相关论文: Identification of nonlinear heat conduction laws

We study heat transport in the context of Hamiltonian and related stochastic models with nearest-neighbor coupling, and derive a universal law for the temperature profiles of a large class of such models. This law contains a parameter…

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 continue the study of a model for heat conduction consisting of a chain of non-linear oscillators coupled to two Hamiltonian heat reservoirs at different temperatures. We establish existence of a Liapunov function for the chain dynamics…

A boundary value problem, which could represent a transcendent temperature conduction problem with evaporation in a part of the boundary, was studied to determine unknown thermophysical parameters, which can be constants or time dependent…

This investigation deals with the analysis of stagnation point heat transfer and corresponding flow features of hydromagnetic viscous incompressible fluid over a vertical shrinking sheet. The considered sheet is assumed to be permeable and…

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 consider a non-linear, one-dimensional wave equation system with finite-dimensional stochastic driving terms and with weak dissipation. A stationary process that solves the system is used to model steady-state non-equilibrium heat flow…

A framework for studying the effect of the coupling to the heat bath in models exhibiting anomalous heat conduction is described. The framework is applied to the harmonic chain with momentum exchange model where the non-trivial temperature…

We consider a model of heat conduction which consists of a finite nonlinear chain coupled to two heat reservoirs at different temperatures. We study the low temperature asymptotic behavior of the invariant measure. We show that, in this…

The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but…

We consider a semi-linear heat equation with Dirichlet boundary conditions and globally Lipschitz nonlinearity, posed on a bounded domain of R^N (N $\in$ N *), assumed to be an unknown perturbation of a reference domain. We are interested…

We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence,…

We prove existence, uniqueness and regularity of solutions of nonlocal heat equations associated to anisotropic stable diffusion operators. The main features are that the right-hand side has very few regularity and that the spectral measure…

We study heat transport in a chain of harmonic oscillators with random elastic collisions between nearest-neighbours. The equations of motion of the covariance matrix are numerically solved for free and fixed boundary conditions. In the…

In the study of the heat transfer in the Boltzmann theory, the basic problem is to construct solutions to the steady problem for the Boltzmann equation in a general bounded domain with diffuse reflection boundary conditions corresponding to…

We review recent developments in nonlinear quantum transport through nanostructures and mesoscopic systems driven by thermal gradients or in combination with voltage biases. Low-dimensional conductors are excellent platforms to analyze both…

We study a Boussinesq system in a bounded domain with an outlet boundary portion where fluid can leave or re-enter. On this boundary part, we consider a do-nothing condition for the fluid flow, and a new artificial condition for the heat…

We consider convection in an internally heated layer of fluid that is bounded below by a perfect insulator and above by a poor conductor. The poorly conducting boundary is modelled by a fixed heat flux. Using solely analytical methods, we…

The effects of MHD boundary layer flow of non-linear thermal radiation with convective heat transfer and non-uniform heat source/sink in presence of thermophortic velocity and chemical reaction investigated in this study. Suitable…

The flow of fluid confined between a heated rotating cylinder and a cooled stationary cylinder is a canonical experiment for the study of heat transfer in engineering. The theoretical treatment of this system is greatly simplified if the…