REGIME SUFFER FROM ONE OF TWO DEFICITS: either their dissipation is not causal or no profiles for strong shock waves exist. This paper proposes a relativistic Navier-Stokes-Fourier-type viscosity and heat conduction tensor such that the resulting second-order system of partial differential equations for the fluid dynamics of pure radiation is ...

Some of our recent studies on the heat conduction of single-walled carbon nanotubes (SWNTs) using molecular dynamics (MD) simulations are reported. The length-dependence of pure SWNTs is investigated in a range of nanotube lengths up to 3.2μm. Non-equilibrium MD simulations were performed by minimizing the thermal boundary resistance between the thermally controlled layers and the rest of the n...

Radiative heat transfer in participating medium has been carried out using the finite volume method. The radiative transfer equations are formulated for absorbing and anisotropically scattering and emitting medium. The solution strategy is discussed and the conditions for computational stability are conferred. The equations have been solved for transient radiative medium and transient radiation...

Context. The interstellar medium contains warm clouds that are embedded in a hot dilute gas produced by supernovae. Because both gas phases are in contact, an interface forms where mass and energy are exchanged. Whether heat conduction leads to evaporation of these clouds or whether condensation dominates has been analytically derived. Both phases behave differently dynamically so that their re...

1. Everything is number 2. Ancient Astronomy 3. Optics and statics 4. The middle ages and the renaissance 5. Mechanics of motion 6. Newtonian mechanics 7. Early differential equations 8. The Brachistochrone 9. Early methods of solutionLinear differential equations 10 Newton’s second law as a differential equationThe method of perturbations 11. The vibrating stringPartial differential equations ...

Constitutive models in nanoscience and engineering often poorly represent the physics due to significant deviations in model form from their macroscale counterparts. In Part 1 of this study, this problem was explored by considering a continuum scale heat conduction constitutive law inferred directly from molecular dynamics (MD) simulations. In contrast, this work uses Bayesian inference based o...

In this paper the description of the simplest variant of conservative averaging method for partial differential (or integro-differential) equations in cylinder type domain is given. Different types of boundary conditions (both linear and non-linear) are considered. As application of the method the process of intensive steel quenching as the time inverse ill-posed problem for the hyperbolic heat...

In this paper, we study a generalisation of the Caginalp phase field system obtained by considering Fourier law as heat conduction and involving two temperatures. first section, are interested in existence uniqueness solutions. section 2, address question asymptotic behaviour solutions, particular with demonstration global attractor. For this, needed to show that is dissipative know regularity ...