Related papers: Heat flow in polygons with reflecting edges

Surface heat flow is a key parameter for the geothermal structure, rheology, and hence the dynamics of continents. However, the coverage of heat flow measurements is still poor in many continental areas. By transforming the stable nonlinear…

We study the short time heat content asymptotics for spectral boundary conditions. The heat content coefficients are shown to be non-local and some preliminary results concerning the structure of the first few terms are given.

Bismuth is one of the rare materials in which second sound has been experimentally observed. Our exact calculations of thermal transport with the Boltzmann equation predict the occurrence of this Poiseuille phonon flow between $\approx$ 1.5…

To simulate the energy balance of coronal plasmas on macroscopic scales, we often require the specification of the coronal heating mechanism in some functional form. To go beyond empirical formulations and to build a more physically…

A series of numerical simulations of Rayleigh-B{\'e}nard convection in a cubic cavity are conducted in order to examine the structure of the thermal boundary layer in case of mixed boundary conditions. The main goal of the study is the…

We consider the nonlinear heat equations with Neumann boundary conditions $$ \begin{cases} u_{t}=\Delta u & \text{in}\ \mathbb{R}_{+}^{4} \times(0, T) ,\\ -\frac{d u}{d x_{4}}(\tilde{x}, 0, t) \ =u^2(\tilde{x}, 0, t)& \text{in}\…

Microwave electromagnetic heating are widely used in many industrial processes. The mathematics involved is based on the Maxwell's equations coupled with the heat equation. The thermal conductivity is strongly dependent on the temperature,…

We present a model for nonlocal diffusion with Neumann boundary conditions in a bounded smooth domain prescribing the flux through the boundary. We study the limit of this family of nonlocal diffusion operators when a rescaling parameter…

Calculating the thermal diffusivity of solid materials is commonly carried out using the laser flash experiment. This classical experiment considers a small (usually thin disc-shaped) sample of the material with parallel front and rear…

We derive the dynamic boundary condition for the heat equation as a limit of boundary layer problems. We study convergence of their weak and strong solutions as the width of the layer tends to zero. We also discuss $\Gamma$-convergence of…

It has recently been shown theoretically that the time-dependent heat conduction equation is form-invariant under curvilinear coordinate transformations. Thus, in analogy to transformation optics, fictitious transformed space can be mapped…

We consider the Navier--Stokes equations for compressible heat-conducting ideal polytropic gases in a bounded annular domain when the viscosity and thermal conductivity coefficients are general smooth functions of temperature. A…

We consider the Dirichlet-Neumann iteration for partitioned simulation of thermal fluid-structure interaction, also called conjugate heat transfer. We analyze its convergence rate for two coupled fully discretized 1D linear heat equations…

Let $S$ be a smooth hypersurface properly embedded in $\mathbb R^N$ with $N \geq 3$ and consider its tubular neighborhood $\mathcal N$. We show that, if a heat flow over $\mathcal N$ with appropriate initial and boundary conditions has $S$…

We study the transition between steady flows of non-cohesive granular materials in quasi-2D bounded heaps by suddenly changing the feed rate. In both experiments and simulations, the primary feature of the transition is a wedge of flowing…

We study the thermal insulation of a bounded body $\Omega\subset\mathbb{R}^n$, under a prescribed heat source $f>0$, via a bulk layer of insulating material. We consider a model of heat transfer between the insulated body and the…

This paper is divided into three parts. The first part focuses on periodic layer heat potentials, demonstrating their smooth dependence on regular perturbations of the support of integration. In the second part, we present an application of…

We study systems containing electrons and nuclei. Based on the fact that the thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such…

New thickness and shape parameters for describing the thermal boundary layer formed by 2-D fluid flow along a heated (cooled) wall are presented. The parameters are based on probability distribution function methodology in which the thermal…

The equations governing the magnetohydrodynamic stagnation point flow toward a non-conducting, thermally insulated, nonporous, linearly stretching sheet are cast in a self similar form. Consistent boundary conditions on the velocity,…