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Supercritical cryogenic hydrogen is being considered as a coolant for certain high heat flux thermal management applications, including hypersonic vehicles such as the National Aero-Space Plane and high power spacecraft systems for the Strategic Defense Initiative. The safety issues associated with hydrogen make testing with this coolant difficult and costly. Supercritical cryogenic helium is an attractive alternate coolant for prototype component testing. This paper presents a comparative analytical study of the behavior of supercritical cryogenic hydrogen and helium coolants. A detailed three-dimensional finite element analysis of a coolant channel in a test panel was used to compare the calculated heat transfer coefficient and panel temperatures for four different, commonly used turbulent flow heat transfer coefficient correlations for supercritical hydrogen and helium.