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We simplify the formalism of Polder and Van Hove [Phys.Rev.B {\bf 4}, 3303(1971)], which was developed to calculate the heat transfer between macroscopic and nanoscale bodies of arbitrary shape, dispersive and adsorptive dielectric…
We consider the model for the distribution of a long homopolymer in a potential field. The typical shape of the polymer depends on the temperature parameter. We show that at a critical value of the temperature the transition occurs from a…
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…
In this paper we study the time differential dual-phase-lag model of heat conduction incorporating the microstructural interaction effect in the fast-transient process of heat transport. We analyse the influence of the delay times upon some…
We consider the scattering problem for an asymmetric composite photonic structure with a component experiencing a thermally driven phase transition. Using a numerical example, we show that if the heating is caused by the incident light, the…
We consider the Cauchy problem for the heat diffusion equation in the whole space consisting of three layers with different constant conductivities, where initially the upper and middle layers have temperature 0 and the lower layer has…
Heating plates describe the transfer of heat from actuators to a target object. In other words, they separate the heat sources and heated object and can be further used to apply a specific heat distribution on this object. Therefore, an…
Structural materials are broadly used in applications such as nuclear vessels, high-temperature processes, and civil construction. Usually, during their placing and lifespan, they may present free or chemically bonded liquid phases in their…
The heat equation is considered in the complex system consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies a Newton-type boundary condition is imposed. An equation for the limiting…
The present paper deals with mathematical models of heat and moisture transport in layered building envelopes. The study of such processes generates a system of two doubly nonlinear evolution partial differential equations with appropriate…
This paper concerns the final value problem for the heat equation under the homogeneous Neumann condition on the boundary of a smooth open set in Euclidean space. The problem is here shown to be isomorphically well posed in the sense that…
The heat transfer model for a one-dimensional supercooled melt during the final stage of solidification is considered. The Stefan problem for the determination of the temperature distribution is solved under the condition that (i) the…
Controlling the temperature in architectures involving nanoparticles and substrates is a key issue for applications involving micro and nanoscale heat transfer. We study the thermal behavior of a single nanoparticle interacting with a flat…
We use Maxwell's equations in a sourceless, inhomogeneous medium with continuous permeability $\mu (\mathbf{r}) $ and permittivity $% \epsilon (\mathbf{r}) $ to study the wave propagation. The general form of the wave equation is derived…
The evolution of multi-mode instabilities in a hypersonic boundary layer and their effects on aerodynamic heating are investigated. Experiments are conducted in a Mach 6 wind tunnel using Rayleigh-scattering flow visualization,…
The present work is the continuation of the investigation of aspects of wave turbulence in preheating we have started in Refs. [1, 2] but considering several classes of inflationary two-fields models. We exhibit the main elements of the…
This paper is concerned with the Cauchy problem of a multivalued ordinary differential equation governed by the hypergraph Laplacian, which describes the diffusion of ``heat'' or ``particles'' on the vertices of hypergraph. We consider the…
We consider the asymptotic solutions of an interface problem corresponding to an elliptic partial differential equation with Dirich- let boundary condition and transmission condition, subject to the small geometric perturbation and the high…
We address the existence and uniqueness of the so-called modified error function that arises in the study of phase-change problems with specific heat and thermal conductivity given by linear functions of the material temperature. This…
We describe a fluctuating surface-current formulation of radiative heat transfer, applicable to arbitrary geometries, that directly exploits standard, efficient, and sophisticated techniques from the boundary-element method. We validate as…