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Data centers are facilities that house large numbers of computer servers that dissipate high power. Due to varying operational loads their efficient thermal management is a big challenge that needs to be addressed. Computational modeling using a CFD code is a very useful technique for studying the cooling requirements for different data center power loading and room configuration. Much of the existing numerical modeling research literature focuses on simulating the data center thermal environment with constant operating conditions. In reality, data centers have highly time dependent operating conditions i.e. fluctuations in server power and A/C flow rates. Recent computational studies have shown that time dependent fluctuations in server rack power can lead to rapid fluctuations in rack inlet temperatures. For optimal data center performance, the cold air supply should also increase or decrease with the rack power. In this paper, a detailed numerical study of data center thermal performance is presented with time dependent power and cooling air supply conditions. Results are presented for average rack inlet temperatures as a function of time for different case studies. Fluctuations in inlet temperatures are explained by evaluation of the temperature and flow fields in a basic data center configuration.