Experimental investigation of the Reynolds analogy for high Prandtl number fluid with repeated rib roughness

Reynolds analogy describes the relationship between friction (f/2) and heat transfer (St) owing to their superficial resemblance. However, Reynolds analogy is limited to simple geometries with a Prandtl number (Pr) close to unity. To extend Reynolds analogy, we measured the St and f/2 simultaneously using a high Pr fluid in duct flow in vertical duct flow with repeated rib roughness. The experiments were performed at a fixed value of Pr, 2014, Reynolds number (Re) ranging from 9.1 × 10³ to 9.6 × 10⁴, and relative roughness (e/D) ranging from 0.01 to 0.04. In the high Pr fluid, the St was much lower than f/2, as most of heat exchange occurred in the conduction sublayer, resulting from a thin thermal boundary layer. On the rough surface, both f/2 and St were higher than on the smooth surface. However, the influence of Re and e/D was different. The differences stem from that the corresponding phenomenon to pressure drag in friction does not exist in heat transfer. The extended Reynolds analogy correlation was developed. In addition, the efficiency factor was defined as the ratio of the enhancement rates of St and f/2 on the rough surface to those on the smooth surface. The efficiency factor decreased with Re and e/D, while it increased with Pr.