Friction Factors in Fully Developed MHD Laminar Flows for Oblique Magnetic Fields and High Hartmann Numbers in Rectangular Channels

Abstract

Self-cooled liquid metal blanket of a thermonuclear fusion reactor has the most critical issue of strong MHD effects which influence the thermal efficiency of the reactor. Special attention needs to be paid to the MHD friction factors for flow in rectangular channels at low as well as at high Hartmann numbers. The effect on MHD friction factors of a magnetic field oblique to the channel walls for various channel wall conductivities and aspect ratios at different Hartmann numbers is investigated numerically. Even for relatively small channel wall conductivity at high Hartmann numbers, velocity jets are developed near the channel walls. Due to these jets, MHD friction factors increase by the orders of magnitude which can be observed in the numerical results. The finite-difference method has been used to discretize the coupled second-order linear partial differential equations of MHD by using both uniform and nonuniform grids. Nonuniform discretization of the mesh is more efficient than the uniform mesh due to steep velocity gradients near the walls. For parallel plates, an analytical solution for MHD friction factor has been developed, and then compared with the numerical solutions. It is found that an oblique magnetic field has a significant effect on MHD friction factors for different channel wall conductivities and aspect ratios at various Hartmann numbers.