Entry-Length Effect on the Thermal-Hydraulic Design of Plasma Facing Components of Fusion Reactors, Part II: MHD Flow

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Abstract
Convective heat transfer in the thermally developing region in a coolant channel of the first wall and limiter/divertor plates of a fusion reactor has been analyzed numerically. The surface heat flux on a coolant channel in these plasma facing components varies circumferentially. The flow is assumed MHD fully developed laminar in a circular tube with insulating wall and in the presence of a transverse magnetic field. Both the circumferential variation of the surface heat flux and the presence of a transverse magnetic field greatly affect the steady-state Nusselt number and thermal entry length. At the point where the magnetic field is normal to the tube wall, the steady-state Nusselt number can be increased as much as by a factor of 2 compared with 4.36 for non-MHD flow (parabolic velocity profile) and uniform surface heat flux. The nonuniformity of surface heat flux, on the other hand, can reduce the Nusselt number at the same location (also the point of maximum heat flux) to about 3.0. The transverse magnetic field can increase the thermal entry length by about 40% compared with that for non-MHD flow and uniform heat flux. The nonuniformity of surface heat flux and transverse magnetic field combined can increase the thermal entry length by a factor of 4.6. Neglect of this decrease in Nusselt number can result in an underestimation of the film temperature drop by 38% to 64%. The increase in the entry length would not affect the thermal-hydraulic designs of the first wall and divertor plate because, even with this increase, the entry length is short for liquid-metal coolants.