Numerical Study Using Microstructure Based Finite Element Modeling of the Onset of Convective Heat Transfer in Closed-Cell Polymeric Foam

Abstract

The thermal performance of closed-cell foams as an insulation device depends on the thermal conductivity. In these systems, the heat transfer mode associated with the convective contribution is generally ignored, and studies are based on the thermo-physical properties that emerge from the conductive contribution, while others include a term for radiative transport. The criterion found in the literature for disregarding convective heat flux is the cell diameter; however, the cell size for which convection is effectively suppressed has not been clearly disclosed, and it is variously quoted in the range 3–10 mm. In practice, changes in thermal conductivity are also attributed to the convection heat transfer mode; hence, natural convection in porous materials is worthy of research. This work extends the field of study of conjugate heat transfer (convection and conduction) in cellular materials using microstructure-based finite element analysis. For air-based insulating materials, the criteria to consider natural convection (Ra=103) is met by cavities with sizes of 9.06 mm; however, convection is developed into several cavities despite their sizes being lower than 9.06 mm, hence, the average pore size that can effectively suppress the convective heat transfer is 6.0 mm. The amount of heat transported by convection is about 20% of the heat transported by conduction within the foam in a Ra=103, which, in turn, produces an increasing average of the conductivity of about 4.5%, with respect to a constant value.

Study on the Coupled Heat Transfer of Conduction, Convection, and Radiation in Foam Concrete Based on a Microstructure Numerical Model

“…Foam concrete can be regarded as a two-phase material composed of a hardened cementitious matrix and air; macroscopically, the inhomogeneous material can be considered as a homogeneous medium [50]. Therefore, heat transfer in foam concrete includes thermal conduction through the solid matrix, thermal conduction and convection in the gas-filled pores, and thermal radiation between different parts of the material.…”

“…Although existing numerical models can consider the randomness and complexity of the microstructure, they only address heat transfer problems under pure conduction. There is limited involvement in the study of convective heat transfer and radiative coupled heat transfer within pores, and no studies have been conducted on convective and radiative heat transfer in foam concrete using real microstructures [50].…”

Effect of Crosslink Density on Thermal Aging of Bio-Based Rigid Low-Density Closed-Cell Polyurethane Foams

“…Of the three principal heat transport mechanisms in foamsconduction (by the solid cell wall material and by gases filling the foam cells), radiation, and convection thermal conductivity in low-density PU foams is governed by the first two, because heat transfer by convection is negligible at the sub-millimeter cell size and moderate temperature gradients characteristic for such foams. , The thermal conductivity λ f of homogeneous low-density foams can be accurately approximated by the sum of the respective conductivities ,, λ normalf = λ normals normalo normall + λ normalr normala normald + ε λ normalg where the solid conductivity is denoted by λ sol , that due to radiation by λ rad and λ g stands for the conductivity of cell gas. The contribution of gas conductivity to that of the foams is proportional to foam porosity ε, which can be expressed by the foam and solid densities as ε = 1 − ρ f / ρ s .…”

“…Of the three principal heat transport mechanisms in foams�conduction (by the solid cell wall material and by gases filling the foam cells), radiation, and convection� thermal conductivity in low-density PU foams is governed by the first two, because heat transfer by convection is negligible at the sub-millimeter cell size and moderate temperature gradients characteristic for such foams. 6,26 The thermal conductivity λ f of homogeneous low-density foams can be accurately approximated by the sum of the respective conductivities 6,25,27…”