In the present work, based on half-wall thickness multi-periodic boundary conditions, a 3D fluid-solid coupled heat transfer model considering variable properties and mutual influence between high temperature hot gas and compressed cold air is established to predict the flow and heat transfer in the cross wavy (CW) channels. The present model is verified by comparing the Nusselt numbers of the numerical results with those of experimental results. On the base of model validation, the flow and heat transfer characteristics of the different CW channels are further investigated in a wide Reynolds number range (gas side: 100-2200; air side: 100-2800). The secondary flow which is responsible for the enhancement of heat transfer and the increase of the pressure loss is successfully captured, and its influence on the thermal and flow boundary layers is analyzed. By comparing the heat transfer and pressure loss of five configurations, the effecting law of geometrical parameters is revealed. Based on a large number of simulation results, the correlations of heat transfer and Fanning friction factor involving Reynolds number, Prandtl number and geometrical parameters are proposed using the least-squares method, which are helpful to the design of CW primary surface recuperator in the microturbine. (C) 2018 Elsevier Ltd. All rights reserved.