A Beer-Lambert Law-Based general acceleration approach for numerical computation of radiative heat transfer within silica aerogel

Radiative heat transfer plays a crucial role in heat transfer within silica aerogel. Due to the complex optical properties of silica aerogel, approximate models often introduce non-negligible deviations in radiative thermal conductivity estimation. Although partitioning radiation into spectral bands is adequate for achieving accurate numerical modeling of radiative heat transfer, this approach incurs high computational costs. In this study, a Beer-Lambert law-based general acceleration approach is proposed to simplify the radiative heat transfer calculations in silica aerogel. The proposed approach exploits the significant variation in spectral optical thickness across bands. Specifically, it truncates the source function integration in the incident radiation calculation and neglects contributions from distant regions in bands with large optical thickness. Results show that the proposed approach reduces computational time by up to 33% while keeping the relative deviation in radiative heat flux below 0.01%. Moreover, the computational efficiency further improves as the optical thickness increases.