Analytical Study of Magneto-Hydrodynamic Flow Behavior in Liquid Metal Coolant Channels Relevant to Nigerian Research Reactor Design

Magneto-hydrodynamic flow in liquid metal coolants arises when electrically conducting fluids flow through magnetic fields, generating induced currents and Lorentz forces that substantially modify velocity profiles and heat transfer characteristics. Understanding these effects is important for the thermal-hydraulic design of liquid metal-cooled reactor concepts under evaluation by the Nigerian Atomic Energy Commission for the country's nascent civilian nuclear energy program. This study analytically investigates magneto-hydrodynamic flow behavior in rectangular coolant channels carrying liquid sodium under transverse magnetic fields representative of conditions anticipated in a small modular reactor design. The Hartmann flow solution for fully developed laminar magneto-hydrodynamic flow in a rectangular duct is extended to include thermal boundary conditions appropriate for reactor fuel assembly heat generation patterns. A parametric study of Hartmann number, aspect ratio, and Nusselt number variation is conducted using both analytical solutions and finite-difference numerical solutions to the magneto-hydrodynamic momentum and energy equations. Results quantify the progressive flattening of the velocity profile with increasing Hartmann number, leading to reduced mixing and decreased Nusselt number for heat transfer at high Hartmann numbers relevant to strong magnetic fields. The study identifies flow regimes and geometric configurations that maintain adequate heat transfer while minimizing magneto-hydrodynamic pressure drop penalties. The analytical results are benchmarked against published experimental data from European liquid metal facility databases. Implications for the thermal design of the Nigerian Atomic Energy Commission's proposed 10 MWth research reactor are discussed. Keywords: magneto-hydrodynamics, liquid metal coolant, reactor design, Hartmann flow, nuclear thermal hydraulics