Experimental Investigation of Mixed Convective Heat Transfer from Two Heated Copper Cylinders in a Metal Foam-Filled Vented Duct

Multi-heat-source thermal management in compact electronic and process systems increasingly relies on porous metal inserts to intensify convective transport, yet experimental data for duct-embedded configurations that combine mixed convection, multiple heat sources, and high-porosity metal foam remain scarce. To address this gap, we experimentally investigate mixed convective heat transfer from two heated copper cylinders embedded in a high-porosity (95%, 40 PPI) open-cell copper metal foam inside a vented acrylic duct, using a spatially resolved twelve-point thermocouple array together with directly measured air velocity and static pressure. Following review, all cylinder-scale dimensionless groups are defined on a single characteristic length, the cylinder diameter D: ReD = ρVD/μ, GrD = gβ(Ts − T∞)D3/ν2, RiD = GrD/ReD2 and Nu = hD/k. Five fan settings, with velocities measured by a calibrated low-range thermal anemometer (0.05–1 m/s range), gave ReD = 117–498 and RiD = 0.204–5.200; all five cases lie within the mixed-convection band 0.1 ≤ Ri ≤ 10. The average Nusselt number, obtained from electrical power and measured temperatures and therefore independent of the velocity measurement, increased from 32 to 58 across the fan settings. In terms of the indicated ReD it follows Nu = 4.68 ReD0.399 (R2 = 0.978, five points); so, this fit is a provisional description of the present dataset and not a design correlation. Based on this preliminary comparison, the measured Nu exceeds the classical Hilpert correlation by an apparent factor of 467–541%. This discrepancy reflects a combination of inferred mechanisms: the foam’s extended surface area, duct confinement, cylinder interaction, and the use of a foam-embedded temperature proxy, and should not be interpreted as a direct measure of the foam’s intrinsic heat transfer coefficient. The static pressure drop across the foam follows a Darcy–Forchheimer relation, ΔP = 95.7V + 92.8V2 (Pa), analyzed on the foam thickness Lf, which is the physically appropriate length scale for the porous matrix. These results provide original, design-oriented experimental data on the thermal-hydraulic behavior of a dual-cylinder, foam-filled vented duct, together with a preliminary correlation and clearly identified limitations, including an air-side energy-balance imbalance whose cause could not be verified, to guide future generalization. To isolate the individual contributions of the foam, duct confinement, and cylinder interaction, additional baseline experiments were performed. At ReD = 348, the empty-duct configuration yields Nu = 15.4 (+90% over the unconfined Hilpert baseline), while the foam-filled configuration yields Nu = 46.0 (+467% over Hilpert), with a corresponding Performance Evaluation Criterion (PEC) of 0.91, indicating a substantial thermal gain at the cost of a significant hydraulic penalty. The air-side energy balance does not close: the air-side heat gain computed from the point-measured outlet velocity and temperature exceeds the electrical input by 15–180%. Thermocouple radiation error was bounded at about 1–3 K and excluded as the cause; the discrepancy is attributed, without direct verification, to non-representative single-point sampling of the outlet flow, and it does not affect the electrically derived Nusselt numbers.