Uniquely shaped tubes extruded with an inner circular flow passage and an outer streamlined profile are proposed to withstand the inside fluid pressure and simultaneously to reduce the pressure drop across heat exchanger tube bundles comprising hundreds of small-diameter, thin-walled polymer tubes. Heat transfer rates are characterized by treating the tubes as the combination of a base circular tube and longitudinal fin(s) of oval or lenticular profile. Numerical solution of the non-linear differential equation for surface temperature provides the shaped tube efficiency, similar in function to fin efficiency. The effects of Biot number and a dimensionless shape factor on the tube efficiency and the convective heat transfer rate are discussed. A comparison of a circular to an oval shaped tube indicates that convective heat transfer is enhanced for 2000 ≤ Re ≤ 20,000 when Bi < 0.3.