The effect of surface vibrations on the propulsion augmentation and resistance in the relative movement of parallel plates has been studied. The analysis was focused on monochromatic waves and laminar flows. The effectiveness of the vibrations was gauged by determining the external force required to maintain the movement of one of the plates at a prescribed velocity. It is shown that waves propagating upstream always increase the resistance but the flow response to waves propagating downstream is more intricate and is a function of the flow Reynolds number. In general, waves must be sufficiently fast to reduce the flow resistance. This leads to a natural division between slow and fast waves; a characterization that is helpful for flows at a sufficiently small Reynolds number Re. An increase in Re brings into play the complication of possible resonances with the natural flow frequencies. Resonances are not possible with waves faster than the plate velocity and these supercritical waves generally decrease the flow resistance. More complex flow responses can occur with slower (subcritical) waves which tend to increase the flow resistance. A complete elimination of the resistance is possible if the waves are of sufficiently short wavelength and travel quickly. This suggests that our mechanism has great potential in the development of propulsion augmentation systems. None of the waves produced net energy savings.

Propulsion generated by wall vibrations in the form of travelling waves was investigated. A model problem consisting of two parallel plates free to move with respect to each other was used. Vibrations of one of these plates generated movement of the other plate whose velocity was used to assess the effectiveness of such propulsion. Three types of responses were identified: a "sloshing" response for long waves, a "moving wall" response for short waves, and an "intermediate" response for in-between waves. Long and transitional waves produced propulsion of marginal interest. Short waves produced effective propulsion with the velocity of the plate increasing proportionally to the second power of the wave number and the second power of the amplitude, and approximately proportionally to the wave velocity. The vibrating wall appeared in this limit to the bulk of the fluid as a moving wall. The effectiveness of vibrations significantly increased by tilting waves. The best response for short fast waves was achieved using adjacent discrete elements spaced by about three fourths of the wavelength. An analysis of waves of arbitrary shapes demonstrated that concentrating the vibration energy in the largest available and dominant wave number (monochromatic waves) resulted in the best system performance.

An analysis of natural convection in horizontal slots has been carried out. It is demonstrated that a proper combination of heating and groove patterns can create a net horizontal fluid movement which we refer to as the horizontal chimney effect. Groove shapes that can be easily manufactured as well as heating patterns that can be easily created using heating wires were considered. It has been shown that both patterns must be properly tuned. The direction of the net horizontal flow can be changed by changing the relative positions of the patterns. Changes of groove geometry can change the flow rate by up to 100%. Simultaneous use of grooves and heating at both plates can nearly double the system effectiveness. The strength of the flow increases with reduction of the Prandtl number.

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The effect of surface vibrations on the pressure-gradient-driven flows in channels has been studied. The analysis considered monochromatic waves and laminar flows. The effectiveness of the vibrations was gauged by determining the pressure gradient correction required to maintain the same flow rate as without vibrations. Waves propagating upstream always increase pressure losses. Flow response to waves propagating downstream is more complex and changes as a function of the flow Reynolds number. Such waves reduce losses if the Reynolds number $Re <\ \sim\!\!100$ , but these waves must be sufficiently fast to reduce pressure losses for larger Re values. In general, the supercritical waves, i.e. waves faster than the reference flow, reduce pressure losses with the magnitude of reduction increasing monotonically with the wave phase speed and wavenumber. The need for an external pressure gradient is eliminated if sufficiently short and fast waves are used. Generally, the subcritical waves, i.e. waves with velocities similar to the reference flow, increase pressure losses. This increase changes somewhat irregularly as a function of the wave phase speed and wavenumber forming local maxima and minima. These waves can reduce pressure losses only if the Reynolds number becomes large enough. It is shown that subcritical waves with very small amplitudes but matching the natural flow frequencies produce significant pressure losses.