Numerical study of effective heat conductivities of foams by coupled conduction and radiation

Abstract

E↵ective thermal conductivities (ETC) under vacuum were computed numerically on 3D blocks of open-cell foams either obtained by X-ray tomography or generated by Computer-Aided Design (CAD) with ideal geometries.For the first time a Monte-Carlo/Random Walk code accounting for the coupling of conduction in the solid phase and of radiation in the pore space has been used. The whole range of conduction/radiation ratio, parameterized by a Nusselt number, has been scanned; a law relating the ETC to this parameter has been obtained. In all cases the conductive and radiative contributions are additive. The slope of the radiative contribution to the ETC is found to display a distinct behavior, depending on whether radiation or conduction dominates. The low-temperature regime has an emissivity-dependent ETC slope, while the high-temperature regime does not.The critical ratio between both regimes is related to the ratio between cell and strut diameters. In all cases, it is found that the ETC anisotropy decreases with temperature. Closing some windows enhances conduction parallel to the closing walls and reduces radiation perpendicular to them. This e↵ect is shown to influence the ETC eigendirections in actual media.

Modeling the Flash Method by Using a Conducto-Radiative Monte Carlo Algorithm : Application to Porous Media

“…These results show that an effective optical thickness β ef f , characteristic of the radiative transfer of the medium, is not a pure constant. It is function of the emissivity, as it was also very recently evidenced by Vignoles et Ortona [15].…”

Numerical quantification of coupling effects for radiation-conduction heat transfer in participating macroporous media: Investigation of a model geometry

“…In that case the interaction will be limited to the interfaces. The vanishing of the coupling effects is also confirmed by [31]. Results for higher optical thicknesses could only be obtained by using a refined mesh according to the logic outlined in Section 4.2.…”

“…Interaction between the two modes is limited to the interfaces and becomes negligible. A similar case where the interaction is limited to the interface, namely the situation of an opaque phase and a transparent phase was investigated in [31] which concluded that no coupling effects exist in that case.…”

Toward the Use of Symbolic Monte Carlo for Conduction-Radiation Coupling in Complex Geometries

“…The solid properties are homogeneous and independent of temperature: λ is the thermal conductivity, k a the absorption coefficient and k s the scattering coefficient. The fluid is assumed perfectly mixed at a known temperature T f : the boundary layer is only represented using a convective heat transfer coefficient h at the solid/fluid interface (equation (3)). Incoming radiation at the boundary of this system is fixed by assuming a black bounding box (∂Ω) at temperature T ∞ .…”

“…Numerous research efforts have been reported, nearly since the origin of the Monte Carlo method, attempting to extend this handling of physically and geometrically highly refined objects to other heat transfer modes [1,2]. Todays specifically, numerous theoretical developments are being proposed along this line [3,4] trying to address the geometrical refinement of multiscale engineering requirements. Among these theoretical attempts, Fournier et al [5] proposed a statistical formulation starting from Green formalism that allows the extension to combined heat transfer of the computer graphics techniques used for rendering images of complex scenes.…”