Solid phase thermal conductivity of a resorcinol formaldehyde aerogel

This example illustrates how to estimate the effective solid phase thermal conductivity of a resorcinol formaldehyde (rf) aerogel developed at DLR [1] by virtual materials testing.

Problem statement:

Considering a model domain without internal heat source, as shown below, the steady-state heat equilibrium reads

According to Fourier's law, the constitutive equation relating heat flux and temperature gradient is given by

.

Virtual testing:

A generic model domain of the rf aerogel microstructure with 1 mm edge length and 60% porosity was generated using Mote3D [2] (see below).

The microstructure model was then discretized using voxel elements. Three uncoupled steady-state finite element heat transfer analyses using an imposed temperature gradient of 100 K and periodic boundary conditions

were performed to estimate the effective thermal conductivity of the microstructure model in each spatial direction, assuming a bulk thermal conductivity of 0.5 Wm^-1K^-1 for rf resin.

Results:

Plots of the resulting heat flux distribution computed during the finite element heat transfer analyses are shown below.

The effective heat fluxes across the boundary in each of the three spatial directions were determined by volume averaging

With the resulting effective heat fluxes and the known temperature gradient, the direction-dependent effective thermal conductivities were found to be

The variations in the effective thermal conductivities are attributed to the limited size of the microstructure model. For comparison, the solid phase thermal conductivity of a rf aerogel with approximately 83% porosity reported in literature is 0.007 Wm^-1K^-1 at room temperature [3].

References:

[1] J. Laskowski, B. Milow and L. Ratke, Novel stiff aerogel-aerogel composites for thermal insulation applications, 20th International Conference on Composite Materials, 2015.
[2] H. Richter, Mote3D: an open-source toolbox for modelling periodic random particulate microstructures, Modelling Simul. Mater. Sci. Eng. 25 (3), 2017.
[3] K. E. Wilkes, R. B. Dinwiddie and R. S. Graves (Eds.), Thermal Conductivity 23, Technomic Publishing, 1996.