A numerical and experimental study of the flow fields and convective heat transfer characteristics in communicating channels is performed to gain insight into the operation of compact heat exchange surfaces with interrupted plates. The geometric parameters are selected to excite and sustain the normally damped Tollmien-Schlichting modes. Travelling waves are observed at relatively low Reynolds numbers, inducing self-sustained oscillatory flows that significantly enhance mixing. The critical Reynolds number, at which periodic oscillations are first observed in the fully-developed region of the flow, is determined. The numerical results are obtained by direct numerical simulation of the time-dependent energy and Navier-Stokes equations using a spectral element-Fourier method. The oscillatory heat transfer phenomenon is visualized experimentally using real-time, holographic interferometry. For hydrodynamically fully-developed flow conditions, the temperature fields have been recorded using high-speed cinematography. The experimental visualizations of the thermal waves verify the numerical predictions of the thermal-hydraulic structure and evolution of communicating-channels flows.