In the present work, constructal design of annular finned tube has been studied. Geometrical parameters include fin diameter, fin thickness, fin pitch, tube outer diameter, tube length while physical parameters involve pressure drop number, Stanton number, fin-to-air conductivity ratio, and in-tube fluid-to- air conductivity ratio. The aim of this study is to enhance heat transfer by letting the geometrical degrees of freedom to morph. It was observed that at certain flow conditions, there exist optimal geometry and fin number for the finned tube construct in which its thermal resistance is minimum. Fin efficiency and tube-side convective heat transfer coefficient are higher at low pressure drops and Stanton numbers. In these conditions, analytical relationships were proposed to predict optimal heat transfer, optimal fin number and optimal geometry. It was seen that the optimal fin thickness-to-fin pitch ratio is merely dependent on the fin volume fraction; and it rises with the increase in fin volume fraction. Moreover, the optimum fin number is directly proportional to fin spacing – to- fin pitch ratio and inversely proportional to Stanton number. Furthermore, it was seen that in the range of parameters considered in this study, the tube with 3400 fins and aspect ratio of 0.63 has the most heat transfer rate.