This research is devoted to geometrical optimization of internal longitudinal fins based on constructal theory. These fins are extended inward from the pipe perimeter to a prescribed radiu and would have an optimal length, which have been determined analytically by means of constructal theory. Constructal theory and design serves as a reminder that flow systems that must be designed (configured) must be treated as malleable, i.e., as morphing structures that are as free to change as possible. The first challenge is to understand the functioning of elemental systems, and to optimize their performance subject to their own, smallest-scale space constraints. Next is the challenge to assemble and optimize the relative positions of a number of elemental systems into a larger and fixed space. For a round tube with two thermal boundary conditions, i.e constant heat flux and constant temperature, the optimization length and also the corresponding thickness of fins for a known material ratioare determined parametrically which ensures maximum heat transfer and thermal efficiency. In analytic solution,two different velocity profiles are assumed while the flow regime is considered to be laminar. In addition, dominancy of conduction heat transfer between fins and convection in the core of pipe is the main assumptions of this research. Finally, our analytical results are verified with numerical results obtained from commercial software, Fluent. Keywords: Constructal theory; Longitudinal fin; Optimization; Laminar flow; Internal fin.
