Pore resolved simulations of joule heating in fibrous media using an embedded boundary method

Joule heating has been regarded as an energy-efficient and sustainable method for heating various materials and gases at large scales. The modeling of Joule heating at pore-resolved scales for such systems, however, has been challenging due to intricacies involved in coupling complex electric and thermo-chemical processes in porous media, and modeling heat transfer across different phases in large representative volume elements (RVEs). To this end, we developed an electro-thermal model at the pore scale to study Joule heating effects in large heterogeneous systems. This was achieved using a level set method to implicitly delineate distinct regions within the domain, and an embedded boundary method to facilitate heat exchange across the fluid-solid interface. Moreover, we applied this method to investigate unsteady non-linear electro-thermal effects in non-woven fibrous graphite conductors for RVEs of characteristic lengths 2 mm, having different fiber orientations, porosity (80 % – 90 %) and fiber diameters (10 – 20 μm). The coupled equations were solved numerically and they produced peak temperatures greater than 2000 K resulting in heating rates as high as 80,000 K/s. Moreover, the results depended strongly on the microstructure of the fiber skeleton and current density distribution. Geometries with large fibers (∼ 20 μm) had the highest average and peak temperatures with the mean temperature increasing by 3.9 % while the peak temperature increased by 9.9 % relative to a base geometry with a diameter of 10 μ m. Anisotropic domains on the other hand had the lowest mean and peak temperatures with peak and mean temperatures of 2293 K and 1437.7 K respectively representing a corresponding 12.1 % and 5.1 % drop in the temperatures. An increase in porosity from 80 % to 90 %, however, led to an increase in the peak temperature by 5.1 %.