Natural convection of large Prandtl number fluids: A controversy answered by a new thermal lattice Boltzmann model

Abstract

The purpose of this work is to deepen our understanding of natural convection with large Prandtl number fluids and to resolve some controversies in the previous publications. To achieve this purpose, a new thermal multiple-relaxation-time lattice Boltzmann model is proposed. Natural convection in a square cavity, a benchmark test case, is investigated numerically using the new model. The Prandtl number is up to 100. For the first time, it is numerically observed that there are two critical Prandtl numbers in the natural convection, which will affect the correlation between the Nusselt number and Prandtl number critically. Three heat transfer characteristic ranges of natural convection are defined in this work, according to the two critical Prandtl numbers. In each range, the dominant heat transfer mechanism is different, which can solve a long-standing issue in the discipline of heat and mass transfer: completely opposing statements on the correlation between the Nusselt number and Prandtl number for natural convection, were published in the open literature. For the first time, this work reveals cause behind the controversial reports and provides the guidance for the future research.