# Numerical Evaluation of Hot Air Recirculation in Server Rack
## 1 Introduction  
Energy is at the core of the sustainability debate, impacting all three components of sustainability: economic, social, and environmental [1]. In recent years, internet service utilization has increased exponentially, leading to a high energy demand and consumption in data centers. A data center is an environmentally controlled physical space with clean electrical power and network connectivity optimized for hosting servers [2]. Current power consumption trends are continuously increasing to satisfy the growing needs of e-commerce and other novel technologies such as cloud computing [3]. [PERSON] et al. [4] found that global data centers accounted for between 1.1% and 1.5% of the global total electricity consumption. The high demand for computation speed has led to a surge in the utilization of high-power density rack servers (processing and storage ITE) in cloud computation data centers. A third of the total power consumption in data centers does not go towards computation and data storage functions, but towards cooling ITE (servers, storage, and networking) [5]. [PERSON] et al. [6] noted that in traditional data centers, the cooling system infrastructure consumes 40-50% of the data center's total power supply. In most data centers, cooling is provided through air-cooling systems because of their high reliability and low initial capital cost [7]. The air-cooled data center cooling system comprised cooling units (CRAH/CRAC units), air containment, and air-path plenums. The conditioned cold air is supplied to the servers, which are equipped with fans responsible for drawing airfrom the cold aisle through the front air intake into the server to cool the internal components, such as the central processing unit (CPU, memory modules, motherboard, and power supply), and discharge air into the hot aisle [8]. Thus, improving the server cooling efficiency affects the overall data center efficiency. [PERSON] et al. [9] performed an energy analysis of a data center cooling system, and the results revealed an overall cooling system inefficiency of 20%. A substantial portion of the wasted cooling energy is apportioned to local hotspots in data centers [10]. [PERSON] et al. [11] stated that when the server is fully stressed or under maximum IT load, it generates a significant amount of heat, without sufficient cooling capacity it can become a hotspot, which will subsequently lead to a failure. The serve inlet and outlet air temperatures were previously used as indicators of hotspots in the data center. [PERSON] et al. [10] experimentally studied the impact of internal design on the efficiency of IT equipment in a hot aisle containment system. The server CPU and inlet/outlet temperatures were used as indicators to identify hotspots on the server under various operating conditions. [PERSON] et al. [12] found that server IT workload or node arrangement affects the fan speed, where CPU temperatures are used to show the impact. [PERSON] et al. [11] conducted overview research on data center local hotspot management strategies, where non-uniform airflow distribution, unbalanced airflow supply and demand, and airflow were stated as the primary causes for hotspot formation in air-cooled data centers. All these issues cause insufficient cold air supply to the server or negative pressure in front of the server, which eventually draws hot air from the hot aisle to fill the suction side of the server and mix with the cold air. Mixed air increases the inlet air temperature, which subsequently leads to insufficient cooling of the server or the formation of a hotspot (Figure 1). [PERSON] et al. [11] approach accounts for the hot recirculation at rack-level only, where the hot air recirculates by going over the rack to mix in the cold aisle before entering the server. This mixing is likely to occur in non-containerized cold or hot aisles. [PERSON] et al. [10] studied the impact of internal design on the efficiency of IT equipment in the hot aisle containment system.