Heat transfer enhancement and pressure drop penalty in annuli with spirally fluted inner tubes were evaluated for the laminar, transition, and turbulent flow regimes for the Prandtl number range 4.37 < Pr < 10.31. Recent experimental studies that reported Nusselt number and friction factor correlations for these annuli were used as the basis for this parametric evaluation. On the basis of flow-visualization tests and tube-surface temperature-profile measurements, it is known that the fluted inner tubes induce a significant degree of swirl in the flow. In the laminar regime, friction factor enhancements relative to smooth-tube annuli are typically between 1.1 and 2.0, while enhancements of up to 10 occur in the turbulent regime. Nusselt numbers in the laminar regime are between 4 and 20 times the smooth annulus values, while turbulent enhancements are between 1.1 and 4.0. These respective enhancements are functions of the flute depth, pitch and angle, and annulus radius ratio. The enhancement efficiency of these tubes was defined as the ratio of the Nu enhancement to the friction factor enhancement. This figure of merit for spirally enhanced annuli was characterized for a wine range of annulus geometries and explained in terms of the fluid flow mechanisms. One of the more significant findings of this study is that in the low Reynolds number range (Re < 3000), fluted inner tubes in annuli cause enhancements in heat transfer that are up to 7 times the corresponding increase in friction factor. The dependence of heat transfer and fiction factor enhancement on geometric and flow variables was used to develop guidelines for the optimum range of applicability of spirally fluted annuli.