###### Abstract
[15] presented a numerical study in which the use of a VHCS in a residential building could reduce thermal discomfort by up to 80% and cooling needs by up to 70% [16] and proposed a combination of a ventilated roof and the use of thermo-reflective paint to reduce the cooling load by 66% when optimizing the thermal performance of a roof. More recently, ref. [17] proposed a new roof system consisting of a combination of a VHCS with white coating and lightweight foam concrete, which reached savings in cooling demand by up to 20%. Nonetheless, to the best knowledge of the authors, in all cases, a VHCS system is designed as a precast slab with embedded ducts for the passage of air, which is an appropriate system for a new building or any scenario involving the complete replacement of the existing slab. No studies or examples of the implementation of a VHCS in the rehabilitation of buildings in which the original slab is preserved have been found in the literature. This design also presents problems due to the high pressure drops and consequent high energy consumption by fans and a decrease in the capacity to transfer heat from the inlet to the air outlet, which leads to differences in the surface temperatures of the slab. The heat transfer can be increased if the air speed is increased, but a negative consequence is that the pressure drop and ventilation energy increase too. Therefore, a compromise solution, or optimum point, should be found between the energy consumption of the ventilation system and the heat evacuated by the air. The latter has not been studied in sufficient depth for these systems. No studies have been found where a VHCS is implemented in building retrofitting and does not involve the total replacement of the existing floor slab, nor have there been studies found where the balance between the energy consumed by the ventilation system and the heat evacuated by the VHCS is studied in depth. There is a gap knowledge in this respect. This work focuses on the study of a VHCS for existing buildings where preserving the existing floor slab is desired and it is not possible to use a prefabricated solution, as is the case with the VHCS studied in the scientific literature. For this reason, in this work, we propose the in situ construction of an air chamber over the existing slab, and we also study the methodology to optimize the design of the interior partition walls to conduct the air from the inlet to the outlet and to maximize the heat transfer between the original concrete slab and the circulating air. For this purpose, a methodology with different configurations has been used to find the optimal geometrical distribution from the aero-thermal point of view. Finally, the results obtained have been expressed similarly to a heat exchanger using the effectiveness-NTU methodology, and the relationship between thermal performance and air pressure drops has been evaluated through the thermo-hydraulic performance factor. The work presented is organized as follows: The Material and Methods section defines the geometry of the problem, the variables of interest studied, the computational model used, and the geometry and boundary conditions of the cases to be studied. The Results section compares the temperature distribution, the thermo-hydraulic performance, the efficiency, and the exchanged heat flow of the proposed cases, and conducts a more detailed study of the best configuration. Finally, the Conclusions section summarizes the most important milestones and the future improvements proposed.