The use of polymer tubes for heat exchanger tube bundles is of interest in many applications where corrosion, mineral build-up and/or weight are important. The challenge of overcoming the low thermal conductivity of polymers may be met by using many small-diameter, thin-walled polymer tubes and this route is being pursued by industry. We propose the use of unique shaped tubes that are easily extruded using polymeric materials. The shaped tubes are streamlined to reduce form drag yet the inside flow passage is kept circular to maintain the pressure capability of the tube. Special treatment is required to predict convective heat transfer rates because the temperature distribution along the outer surface of the shaped tubes is nonuniform. The average forced convection Nusselt number correlations developed for these noncircular tubes can not be used directly to determine heat transfer rate. In this paper, heat transfer rates of shaped tubes are characterized by treating the tubes as a base circular tube to which longitudinal fin(s) are added. Numerical solution of an energy balance on the fin provides the surface temperature distribution and a shaped tube efficiency, which can be used in the same manner as a fin efficiency to determine the outside convective resistance. The approach is illustrated for three streamlined shapes with fins of lenticular and oval profile. The presentation highlights the effects of the geometry and the Biot number on the tube efficiency and heat transfer enhancement. Convective heat transfer is enhanced for the oval shaped tube for 2000≤Re≤20,000 when Bi<0.3. For polymeric materials, the Biot number in most applications will be greater than 0.3, and adding material to the base tube reduces the heat transfer rate. The potential benefit of reduced form drag remains.