The present paper studies the geometric optimization of a fin plate under free heat transfer convection using the constructal theory. In order to check this mode, certain factors are considered, including temperature, heating plate dimensions, and the mass of the materials used for constructing the fins. The used fins are rectangular and the supposed fluid of the environment is air. The main goal here is to determine the role of the arrangement type of the fins in terms of geometric optimization for cooling of the heating plate. In so doing, two types of arrangements have been considered longitudinal and transverse and the solution steps are carried out separately for each arrangement. First, the optimization was studied using the analytical solution via the intersection of asymptotes. Then, in order to validate the analytical method used on the basis of the constructal theory, the numerical method was used for numerical simulation of the work. The results were finally compared and the best and most efficient possible construct for fin arrangement were selected. This optimal geometry in the longitudinal arrangement was achieved with six fins and a heat transfer rate of 34.47 W. (C) 2017 Elsevier Ltd. All rights reserved.