A theoretical model of thermo-dynamic interpretation for the Pettit effect and associated heat transport processes

Abstract

Based on several fundamental preassumptions, a one-dimensional convection-diffusion equation for heat transport inside liquid wedges causing the Pettit effect is proposed. With a hot or cold thermode placed at the middle of the liquid wedge, the average temperature of the liquid wedge determined from the convection-diffusion equation proposed shows a maximum, which corresponds to a particular liquid flow rate. The state achieved at this maximum temperature is believed to be the most stable for its minimum interfacial energy. The theory suggests a thermodynamic mechanism, which drives the liquid to flow in directions corresponding to those observed in experiments. It is believed that this work improves the thermodynamic interpretation proposed previously since the new-form convection-diffusion equation is more rigorously deduced and is thus more accurate. In addition, the work also presents a detailed theoretical analysis for heat transport. The results show that, in practical situations, the manifested heat-transport behaviors of a liquid wedge are governed by conductive heat transfer because convective heat flow is self-balancing due to the restriction by the law of mass conservation. Meanwhile, based on the asymmetric features of the conductive heat flows transiting within two different halves of the liquid wedge, a closed-loop formed by connecting a hot-thermode-driven liquid wedge and a cold-thermode-driven liquid wedge is proposed such that a hot thermode-cold thermode loop can lead to controllable heat transfer with which targeted heating or cooling may be realized. The effect may reveal the technical principles upon which novel small-size thermal engines, pumps, heaters, and coolers can be built.