Experimental and theoretical studies in recent years have shown that heat transfer in nanostructures differs significantly from in macrostructures. This paper summarizes some of the past experimental and modeling work and our current understanding of the heat conduction mechanisms in nanostructures. Applications of the nanoscale heat conduction phenomena in energy conversion and photothermal sp...

Some noteworthy and historical perspectives and overview of macroscale and microscale heat transport behavior in materials and structures are presented. The topic of heat waves is also discussed. The signiicance of constitutive models for both macroscale and microscale heat conduction are described in conjunction with generalizations drawn concerning the physical relevance and the role of relax...

We investigate the well-posedness, the exponential stability, or the lack thereof, of thermoelastic systems in materials where, in contrast to classical thermoelastic models for Kirchhoff type plates, two temperatures are involved, related by an elliptic equation. The arising initial boundary value problems for different boundary conditions deal with systems of partial differential equations in...

We consider a differential model describing nonisothermal fast phase separation processes taking place in a three-dimensional bounded domain. This model consists of a viscous Cahn-Hilliard equation characterized by the presence of an inertial term χtt, χ being the order parameter, which is linearly coupled with an evolution equation for the (relative) temperature θ. The latter can be of hyperbo...

The effects of metal foams on heat transfer enhancement in Phase Change Materials (PCMs) are investigated. The numerical investigation is based on the two-equation non-equilibrium heat transfer model, in which the coupled heat conduction and natural convection are considered at phase transition and liquid zones. The numerical results are validated by experimental data. The main findings of the ...

In this paper we propose an asymptotic preserving scheme for a family of Friedrichs systems on unstructured meshes based on a decomposition between the hyperbolic heat equation and a linear hyperbolic which not involved in the diffusive regime. For the hyperbolic heat equation we use asymptotic preserving schemes recently designed in [FHSN11]-[BDF11]. To discretize the second part we use classi...

the present study is concerned with optimal shape determination of inhomogeneous and temperature dependent domains under steady state heat conduction. such situations are important in many thermal design problems, especially in shape design of electronic components and chips. in the present paper, we formulate the shape optimization problem based on volume minimization of heat conductive materi...

The usual way to model heat conduction is to solve a partial differential equation (PDE) with boundary conditions (BCs), i.e., a boundary value problem (BVP). For the case of steady-state heat conduction in a homogeneous isotropic solid with thermal conductivity independent of temperature and with no heat source inside the solid, temperature T (x, y, z) in the solid verifies Laplace equation [5] :

The paper deals with the inverse determination of heat source in an unsteady heat conduction problem. The governing equation for the unsteady Fourier heat conduction in 2D region with unknown internal heat source is known as the inverse boundary-initial-value problem. The identification of strength of the heat source is achieved by using the boundary condition, initial condition and a known val...

In this paper we study the spatial behavior of solutions to the equations obtained by taking formal Taylor approximations to the heat conduction dual-phase-lag and three-phaselag theories, reflecting Saint-Venant’s principle. Depending on the relative order of derivation with respect to the time we propose different arguments. One is inspired by the arguments for parabolic problems and the othe...