Obtaining Experimental Closure for the VAT-Based Energy Equations Modeling a Heat Sink as a Porous Medium

Experimentally determining internal heat transfer coefficients in porous structures has been a challenge in the design of heat exchangers. In this study, a novel combined experimental and computational method for determining the internal heat transfer coefficient within a heat sink is explored and results are obtained for air flow through basic pin fin heat sinks. These measurements along with the pressure drop allow for thermal-fluid modeling of a heat sink by closing the Volume Averaging Theory (VAT)-based governing equations, providing an avenue towards optimization. To obtain the heat transfer coefficient the solid phase is subjected to a step change in heat generation rate via induction heating, while the fluid flows through under steady state conditions. The fluid phase temperature response is measured. The heat transfer coefficient is determined by comparing the results of a numerical simulation based on volume averaging theory with the experimental results. The only information needed is the basic material properties, the flow rate, and the experimental data. The computational procedure alleviates the need for internal solid and fluid phase temperature measurements, which are difficult to make and can disturb the solid-fluid interaction. Moreover, a simple analysis allows us to proceed without knowledge of the heat generation rate, which is difficult to determine precisely. Multiple pin fin heat sink morphologies were selected for this study. Moreover, volume averaging theory scaling arguments allow a single correlation for both the heat transfer coefficient and friction factor that encompass a wide range of pin fin morphologies. It is expected that a precise tool for experimental closure of the VAT-based equations modeling a heat sink as a porous medium will allow for better modeling, and subsequent optimization, of heat sinks.