Internal Heat Generated Convection in Nanofluids with Rigid Boundaries:Linear and Nonlinear Regimes

This paper investigates the linear and nonlinear stability characteristics of convection driven by internal heat generation in well-dispersed nanoliquids. Water and ethylene glycol are taken as base fluids, each uniformly seeded with nanoparticles of gold, silver, platinum, or diamond. Using mixture theory and phenomenological models, the thermophysical properties of the nanoliquids are incorporated into a modified Rayleigh number that includes a dimensionless parameter F representing nanoparticle loading. In this framework, the Rayleigh number associated with internal heat generation naturally emerges as an eigenvalue. Linear stability is analyzed using a Maclaurin-series expansion, which provides the critical conditions for the onset of convection. For the nonlinear regime, a Fourier–Galerkin procedure is employed to derive a generalized Lorenz system, and a corresponding Ginzburg–Landau equation is obtained to describe amplitude evolution near the convection threshold. This integrated analytical approach offers deeper insight into the behavior of internally heated nanoliquid convection and has potential applications in thermal management and energy system design. The inclusion of high-conductivity noble metal nanoparticles highlights distinct heat transfer and stability responses arising from internal heat generation.