A three-dimensional Galerkin scheme using scalar product to obtain residual equations is developed and compared with that using vector product ; the latter is proved unsuitable. In addition to the reported two-dimensional multiple solutions (1), three-dimensional solutions are obtained corresponding to different initial conditions. It is found that the three-dimensional flow cannot be obtained unless the initial perturbation is strong enough. The structure of the three-dimensional spiral flow is clarified. At the top of the annulus, there exist secondary flow cells with closed streakines of co-axial double helix similar to that observed in inclined rectangular box. This increases maximum local and overall heat transfer rates compared with those for the simple two-dimensional unicellular flow.