Influence of Prandtl number on the chaos transition for pure natural and Rayleigh–Bénard convections inside a rectangular cavity

Abstract

A peculiar flow instability known as multiple chaos transitions was recently reported for the free convection in an enclosure where the direction of the temperature gradient changes continuously; it has been explained to be attributed to the competition for dominance between pure natural and Rayleigh–Bérnard convections. In this study, the chaos transition of free convection is investigated when a horizontal or vertical temperature gradient forms in a rectangular cavity. Analyses are conducted under a laminar flow regime, with Prandtl numbers ranging from 0.01 to 50 and Rayleigh numbers up to 109. In the horizontal temperature gradient, the chaos-transition Rayleigh number increases monotonically with the Prandtl number. However, under vertical temperature gradient conditions, it reaches the maximum value at approximately Pr = 0.5. Contrary to the general knowledge that higher-Prandtl number fluids effectively stabilize natural convection, a free convection in a vertical temperature gradient initiates a new flow instability when the Prandtl number is over 1.0, where momentum and thermal diffusions balance each other. The oscillation pattern, 2D phase trajectory, power spectral density, and Poincaré point of equivalent thermal conductivity are used to assess the free-convection flow instability.