Related papers: Heat flow in polygons with reflecting edges
The exact evolution in time and space of a distribution of the temperature (or density of diffusing matter) in an isotropic homogeneous medium is determined where the initial distribution is described by a piecewise polynomial. In two…
In this article, we present a model of heat transfer occurring through a li\-quid film flowing down a vertical wall. This new model is formally derived using the method of asymptotic expansions by introducing appropriately chosen…
We give large-time asymptotic estimates, both in uniform and $L^1$ norms, for solutions of the Dirichlet heat equation in the complement of a bounded open set of $\mathbb{R}^d$ satisfying certain technical assumptions. We always assume that…
The influence of fixed temperature and fixed heat flux thermal boundary conditions on rapidly rotating convection in the plane layer geometry is investigated for the case of stress-free mechanical boundary conditions. It is shown that…
We give a rigorous derivation of Fourier's law from a system of closure equations for a nonequilibrium stationary state of a Hamiltonian system of coupled oscillators subjected to heat baths on the boundary. The local heat flux is…
The swelling dynamics of polymer gels are characterized by the (collective) diffusion coefficient $D$ of the polymer network. Here, we measure the temperature dependence of $D$ of polymer gels with controlled homogeneous network structures…
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…
We study the existence and uniqueness of a solution to a linear stationary convection-diffusion equation stated in an infinite cylinder, Neumann boundary condition being imposed on the boundary. We assume that the cylinder is a junction of…
We derive the incompressible Euler equations with heat convection with the no-penetration boundary condition from the Boltzmann equation with the diffuse boundary in the hydrodynamic limit for the scale of large Reynold number. Inspired by…
We study the following nonlinear heat equation with damping and pumping effects (a reaction-diffusion equation) posed on a bounded simply connected convex domain $\Omega \subset \mathbb{R}^d$, $d \geq 1$ with Lipschitz boundary…
Numerical simulation has been conducted for the chaotic flow in a 3D closed-loop pulsating heat pipe (PHP). Heat flux and constant temperature boundary conditions were applied for evaporator and condenser sections, respectively. Water and…
In this paper, we consider solutions of the backward heat equation with Ricci flow on manifolds as a type of infinite dimensional limit of solutions of a wave equation on a larger manifold with an analysis of wavefront set. Specifically,…
We investigate the stationary nonequilibrium states of a quasi one-dimensional system of heavy particles whose interaction is mediated by purely elastic collisions with light particles, in contact at the boundary with two heat baths with…
This paper investigates the Knudsen layer equation in half-space, arising from the hydrodynamic limit of the Boltzmann equation to fluid dynamics. We consider the Maxwell reflection boundary condition with accommodation coefficient…
Thermoelectric conductance of an edge mode is investigated. The edge modes of a $2D $ and $3D$ two band model with parabolic dispersion is considered. For the the one dimensional non interacting fermions the thermal conductivity computed…
In the paper, we investigate the nonlinear thermoelasticity model in two- and three-dimensional convex and bounded domains. We propose new boundary conditions for the displacement. These conditions are not usual in thermoelasticity.…
We present a very quick and powerful method for the calculation of heat-kernel coefficients. It makes use of rather common ideas, as integral representations of the spectral sum, Mellin transforms, non-trivial commutation of series and…
Let $M$ be a complete Riemannian manifold and $D\subset M$ a smoothly bounded domain with compact closure. We use Brownian motion and the classic results on the Stieltjes moment problem to study the relationship between the Dirichlet…
This paper deals with the heat equation posed in a bounded regular domain coupled with a dynamical boundary condition of reactive-diffusive type, involving the Laplace-Beltrami operator. We prove well-posedness of the problem together with…
A simple vibrational model of heat transfer in two-dimensional (2D) fluids relates the heat conductivity coefficient to the longitudinal and transverse sound velocities, specific heat, and the mean interatomic separation. This model is…