Mathematical and computational fluid dynamics (CFD) investigation of thermo-hydraulic behaviour and cooling performance of an air-cooled server rack under steady information technology (IT) loads

This study presents mathematical and three-dimensional computational fluid dynamics (CFD) assessments of an operational 42U air-cooled server rack under five steady information technology (IT) loads from 10 to 20 kW. The principal contribution is not a new CFD algorithm, but a load-dependent integration of rack-scale thermal, hydraulic, turbulence, convective heat-transfer and facility-energy indicators within a single validated framework. The realizable k–ε model reproduced the measured thermal and hydraulic responses with R 2 = 0.985–0.993 and a maximum Mean Absolute Percentage Error (MAPE) below 3.61%. Increasing IT load raised the maximum rack temperature from 307.6 to 328.8 K and the pressure drop from 35.2 to 68.1 Pa, while rack-average cooling effectiveness decreased from approximately 0.91 to 0.74, corresponding to an 18.7% reduction. Although the inlet condition remained unchanged, the Reynolds number remained approximately 1.92 × 10 5 , whereas the Grashof number increased from 1.64 × 10 10 to 3.76 × 10 10 and the Richardson number from 0.45 to 1.02, demonstrating a progressive shift from predominantly forced convection toward mixed-convection behaviour. The resulting buoyancy-assisted redistribution promoted upper-rack recirculation, hotspot expansion and increasingly localized turbulence and convective cooling. Numerical energy closure remained above 97% for all cases. In contrast to the deteriorating rack-level thermal performance, facility Power Usage Effectiveness (PUE) improved from 1.61 to 1.42 as IT utilization increased. This divergence shows that minimum PUE does not necessarily correspond to the thermally preferable operating state. For the investigated configuration, 15–17.5 kW is therefore identified as a practical compromise operating range between facility energy utilization and rack-level thermal reliability, rather than a universal optimum.