The Cross-Wavy primary surface heat exchanger is one of the most promising candidates for microturbine recuperators. In this paper, naphthalene sublimation experiments are performed for Cross-Wavy channels in a wind tunnel. The experimental results indicate that the entrance region has a small "effect on the unit-averaged heat transfer coefficient of whole Cross-Wavy channels. Correlations of Nusselt number and friction factor in the Cross-Wavy channel are obtained. However, only the Cross-Wavy channel with a large equivalent diameter is tested because the actual Cross-Wavy channels are very complicated and small. Therefore, based on the similarity rules, five Cross-Wavy channels with similar structures but different equivalent diameters are further investigated by numerical simulations. The numerical results indicate that the Cross-Wavy channels with similar structures but different equivalent diameters have similar thermal -hydraulic performance in the studied Reynolds number range. (C) 2016 Elsevier Ltd. All rights reserved.