Thermal systems often involve multiple spatial and temporal scales, where transport information from one scale is relevant at others. Optimized thermal design of such systems and their control require approaches for their rapid simulation. These activities are of increasing significance due to the need for energy efficiency in the operation of these systems. Traditional full-field simulation methodologies are typically unable to resolve these scales in a computationally efficient manner. We summarize recent work on simulations of conjugate transport processes over multiple length scales via reduced order modeling through approaches such as compact finite elements and proper orthogonal decomposition. In order to incorporate the influence of length scales beyond those explicitly considered, lumped models are invoked, with appropriate handshaking between the two frameworks. We illustrate the methodology through selected examples, with a focus on information technology systems.
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