A 3D microscale model for predicting the heat flow through porous building materials

Highly porous materials find frequent use in numerous thermal applications, due to their relatively high resistance to heat transfer. Typical examples include the automotive industry and aerospace engineering for the protection of thermally sensitive components, but also the building industry to reduce the heating energy demand of buildings. However, with the built environment still being responsible for almost 40 % of global CO2 emissions, better performing thermal porous building materials are highly necessary. The heat flow through such materials is usually described with Fourier’s law using the macroscopic effective thermal conductivity (ETC), while in fact it originates from the aggregation of several complex heat transfer mechanisms at the pore scale: conductive heat transfer through the matrix and through the gaseous phase in the pores, thermal radiation between the pore walls and convective heat transfer via the gaseous phase. The relative contribution of these heat transfer mechanisms depends strongly on the microstructural parameters, i.e. porosity, pore size, matrix connectivity etc. [1,2]. A correct understanding of the direct relation between these microstructural parameters and the total heat transfer is therefore crucial in the development of improved thermal materials. However, current models attempting to study this influence still exhibit large errors due to 2D simplifications, neglect of thermal radiation or their very limited applicability for a restricted class of materials. This study presents a newly developed 3D FEM model for simulating the heat transfer through a porous structure on the micro-scale. The model is based on 3D voxel images of the material as input for the meshing code, hence ensuring the incorporation of the true microstructural parameters. Moreover, this approach allows performing simulations on both real materials using micro-CT scanning and synthetic materials using random generation algorithms. Other needed geometrical parameters are acquired from the 3D voxel image via a set of image processing routines. After the meshing procedure the heat flow is simulated using a finite element code. A method for modelling thermal radiation as a diffusion process at the pore scale is investigated, resulting in a definition of a radiative conductivity coefficient as a function of geometrical and physical parameters. The model is validated by comparing the simulation results of several elementary pore structures with the values given by conventional analytical models and other numerical simulation packages, showing good agreement. An in-depth study of the influence of the mesh and voxel discretization is performed for a correct and optimal use of the model. Subsequently, the model is used for a preliminary study on the influence of different material parameters, including porosity, pore size distribution, ratio of solid and gaseous thermal conductivity etc. This results in a clearer understanding of the microscopic parameters and their effect on the macroscopic thermal conductivity. [1] Bakker, K. (1997). Using the Finite Element Method to Compute the Influence of Complex Porosity and Inclusion Structures on the Thermal and Electrical Conductivity. International Journal of Heat and Mass Transfer, 10 (15), 3503-3511. [2] Carson, J. K., Lovatt, S. J., Tanner, D. J. & Cleland, A. C. (2003). An analysis of the influence of material structure on the effective thermal conductivity of theoretical porous materials using finite element simulations. International Journal of Refrigeration, 26 (8), 873-880.status: publishe