Heat transfer in laminar and turbulent liquid-metal MHD flows in square ducts with thin conducting or insulating walls

Abstract

The heat transfer in fully-developed liquid-metal flows in a square duct with a uniform, transverse magnetic field is analyzed. Velocity profiles obtained for laminar and turbulent regimes [Cuevas, S., Picologlou, B. F., Walker, J. S. and Talmage, G., Int. J. Engng Sci., 1997, 35, 485] are employed to solve the heat transfer equation through finite differences, in a duct with one side wall (parallel to the magnetic field) uniformly heated and three adiabatic walls. Turbulent effects are introduced through eddy viscous and thermal diffusivity models from the renormalization group theory of turbulence [Yakhot, V. and Orszag, S. A., J. Sci. Comput., 1986, 1(1), 3]. Analysis focuses in determining how the structure of the side-layer flow, influenced by the wall conductance ratio and Hartmann and Péclet numbers in the ranges of interest of fusion blanket applications, affects the heat transfer processes. Numerical calculations for liquid lithium show that for thin conducting wall duct cases, the laminar MHD heat transfer mechanism, characterized by high-velocity side-wall jets, appears to be more efficient than turbulent mixing in the boundary layer for a given Péclet number.