Study of Pre-Chaotic and Post-Chaotic Motions in Internal Heat Generation Driven Convection of Palm Oil-Based Nanoliquids: Rigid-Rigid Boundaries

Abstract

The paper investigates both linear and non-linear regimes of convection in nanoliquids having palm-oil as the base with internal-heat-generation (IH G ) dominating buoyancy. Palm oil is used with well-dispersed nanoparticles of either copper or titanium dioxide. We adopt a formulation that gives an IH G - based Rayleigh number as an eigenvalue. The effective thermophysical properties are evaluated using mixture theory and phenomenological models, leading to a modified Rayleigh number that involves a dimensionless factor, F, representing the influence of nanoparticles loading. The Maclaurin series expansion method is used in the linear stability analysis to represent the eigen function as a power series. For the nonlinear regime, the Galerkin-Fourier method helped in deriving the generalized-Lorenz-model and thereby the Stuart–Landau equation is arrived at to describe the amplitude evolution near the convection threshold. The approach enhances understanding of how internal heat generation affects convective and chaotic flows in nanoliquids and offers valuable guidance for optimizing thermal management and energy system performance. Palm oil-based nanoliquids containing either copper or titanium dioxide nanoparticles have contrasting thermal and chemical properties and lead to distinct enhancements in heat transfer performance, stability, and response to IH G . Chaotic motion is shown to be impossible in the considered palm-oil-based nanoliquids due to them being high Prandtl number liquids. The results of the problem have immense applications in thermal energy problems involving coolants and also in thermal-storage devices.