Related papers: Splitting schemes for hyperbolic heat conduction e…
We present an effective thermal open boundary condition for convective heat transfer problems on domains involving outflow/open boundaries. This boundary condition is energy-stable, and it ensures that the contribution of the open boundary…
Context: Thermal conductivity provides important contributions to the energy evolution of the upper solar atmosphere, behaving as a non-linear concentration-dependent diffusion equation. Recently, different methods have been offered as…
The heat equation is considered in the complex system consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies a Newton-type boundary condition is imposed. An equation for the limiting…
We present a new splitting method for time-dependent convection-dominated diffusion problems. The original convection diffusion system is split into two sub-systems: a pure convection system and a diffusion system. At each time step, a…
The understanding of the underlying dynamical mechanisms which determine the macroscopic laws of heat conduction is a long standing task of non-equilibrium statistical mechanics. A better understanding of the mechanism of heat conduction…
The heat equation is considered in the complex medium consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies an impedance boundary condition is imposed. An equation for the limiting…
This thesis is devoted to the theoretical study of slow thermodynamic processes in non-equilibrium stochastic systems. Its main result is a physically and mathematically consistent construction of relevant thermodynamic quantities in the…
We propose a numerical approach for solving conjugate heat transfer problems using the finite volume method. This approach combines a semi-implicit scheme for fluid flow, governed by the incompressible Navier-Stokes equations, with an…
We present a new method for motion planning for control systems. The method aims to provide a natural computational framework in which a broad class of motion planning problems can be cast; including problems with holonomic and…
This paper deals with the time differential dual-phase-lag heat transfer models aiming, at first, to identify the eventually restrictions that make them thermodynamically consistent. At a first glance it can be observed that the capability…
In this paper thermal conductivity and thermal diffusivity of a two layer system is examined from the theoretical point of view. We use the one dimensional heat diffusion equation with the appropriate solution in each layer and boundary…
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…
We use the multidimensional heat conduction and heat transfer equations to model the temperature distribution of water in a bathtub by solving partial differential equations. We address optimal water addition and bathtub design. First, we…
In this work, we design and analyze a novel, provably conditionally stable, weakly coupled partitioned scheme to solve the conjugate heat transfer (CHT) problem. We consider a model CHT problem consisting of linear advection-diffusion and…
We describe compressible two-phase flows by a single-velocity six-equation flow model, which is composed of the phasic mass and total energy equations, one volume fraction equation, and the mixture momentum equation. The model contains…
Partial Differential Equations (PDEs) are widely used for modeling the physical phenomena and analyzing the dynamical behavior of many engineering and physical systems. The heat equation is one of the most well-known PDEs that captures the…
This work is devoted to the analysis and resolution of a well-posed mathematical model for several processes involved in the artificial circulation of water in a large waterbody. This novel formulation couples the convective heat transfer…
Heating plates describe the transfer of heat from actuators to a target object. In other words, they separate the heat sources and heated object and can be further used to apply a specific heat distribution on this object. Therefore, an…
The local equilibrium thermodynamics is a basic assumption of macroscopic descriptions of the out of equilibrium dynamics for Hamiltonian systems. We numerically analyze the Hamiltonian Potts model in two dimensions to study the violation…
Efficiently enhancing heat conduction through optimized distribution of a limited quantity of high thermal conductivity material is paramount in cooling electronic devices and numerous other applications. This paper introduces a…