Related papers: Heat equation on a network using the Fokas method
Many computational studies on hotspot microfluidic cooling devices found in the literature rely on simplified assumptions and conventions that do not capture the full complexity of the conjugate thermal problem, such as constant…
We study heat conduction in a one-dimensional chain of particles with longitudinal as well as transverse motions. The particles are connected by two-dimensional harmonic springs together with bending angle interactions. The problem is…
Thermal conduction has been suggested as a possible mechanism by which sufficient extra heating is provided in radiation-dominated accretion flows. We consider the extreme case in which the generated energy due to the viscosity and the…
This work deals with the problem of determining a non-homogeneous heat conductivity profile in a steady-state heat conduction boundary-value problem with mixed Dirichlet-Neumann boundary conditions over a bounded domain in $\mathbb{R}^n$,…
A novel equation of heat conduction is derived with the help of a generalized entropy current and internal variables. The obtained system of constitutive relations is compatible with the momentum series expansion of the kinetic theory. The…
We examine the modeling, simulation, and optimization of district heating systems, which are widely used for thermal transport using steam or hot water as a carrier. We propose a generalizable framework to specify network models and…
We show that it is possible to construct microscopic-level discrete equations from macroscopic modeling PDEs for heat conduction in one space dimension. The significance of this result is that, in general, one starts from microscopic…
We introduce the heat method for computing the shortest geodesic distance to a specified subset (e.g., point or curve) of a given domain. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of…
We discuss a relativistic model for heat conduction, building on a convective variational approach to multi-fluid systems where the entropy is treated as a distinct dynamical entity. We demonstrate how this approach leads to a relativistic…
A non-Fourier thermal transport regime characterizes the heat conduction in solids with internal structure. Several thermodynamic theories attempt to explain the separation from the Fourier regime in such kind of systems. Here we develop a…
We study heat conduction in a system of hard disks confined to a narrow two dimensional channel. The system is initially in a high density solid-like phase. We study, through nonequilibrium molecular dynamics simulations, the dependence of…
The non-equilibrium thermodynamics of relativistic systems have a rich phenomenology. The simplest phenomenon in the class of dissipative processes is that of heat. This letter presents a brief summary of the efforts made to tackle the…
A physics-informed neural network is developed to solve conductive heat transfer partial differential equation (PDE), along with convective heat transfer PDEs as boundary conditions (BCs), in manufacturing and engineering applications where…
In this paper we consider the homogenization of a time-dependent heat conduction problem on a planar one-dimensional periodic structure. On the edges of a graph the one-dimensional heat equation is posed, while the Kirchhoff junction…
We investigate the properties of a harmonic chain in contact with a thermal bath at one end and subjected, at its other end, to a periodic force. The particles also undergo a random velocity reversal action, which results in a finite heat…
This work addresses the conjugate heat transfer of a simplified PTT fluid flowing past an unbounded sphere in the Stokes regime ($Re = 0.01$). The problem is numerically solved with the finite-volume method assuming axial symmetry, absence…
A method for density-based topology optimization of heat exchangers with two fluids is proposed. The goal of the optimization process is to maximize the heat transfer from one fluid to the other, under maximum pressure drop constraints for…
We introduce a family of Hamiltonian models for heat conduction with and without momentum conservation. They are analytically solvable in the high temperature limit and can also be efficiently simulated. In all cases Fourier law is verified…
In one-dimensional unbounded domains, we prove global existence of strong solutions to the compressible Navier-Stokes system for a viscous and heat conducting ideal polytropic gas, when the viscosity is constant and the heat conductivity…
A dynamic routing policy, referred to as Heat-Diffusion (HD), is developed for multihop uniclass wireless networks subject to random traffic, time-varying topology and inter-channel interference.The policy uses only current condition of…