Reynolds analogy in a packed bed for a high Prandtl number fluid

The Reynolds analogy, which correlates fluid friction (pressure drop) and heat transfer, is limited to fluids with a Prandtl number (Pr) close to 1 and to simple geometries. To extend its application to packed beds, we simultaneously measured the heat transfer rate and pressure drop in a packed bed using a high Pr fluid. The experiments were conducted for, Reynolds numbers (Re_dh) ranging from 20 to 5,004 and bed height to pebble diameter ratios ranging from 5 to 30 with a fixed Pr value of 2014. Contrary to expectations for similar fluid friction (f/2) and heat transfer rate (St) in a packed bed, f/2 was significantly higher than St due to various flow mixings caused by interaction with pebbles. This discrepancy was attributed to the thin thermal boundary layer adjacent to the pebble surfaces, due to the very high Pr. Even after applying the Colburn analogy, which corrects the Pr effect, the discrepancy remained. This is because a phenomenon corresponding to pressure drag in momentum transfer does not exist in heat transfer. Utilizing the experimental data, Reynolds analogy correlations for packed beds were developed.