The flow of conductive fluids in highly conductive curved pipes is studied analytically in this paper. The flow is assumed to be steady state, laminar, and fully developed. Coupled continuity, Navier–Stokes, and appropriate Maxwell equations are solved in toroidal coordinates. The dimensionless parameters of the problem are Dean number K and Hartmann number Ha. For low Hartmann numbers [Ha2∼θ(1)], the solution is expanded in a power series of K and Ha2. For intermediate Hartmann numbers [Ha2∼θ(1000)], the solution is expressed as a power series of K. The axial velocity contours are shown to be shifted towards the outer wall. For low Ha, these contours are nearly circular. The effect of a strong transverse magnetic field is to enhance the compression of fluid towards the outer wall. The secondary flow field comprises a symmetric pair of counter-rotating vortices. A strong magnetic field is found to confine the secondary flow streamlines to a thin layer near the tube wall. The secondary flow rate in the near-wall boundary layer is increased by the magnetic field. This increase in flow rate raises the possibility of efficient convective cooling of curved first wall tubes in magnetic confinement fusion reactors (MFCR).

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Vapor dynamics of heat pipes during the start-up phase of operation is analyzed. The vapor flow is modeled by a two-dimensional, compressible viscous flow in an enclosure with inflow and outflow boundary conditions. For high-input heat fluxes, a compression wave is created in the evaporator early in the operation. A nonlinear filtering technique, along with the centered difference scheme, is used to capture the shocklike wave and overcome the cell Reynolds number problem. Multiple wave reflections are observed in the evaporation and adiabatic regions. These wave reflections cause a significant increase in the local pressure and flow circulations, which grow with time. It is shown that the maximum and maximum-averaged pressure drops oscillate periodically because of the wave reflections. Although the pressure drops converge to a constant value at steady state, they are significantly higher than their steady-state value at the initiation of the process. The time for the vapor core to reach a steady-state condition was found to be on the order of seconds.

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