Periodic channels with different shapes of straight rib are abstracted from different types of high-efficiency heat exchangers.The heat transfer and fluid flow in the periodic rectangular straight rib channel (A) and the semi-circular straight rib channel (B) were simulated based on the unsteady-state mathematical model under the assumption of periodically fully developed flow.Meanwhile, the heat transfer properties and the demonstrated nonlinear characteristics in two different channels were compared.A low Reynolds number Re, two-dimension, laminar forced convection model was adopted when calculated.It is found that when Re is small, the flow and heat transfer present a steady state;when Re is larger than the critical value, unsteady oscillation occurs, and the system shows rich nonlinear phenomena.In the range of calculation, channel A has experienced steady and periodic oscillation phases with the increase of Re;channel B has experienced steady, periodic oscillations, quasi-periodic oscillations and chaos with the increase of Re.