Influence of the Prandtl Number on Wall-to-Fluid Thermal Transfer Rate in a Cubic Cavity

Abstract

The present paper describes a detailed qualitative and quantitative study of the impacts of the overall Prandtl number on the wall-to-fluid thermal transfer mechanisms in two-phase flows using CFD. The physical model consisted of a bubble inside a cubic cavity subjected to the gravity acceleration and to a non-isothermal field. The variables studied in the present investigation were the size of the bubble radius and the overall Prandtl number of flow. The variations of the overall Prandtl number of the flow and the bubble size were evaluated in order to understand their impact on the spatial mean Nusselt number using a computational fluid dynamics model. The bubble size was controlled modifying the bubbles’ initial radius in the computational simulations and the overall Prandtl number was computed according to the Prandtl number of each phase and its volume fraction. Several computational simulations were performed and the numerical model employed in these simulations were validated with previous numerical results in the literature. The present paper reported the influence of the overall Prandtl number on regulating the thermal transfer rate in the classical problem of a differentially heated cavity. According to the numerical results, the introduction of a dispersed phase in single-phase problems may increase or reduce the thermal transfer rate, depending on the overall Prandtl number. The influence of the bubble size has also played an important role in the variations of the thermal transfer rate, since the bubble movement in the domain was modified according to to the size of this radius, changing the distance between the walls and the dispersed phase. Finally, the generally accepted hypothesis elaborated from the literature regarding the increase of the thermal transfer rate due to the introduction of bubbles in single-phase flows has failed in the cubic cavity configuration from the present research.