相关论文: On the Formalization of the Heat Conduction Proble…
Dynamic Fault Trees (DFTs) is a widely used failure modeling technique that allows capturing the dynamic failure characteristics of systems in a very effective manner. Simulation and model checking have been traditionally used for the…
The theory of heat transfer by electromagnetic radiation is based on the radiative transfer equation (RTE) for the radiation intensity, or equivalently on the Boltzmann transport equation (BTE) for the photon distribution. We focus in this…
The realization of single-molecule thermal conductance measurements has driven the need for theoretical tools to describe conduction processes that occur over atomistic length scales. In macroscale systems, the principle that is typically…
The discussion regarding the numerical integration of the polarized radiative transfer equation is still open and the comparison between the different numerical schemes proposed by different authors in the past is not fully clear. Aiming at…
Heat can generally transfer via thermal conduction, thermal radiation, and thermal convection. All the existing theories of transformation thermotics and optics can treat thermal conduction and thermal radiation, respectively.…
To determine the electron heat flux density on macroscopic scales, the most widely used approach is to solve a diffusion equation through a multi-group technique. This method is however restricted to transport induced by temperature…
A parametric, hybrid reduced order model approach based on the Proper Orthogonal Decomposition with both Galerkin projection and interpolation based on Radial Basis Functions method is presented. This method is tested against a case of…
An accurate analysis of the conduction heat transfer in a cryogenic flask is made and some useful formulae are derived. Taking into account the temperature dependence of conductivity and tensile strength of the supporting rods for a helium…
For the thermal control of electronic components in aerospace, automotive or server systems, the heat sink is often located far from the heat sources. Therefore, heat transport systems are necessary to cool the electronic components…
Thermally aware design of 2.5D and 3D advanced packaging systems will require fast, accurate, and powerful thermal analysis of chiplets, stacks, and packages. These systems contain multiple materials with non-linear heat transfer properties…
Parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) have a wide range of applications. In particular, high-dimensional PDEs with gradient-dependent nonlinearities appear often in the…
The Laplace transform is an algebraic method that is widely used for analyzing physical systems by either solving the differential equations modeling their dynamics or by evaluating their transfer function. The dynamics of the given system…
We suggest a systematic procedure for classifying partial differential equations invariant with respect to low dimensional Lie algebras. This procedure is a proper synthesis of the infinitesimal Lie's method, technique of equivalence…
Heat conduction phenomena are studied theoretically using computer simulation. The systems are crystal with nonlinear interaction, and fluid of hard-core particles. Quasi-one-dimensional system of the size of $L_x\times L_y\times L_z(L_z\gg…
The evolution of infinitesimal, localized perturbations is investigated in a one-dimensional diatomic gas of hard-point particles (HPG) and thereby connected to energy diffusion. As a result, a Levy walk description, which was so far…
Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…
This paper provides a methodology of verified computing for solutions to 1-dimensional advection equations with variable coefficients. The advection equation is typical partial differential equations (PDEs) of hyperbolic type. There are few…
We design a class of spatially inhomogeneous heat spreaders in the context of steady-state thermal conduction leading to spatially uniform thermal fields across a large convective surface. Each spreader has a funnel-shaped design, either in…
Understanding and quantifying the fundamental physical property of coherence of thermal excitations is a long-standing and general problem in physics. The conventional theory, i.e. the phonon gas model, fails to describe coherence and its…
In this article, we present the governing equations for the temperature field upstream and downstream of the periodically developed flow region in channels with arrays of periodic solid structures. From the ansatz that the temperature field…