Measuring Transport Coefficients in Heterogeneous and Hierarchical Heat Transfer Devices

Abstract

Experimental determination of transport coefficients, in particular internal heat transfer coefficients, in heterogeneous and hierarchical heat transfer devices such as compact heat exchangers and high surface density heat sinks has posed a persistent challenge for designers. This study presents a unique treatment of the experimental determination of such design data. A new combined experimental and computational method for determining the internal heat transfer coefficient within a heterogeneous and hierarchical heat transfer medium is explored and results are obtained for the case of cross flow of air over staggered cylinders to provide validation of the method. Along with appropriate pressure drop measurements, these measurements allow for thermalfluid modeling of a heat exchanger by closing the volume averaging theory (VAT)based equations governing transport phenomena in porous media, which have been rigorously derived from the lowerscale Navier–Stokes and thermal energy equations. To experimentally obtain the internal 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 flow conditions. The transient fluid phase temperature response is measured. The heat transfer coefficient is then determined by comparing the results of a numerical simulation based on the VAT model with the experimental results. The friction factor is determined through pressure drop measurements, as is usually done. With the lowerscale heat transfer coefficient and friction factor measured, the VATbased equations governing the transport phenomena in the heat transfer device are closed and readily solved. Several configurations of staggered cylinders in cross flow were selected for this study. Results for the heat transfer coefficient and friction factor are compared to widely accepted correlations and agreement is observed, lending validation to this experimental method and analysis procedure. It is expected that a more convenient and accurate tool for experimental closure of the VATbased equations modeling transport in heterogeneous and hierarchical media, which comes down to measuring the transport coefficients, will allow for easier modeling and subsequent optimization of high performance compact heat exchangers and heat sinks for which design data does not already exist.