Heat conduction [1] is usually modeled as a diffusion process embodied in heat conduction equation. The traditional numerical methods [2, 3] for heat conduction problems such as the finite difference or finite element are well developed. However, these methods are based on discretized mesh systems, thus they are inherently limited in the geometry treatment. This chapter describes the Monte Carl...

In this paper, the Method of Fundamental Solutions (MFS) is extended to solve some special cases of the problem of transient heat conduction in functionally graded materials. First, the problem is transformed to a heat equation with constant coefficients using a suitable new transformation and then the MFS together with the Tikhonov regularization method is used to solve the resulting equation.

In the present work, a modified model of heat conduction including higher order of time derivative is derived by extending Green and Naghdi theory without energy dissipation. We introduce two phase lag times to include the thermal displacement gradient and the heat flux in the heat conduction and depict microscopic responses more precisely. The constructed model is applied to s...

Abstract A non-Fourier thermal transport regime characterizes the heat conduction in solids with internal structure. Several thermodynamic theories attempt to explain separation from Fourier such kind of systems. Here we develop a two-temperature model describe principles non-equilibrium thermodynamics. The basic assumption is existence two well-separated length scales system, namely, one relat...

The low temperature radiant systems are very complex because they involve different mechanisms of heat transfer: heat conduction through the walls, heat convection between the heating panel and the indoor air, heat radiation between the heating panel and the surrounding areas, and the heat conduction between the floor and the ground. The main essence of the low-temperature air systems is to pro...

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...