MHD Mixed Convection Control in an Actuated Vertically Rectangular Vented Cavity with a Rotating Core Cylinder

Technical Summary: MHD Mixed Convection Control in an Actuated Vertically Rectangular Vented Cavity with a Rotating Core Cylinder

Problem Statement
This study addresses the complex thermal management challenges inherent in magnetohydrodynamic (MHD) mixed convection systems. Specifically, it investigates the fluid dynamics and heat transfer characteristics of a CuO-water nanofluid flowing through a vertically rectangular, vented enclosure containing a centrally positioned, rotating adiabatic cylinder. The system is subjected to a uniform horizontal magnetic field, creating a scenario where buoyancy-driven natural convection, forced convection from an inlet and a moving top wall, and rotational mixing interact under the influence of Lorentz forces. The research aims to fill a gap in existing literature by systematically analyzing how the interplay between the cylinder's rotational speed, magnetic field intensity (Hartmann number), Reynolds number, and nanoparticle volume fraction affects flow stability and thermal efficiency in this specific geometric configuration.

Methodology
The research employs a numerical approach using the Galerkin Finite Element Method (GFEM) to solve the governing equations for mass, momentum, and energy. The mathematical model assumes steady, two-dimensional, laminar flow and utilizes the Boussinesq approximation for buoyancy effects, while neglecting viscous dissipation and Joule heating.

• Governing Equations: The dimensional conservation equations are transformed into dimensionless forms using characteristic scales for length, velocity, and temperature. The system is governed by the Reynolds number ($Re$), Grashof number ($Gr$), Hartmann number ($Ha$), Prandtl number ($Pr$), and nanoparticle volume fraction ($\phi$).
• Nanofluid Modeling: The thermophysical properties of the CuO-water nanofluid are calculated using established models, including the Maxwell model for thermal conductivity and the Brinkman model for dynamic viscosity.
• Numerical Implementation: The computational domain is discretized into triangular finite elements, with local mesh refinement near solid walls and the cylinder to resolve boundary layers. A grid independence test confirmed that a mesh of 22,012 elements provides accurate results. The non-linear algebraic equations are solved iteratively until convergence is achieved with a residual tolerance of $10^{-5}$.
• Validation: The numerical code was validated against existing literature for lid-driven cavities and mixed convection scenarios, showing excellent quantitative agreement (error < 0.15%) and qualitative similarity in streamline and isotherm patterns.

Key Contributions and Results
The study conducts a parametric investigation varying the Hartmann number ($0 \le Ha \le 100$), Reynolds number ($10 \le Re \le 500$), cylinder angular velocity ($\omega = 0$ to $50$), and nanoparticle volume fraction ($0\% \le \phi \le 6\%$). The key findings include:

1. Impact of Rotation: Increasing the angular velocity of the cylinder significantly intensifies fluid circulation. Counter-clockwise rotation creates a dominant vortex that enhances mixing. Specifically, for clockwise rotation ($\omega = 10$), increasing the Reynolds number from 10 to 500 resulted in a 195.74% increase in the local Nusselt number. Anticlockwise rotation was found to boost localized heat transfer near the bottom ends by approximately 13.09% compared to a stationary cylinder at $Re=100$.
2. Magnetic Field Suppression: The application of a magnetic field generates a Lorentz force that opposes fluid motion, acting as a damping mechanism. As the Hartmann number increases, circulation zones contract, and flow intensity decreases. At $Ha = 100$, the study observed a significant reduction in heat transfer performance; for $Re = 500$, the heat transfer rate dropped by approximately 47.90% compared to the non-magnetic baseline. The magnetic field effectively shifts the heat transfer mode from convection-dominated to conduction-dominated.
3. Reynolds Number Influence: Higher Reynolds numbers intensify inertial forces, leading to more distorted streamlines, thinner thermal boundary layers, and enhanced convective heat transfer. The average Nusselt number ($Nu_{av}$) consistently increases with rising $Re$.
4. Nanoparticle Concentration: Increasing the volume fraction of CuO nanoparticles enhances the effective thermal conductivity of the fluid. While higher concentrations slightly reduce flow velocity due to increased viscosity, the overall thermal performance improves. A volume fraction of $\phi = 6\%$ yielded approximately a 5.60% enhancement in heat transfer relative to the base fluid ($\phi = 0\%$).
5. Thermal Control: The study demonstrates that while strong magnetic fields suppress convection, the rotational speed of the cylinder can be utilized as a control parameter to mitigate these negative effects and optimize localized heat distribution.

Significance and Claims
The authors assert that this research provides a robust design framework for high-efficiency thermal management systems. The primary significance lies in demonstrating that the detrimental impact of Lorentz forces on heat transfer (which can reduce efficiency by nearly 48%) can be counteracted or managed through the strategic actuation of a rotating cylinder.

The paper claims these insights are directly applicable to advanced compact radiators, electronic thermal controllers, and next-generation energy conversion technologies where space is limited and magnetic fields may be present. By mapping the complex interactions between rotation, magnetic fields, and nanofluids, the study offers critical design benchmarks for optimizing systems that require precise control over fluid flow and thermal transport in vented, actuated enclosures. The work emphasizes that while magnetic fields stabilize flow, they reduce convective efficiency, and rotational actuation serves as a viable mechanism to restore or enhance thermal performance in such environments.