Mixed convection model for predicting the Nusselt number of oscillating vertical plates

Abstract

In this study, we developed a mixed convection model for predicting the Nusselt number of periodically oscillating vertical plates. When a hot or cold vertical plate oscillates, a complex mixed convection flow occurs, a combination of natural and forced convection flow caused by temperature difference and oscillation, respectively. Here, to simplify the analysis, the natural convection flow is treated as a forced convection flow with a certain stream velocity. Then, by superimposing this flow on the forced convection, the mixed convection flow is approximated to a single effective forced convection flow. Based on this approximation, two closed-form correlations of the Nusselt number are suggested, each applicable to vertically and horizontally oscillating plates, respectively. To check the validity of the suggested correlations, we constructed an experimental apparatus to measure the heat transfer coefficient of oscillating plates. We validated the correlation applicable to horizontally oscillating plates using experimental data obtained from this apparatus, while the correlation developed for vertically oscillating plates was validated using experimental data obtained by previous researchers. Our model and experimental data are in good agreement within 8 % for horizontally oscillating plates and 13 % for vertically oscillating plates. To understand the influence of the Grashof and Reynolds numbers on the Nusselt number of oscillating plates, contour maps of the Nusselt number were presented with respect to the Grashof and Reynolds numbers, and then analyzed. Moreover, we suggest convection regime maps with respect to the Richardson and Prandtl numbers, which can be used to calculate the convection regime of oscillating plates. With the absence of empirical constants, the current model is applicable to all the Prandtl numbers in the range of Re<6×104 and 104<Gr×Pr<109. For this reason, our developed model can be widely used for heat transfer analysis of oscillating vertical plates under various conditions.