Analysis of a Hyperbolic Heat Conduction-Radiation Problem With Temperature Dependent Thermal Conductivity

Abstract

This article deals with the analysis of a hyperbolic conduction and radiation heat transfer problem in a planar participating medium. Thermal conductivity of the medium is temperature dependent. Hyperbolic conduction is due to non-Fourier effect. The boundaries of the medium can be either at prescribed temperatures and/or fluxes. With both boundaries insulated, effects of a short pulse internal heat source in the medium are also considered. The problem is analyzed using the lattice Boltzmann method. The finite volume method is employed to compute the radiative information required. Transient temperature distributions in the medium are studied for the effects of various parameters.

Non-Fourier Heat Conduction in Carbon Nanotubes

“…The thermal wave induced by the temporal thermal inertia has been studied in detail by many researchers [3,4]. Later the hyperbolic heat conduction-radiation problem has been studied using lattice Boltzmann method [5]. But it is only the appearance of thermal inertia in the unsteady state, the thermal inertia is not fully described.…”

Macro- to Nanoscale Heat and Mass Transfer: The Lagging Behavior

“…In this paper, a complete sixstep numerical algorithm is introduced for describing the lattice Boltzmann scheme. The problem of hyperbolic conduction and the radiative heat transfer problem in a planar participating medium with a temperature-dependent thermal conductivity are analyzed using the lattice Boltzmann and finite volume schemes [75].…”

“…The hyperbolic conduction and radiation heat transfer problem in a planar participating medium with a temperature-dependent thermal conductivity are analyzed [75]. The hyperbolic heat conduction in a semi-infinite slab with a temperature-dependent thermal conductivity is studied numerically by imposing three types of boundary conditions [76].…”

The dilemma of hyperbolic heat conduction and its settlement by incorporating spatially nonlocal effect at nanoscale

“…To solve hyperbolic heat conductive equation, several numerical approaches are adopted, such as Laplace transform [9], Green's function [1,10,11], electrical network simulation method [12], finite integral transform technique based on the dot product [13], solution structure theorems [8,14,15], space-time discontinuous Galerkin method [16], lattice Boltzmann method [17], multiple scale technique [18], fast precise integration method [19], etc. With the aid of these methods, numerous problems are investigated in the context of HHC law, such as thermal wave phenomena in a thin finite film subjected to nonhomogeneous boundary conditions [14], two-layers slab under periodic boundary temperature with perfect and imperfect thermal contact [12], fast precooling process of a cylindrically shaped food product [20], the effect of a timedependent laser heat source on a moving finite medium [21], HHC problems in an infinitely long layered solid cylinder with radiation surface [22], hyperbolic conduction and radiation heat transfer problem in a planar participating medium [17], thermal waves in a rigid heat conductor [23], a semi-infinite layer in contact with a finite one excited by a modulated heat source [24]. The HHC is also adopted to analyze laser heating or thermal processing of materials employing the internal heat source [21,[25][26][27][28].…”