The Earth-Air Heat Exchanger (EAHE) is a device used to improve the thermal condition of built environments, allowing the reduction of electrical energy consumption of traditional air conditioner systems. Fundamentally, its operational principle is based on fluid mechanics and heat transfer, areas in which Constructal Design has been widely used to seek for the optimal geometries, i.e., which leads to the best performances. In spite of this fact, the employment of Constructal Design for improvement of the EAHE thermal potential has not been performed into literature. Therefore, the main purpose of this work is to perform a numerical investigation on different geometrical configurations of an EAHE using the Constructal Design to obtain the highest thermal potential. Results indicated that, for the same area occupied by the ducts and fixed mass flow rate of air, the increase of the number of ducts (complexity of geometry) improved the EAHE thermal performance up to approximately 73% for cooling and 115% for heating. (C) 2015 Elsevier Ltd. All rights reserved.