Piezoelectric flexing and output voltage of a microchannel heat engine
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In this thesis, a new model is formulated for a piezoelectric membrane and fluid motion in a microchannel heat engine. A new slug flow model is developed for droplet motion in a circular cross-section channel. The model includes friction, pressure, viscous and thermocapillary forces on the droplet. This thesis examines the concept of a piezoelectric device at one end of the channel to generate electricity from thermocapillary pumping of the droplet within the microchannel. The slug flow model is used to predict the flow energy needed to convert the thermocapillary pumping into electrical energy. A thin membrane design of a piezoelectric device is developed and modelled with the slug flow approximation. The deformation of the piezoelectric membrane is analyzed. The deformation is found to be a function of the air pressure in the closed microchannel and the displacement of the droplet along the microchannel. This was formulated based on the bending of a thin plate (representing the membrane). The displacement relates to the final output voltage of the design. The direct piezoelectric effect was also examined to determine a relationship between the output voltage and induced stress on the membrane by the force of air. Results are presented for a micro heat engine configuration containing a single membrane on one side of the droplet. It was found that the deformation of the membrane and the output voltage were directly proportional to the displacement of the droplet. A relatively small output voltage was gained from a complete cycle of the droplet. A sensitivity study was performed by varying the channel dimensions along with the dimensions of the piezoelectric membrane. The coupling factor of the piezoelectric membrane was varied to examine its effect on the output voltage. It was found that a larger channel and thinner membrane resulted in a larger output voltage. Materials with a large piezoelectric constant were found to have the largest output voltage, as opposed to those with a lower dielectric constant.