CU Journal of Non-Linear Fluid Mechanics

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

P S Kruthik, Ruwaidiah Idris — Tue, 23 Dec 2025 00:00:00 +0000

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.

Nonlinear Analysis of the Non-Sinusoidal Temporal Periodic Modulation of Boundary Temperature and Non-Inertial Acceleration on Ferroconvection

Anthony Christy Melson, Shazia, G. N. Sekhara — Tue, 23 Dec 2025 00:00:00 +0000

The paper reports the effects of different types of temporal periodic modulation of boundary temperature (TPMBT) on convective heat transfer in a rotating ferroliquid. The linear stability analysis yields the eigenvalue for the onset of convection. The amplitude equations for nonlinear analysis have been derived with the aid of the truncated double Fourier Series in its minimal mode. The system of amplitude equations which is a Lorenz-like model is a non-autonomous system due to TPMBT. The results for various parameters have been discussed for both terrestrial as well as the microgravity case. It is observed that increasing strength of the magnetic field advances the onset of convection but does not result in enhanced heat transfer. The Coriolis acceleration stabilizes the system and hence results in subdued heat transfer. It is also observed that choice of the waveform and frequency of modulation can be used to control heat transfer. Classical Lorenz model and the results of dielectric liquid can be obtained as a limiting case of the present study.

Heat Transfer Augmentation in Forced Convection Flow Using a Dilute Aqueous Suspension of Molybdenum Disulphide Nanoparticles

Neha Elizabeth Sam, Roxanne Francis — Tue, 23 Dec 2025 00:00:00 +0000

This paper presents a numerical investigation of forced convection heat transfer in a water based molybdenum disulphide (MoS2) nanofluid flowing through a three-dimensional porous enclosure. The flow is governed by the non-Darcy regime, modeled using the Darcy-Brinkman-Forchheimer (DBF) equation, while the energy equation is formulated under the local thermal equilibrium assumption. The highly nonlinear coupled system of equations is solved using a finite difference method (FDM) with a uniform grid, enhanced by the Alternating Direction Implicit (ADI) scheme for computational efficiency. A systematic grid independence study is conducted to ensure solution accuracy. The results quantify the enhancement of thermal performance, demonstrating that the Nusselt number increases significantly with higher nanoparticle volume fractions, greater geometric complexity of the porous medium (shape factor), and increased inertial effects (Forchheimer number). The study conclusively establishes that the use of water-MoS2 nanofluids in structured porous media is a highly effective strategy for augmenting heat transfer, with promising applications in the design of advanced thermal management systems.

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

P. G. Siddheshwar — Tue, 23 Dec 2025 00:00:00 +0000

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.

Derivation of the Ginzburg-Landau Equation and Estimation of the Heat Transfer in a Rayleigh-Bénard Convection of a Micropolar fluid with Time Periodic Body Force

Anirudh P, M S Jagadeesh Kumar, Nur Aisyah Abdul Fataf — Tue, 23 Dec 2025 00:00:00 +0000

This study examines the behavior of a micropolar fluid in a Rayleigh–Bénard configuration under a time-varying gravitational force. A scaled fourth-order Lorenz model is employed to describe weakly nonlinear convection. The model conserves energy and retains all the essential characteristics of the classical Lorenz system. The scaled Rayleigh
number and the Ginzburg-Landau equation are derived using the Venezian method. The graphs showing the variation of the correction Rayleigh number with the modulation frequency for different parameter combinations are plotted, and it is found that the system supports supercritical motion. Furthermore, an analytical expression for the time-average Nusselt number is obtained and plotted for various values of the parameters, and it is found that the presence of micropolar fluid generally promotes the heat transfer.