# Experimental Observations of Heat-Assisted Boycott Effect in Trapezoidal Enclosures
## 1 Introduction
These simulations, conducted with particles of \(2500\,\mathrm{\SIUnitSymbolMicro m}\) in diameter and initial concentrations below 0.1, revealed that local vortices formed at an inclination angle of 30 degrees with respect to the vertical, elongating over time, and eventually transitioning into a single, organized unicellular pattern. Parallel plate sedimentators are widely used in the water treatment industry. These devices utilize the Boycott principle for material separation, with a comprehensive review available in the work by [32]. A device known as a reflux classifier employs inclined plates located on a fluidization channel, enabling the equipment to achieve a more expansive range of particle separation. The historical development of this equipment can be discerned primarily in the work of [33; 34; 35; 36; 37]. The existing literature contains a number of studies conducted by various authors that examine the phenomenon of natural convection in closed containers due to temperature differences over a range of inclination angles. The effect of inclination on heat transfer in an open-ended channel was experimentally investigated by [38] for three heating configurations. The heating configurations were as follows: (1) the upper and lower walls were heated, (2) only the upper wall was heated, and (3) only the lower wall was heated. In this study, the authors propose that the mode of heating does not have an impact on the rate of heat transfer. It should be noted that the authors also mention recirculation in the upper part of the channel for Case 2. Their findings suggest that the penetration of this recirculation increases with the aspect ratio and the Rayleigh number (\(Ra\)). Moreover, in Case 1, an increase in vortices was observed with increasing \(Ra\). Therefore, the flow field was at least visually considered in their work. Subsequently, works such as those by [39; 40; 41] have employed numerical analysis to estimate heat transfer and flow fields in closed containers with varying aspect ratios, inclination angles, and boundary conditions. The results indicate the presence of distinct flow patterns. Ref. [41] observed a single cell flow pattern and observed that the convection strength increases as the aspect ratio increases, i.e., as the container becomes thinner. In contrast, ref. [40] mentions multicellular flow patterns, which disappear as the angle of inclination with respect to the horizontal \(\theta\) increases, and are independent of the aspect ratio. Additionally, it states that the flow pattern is highly sensitive to the initial conditions of the flow field and that in some angles of inclination and regions, the phenomenon of hysteresis occurs. Under the idea of harnessing the Boycott effect and the convection generated by temperature differences, ref. [42] conducted two-dimensional numerical simulations for a heating-assisted sedimentation process. To this end, a rectangular cell measuring 1 m in length and with a separation of 5 cm between the inclined walls was used, with the understanding that the process would operate in a batch mode. They imposed different temperatures on the inclined upper wall above the ambient temperature, generating constant temperature differences \(\Delta T\), for different particle sizes and concentrations. Their findings indicated that a higher \(\Delta T\) reduces the time required for particles to sediment at the bottom, while the temperature gradient generates particle resuspension, necessitating further investigation into the range of variables that allow for leveraging these effects, i.e., increasing the sedimentation velocity and decreasing resuspension. The present work assessed the impact of heating on the Boycott effect. To this end, a trapezoidal cell was built, similar to the experimental setup of [43; 44].