Related papers: Heat equation on a network using the Fokas method

An inverse problem for a stationary heat transfer process is studied for a totally isolated bar on its lateral surface, made up of two consecutive sections of different, isotropic and homogeneous materials, perfectly assembly, where one of…

We present a new analytic expression for the heat current through a general harmonic network coupled with Ohmic reservoirs. We use a new method that enables us to express the stationary state of the network in terms of the eigenvectors and…

The purpose of this work is to produce a family of equations describing the evolution of the temperature in a rigid heat conductor. This is obtained by means of successive approximations of the Fourier law, via memory relaxations and…

Heat conduction experiments are performed in order to identify effects beyond Fourier. Two experimental setups are discussed. First, a simple experiment by a heterogeneous material is investigated from the point of view of generalized heat…

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…

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…

We show the existence and optimal regularity of the optimal temperature configuration in a problem in heat conduction with minimal temperature constraint, interior heating and exterior insulation. Regularity of the two free boundaries is…

We present a simple experiment on thermal diffusion in metal rods that can be used to integrate computation into the advanced lab. An analytical solution exists for the transient heat conduction in an infinite rod with a delta function heat…

A heat conduction equation on a lattice composed of nodes and bonds is formulated assuming the Fourier law and the energy conservation law. Based on this equation, we propose a higher-order topological heat conduction model on the breathing…

A solution to the heat equation between Riemannian manifolds, where the domain is compact and possibly has boundary, will not leave a compact and locally convex set before the image of the boundary does.

The fundamental dynamic stability of heat conduction theories beyond Fourier is analyzed in the framework of nonequilibrium thermodynamics. It is shown, that the thermodynamic framework, concave entropy and nonnegative entropy production,…

We investigate heat conduction and energy relaxation in an InAs semiconductor nanowire using a hybrid semiconductor-superconductor architecture. Local electronic temperatures are measured with an in-situ grown quantum dot thermometer, while…

I revisit the exactly solvable Kipnis--Marchioro--Presutti model of heat conduction [J. Stat. Phys. 27 65 (1982)] and describe, for one-dimensional systems of arbitrary sizes whose ends are in contact with thermal baths at different…

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. Using equilibrium…

A solution of the heat equation with a distribution-valued potential is constructed by regularization. When the potential is the generalized derivative of a H\"{o}lder continuous function, regularity of the resulting solution is in line…

We study the non equilibrium statistical properties of a one dimensional hard-rod fluid undergoing collisions and subject to a spatially non uniform Gaussian heat-bath and periodic potential. The system is able to sustain finite currents…

We study heat conduction in (n, 0)/(2n, 0) intramolecular junctions by using molecular dynamics method. It is found that the heat conduction is asymmetric, namely, heat transports preferably in one direction. This phenomenon is also called…

Within the theory of interacting continua, we develop a model for a heat conducting mixture of two interacting fluids described in terms of the densities and the velocities for each fluid and the temperature field for the mixture as a…

We present a new stochastic analysis for steady and transient one-dimensional heat conduction problem based on the homogenization approach. Thermal conductivity is assumed to be a random field K consisting of random variables of a total…

This article presents a theoretical analysis of a one-dimensional heat transfer problem in two layers involving diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, and heat generation due…