Analytical study of heat transfer by Rayleigh-Benard convection in variable viscosity Newtonian liquids: A weak non-linear theory

Abstract

Chaotic convection finds extensive application across diverse physical and mechanical phenomena, weather prediction, crystal production, satellite motion within our solar system, and ecological dynamics. Its widespread utility underscores its significance in understanding and analyzing complex systems in numerous fields. The study deals with the dynamics of regular and chaotic convection within a Newtonian fluid with variable viscosity confined between two infinitely extended horizontal layers with temperature gradient (Rayleigh-Benard convection problem). Employing the Galerkin technique and using minimal representation of Fourier series, a three-dimensional generalized Lorenz nonlinear model is derived. The generalized Lorenz model derived is numerically solved and phase portraits are utilized to analyze the system’s qualitative dynamics. The onset of chaos in conventional fluid configurations occurs at a scaled Rayleigh number [Formula: see text] of 24.7368. Additionally, a weakly nonlinear analysis is performed to comprehend the heat transport within the fluid layer concerning the variation of the scaled Rayleigh number and thermorheological parameter. It is demonstrated that the onset of convection occurs at significantly lower Rayleigh numbers in fluids with exponentially decreasing viscosity compared with fluids of constant viscosity. Furthermore, an increase in the thermorheological parameter leads to an earlier transition from regular to chaotic convection.