SUMMARY

Data centers are computing infrastructure facilities used by industries with large data processing needs and the rapid increase in power density of high performance computing equipment has caused many thermal issues in these facilities. Systems-level thermal management requires modeling and analysis of complex fluid flow and heat transfer processes across several decades of length scales. Conventional computational fluid dynamics and heat transfer techniques for such systems are severely limited as a design tool because their large model sizes render parameter sensitivity studies and optimization impractically slow. The traditional proper orthogonal decomposition (POD) methodology has been reformulated to construct physics-based models of turbulent flows. Orthogonal complement POD subspaces were developed to parametrize inhomogeneous boundary conditions and a flux matching procedure was devised to overcome the limitations of Galerkin projection methods. An implicit coupling procedure was developed to link the temperature and velocity fields and further extend the low- dimensional modeling methodology to conjugate forced convection heat transfer. The overall framework was able to reduce model size by a factor of 10 4 while still retaining greater that 90% accuracy over the domain. Rigorous a posteriori error bounds were formulated by using the POD subspace to partition the error contributions and dual residual methods were used to show that the flux matching procedure is a computationally superior approach for low-dimensional modeling of steady turbulent convection. To efficiently model large-scale systems, individual reduced-order models were coupled using flow network modeling as the component interconnection procedure. The development of handshaking procedures between low-dimensional component models lays the foundation to quickly analyze and optimize the modular systems encountered in electronics thermal management.