This paper focuses on the interaction and the contribution of the three modes of heat transfer in a stack of parallelogrammic air -filled cavities separated by solid partition walls. The thermal diode potential and the high insulating character of such structures are the main interests of this investigation. The inclination angle, the emissivity of the inner boundaries of the cavity as well as the thickness and the thermal conductivity of the partition walls are the parameters varied in this study. Their respective contributions to the total Nusselt number are assessed. The two-dimensional fluid cavities studied in this work are characterized by an aspect ratio of 1. The vertical boundaries of the enclosures are considered isothermal at specified hot and cold temperatures, and the inclination angle of the partition walls is varied from 60 to 60 with respect to the horizontal. Numerical simulations are carried out using a finite -volume solver. It is shown that the total Nusselt number is highly sensitive to the emissivity of the inner boundaries of the cavities and thus, to the heat transfer through radiation. Moreover, it is found that the conduction heat transfer in the partition walls also plays an important role in most of the cases investigated. The importance of these two modes of heat transfer results in a significant decrease in both the thermal diode potential and the insulating character of the enclosures compared to the classic case for which only convection heat transfer is considered. Nonetheless, this study suggests that a vertical structure composed of a stack of parallelogrammic air-filled enclosures could be successfully designed to provide a practical and economically interesting alternative to polystyrene panels. (C) 2016 Elsevier Ltd. All rights reserved.