Related papers: Mathematical Modeling of Heat Conduction
We study nodal lines of solutions to the heat equations. We are interested in the global geometry of nodal sets, in the whole domain of definition of the solution. The local structure of nodal sets is a well understander subject, while the…
We present a temperature extrapolation technique for self-consistent many-body methods, which provides a causal starting point for converging to a solution at a target temperature. The technique employs the Carath\'eodory formalism for…
In this paper we present a numerical solution for the mathematical modeling of the hot-pressing process applied to medium density fiberboard. The model is based in the work of Humphrey[82], Humphrey and Bolton[89] and Carvalho and…
We present an extended analytic formula for the calculation of the temperature profile along a bondwire embedded in a package. The resulting closed formula is built by coupling the heat transfer equations of the bondwire and the surrounding…
In this paper we consider a mathematical model which describes the equilibrium of two elastic rods attached to a nonlinear spring. We derive the variational formulation of the model which is in the form of an elliptic quasivariational…
We study the problem of heat conduction in general relativity by using Carter's variational formulation. We write the creation rates of the entropy and the particle as combinations of the vorticities of temperature and chemical potential.…
It has been observed in many numerical simulations, experiments and from various theoretical treatments that heat transport in one-dimensional systems of interacting particles cannot be described by the phenomenological Fourier's law. The…
The aim of this paper is to verify the new numerical implementation of a binary fluid, heat conduction dominated solidification model. First, we extend a semi-analytical solution to the heat diffusion equation, next, the range of its…
We discuss a possibility to control a heat conductivity in simple one-dimensional models of dielectrics by means of external mechanical loads. To illustrate such possibilities we consider first a well-studied chain with degenerate…
Data-driven modeling and control of temperature dynamics in mechatronics systems and industrial processes are challenging control engineering problems. This is mainly because the temperature dynamics is inherently infinite-dimensional,…
Relativistic thermodynamics as result of some recent computer simulations is derived.
Effects of ballistic transport on the temperature profiles and thermal resistance in nanowires are studied. Computer simulations of nanowires between a heat source and a heat sink have shown that in the middle of such wires the temperature…
The rate of electron transfer between a molecular species and a metal, each at a different local temperature, is examined theoretically through implementation of a bithermal (characterized by two temperatures) Marcus formalism. Expressions…
We consider the problem of heat conduction with phase change, that is essential for permafrost modeling in Land Surface Models and Dynamic Global Vegetation Models. These models require minimal computational effort and an extremely robust…
Simulation results are presented to demonstrate electron temperature and electrical potential development in dilute and cold plasma development. The simulation method is a hybrid method which adopted fluid model for electrons due to their…
A computational method for numeric resolution of a PDEs system, based on a Finite Differences schema integrated by interpolations of partial results, and an estimate of the error of its solution respect to the normal FD solution.
Energy dependence of specific heat extracted from temperature fluctuation of Au + Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV to 200 GeV was investigated by using a multiphase transport (AMPT) model. The results were compared with those from…
We study the dynamical correlation functions and heat conduction for the simplest model of quasi one-dimensional (1d) dielectric crystal i.e. a chain of classical particles coupled by quadratic and cubic intersite potential. Even in the…
Additive manufacturing and welding processes are highly sensitive to heat dissipation, where improper thermal management leads to residual stresses, distortions, and cracking. Existing heat transfer models, such as Rosenthal's solutions,…
Heat transport in nanoscale systems is both hard to measure microscopically, and hard to interpret. Ballistic and diffusive heat flow coexist, adding confusion. This paper looks at a very simple case: a nanoscale crystal repeated…