Constructal design of evacuation from a three-dimensional living space

• The fundamental relation between the configuration of a building and the evacuation time needed by all the inhabitants.
• Evacuation of inhabitants is treated as a physical flow system.
• The optimal floor shape and profile shape are reported.
• The theoretical predictions are validated by extensive numerical simulations of pedestrian flow.

This paper demonstrates the fundamental relation that exists between the configuration of a three-dimensional living space and the time needed for the evacuation of all the inhabitants. The evacuation is treated as a physical flow system consisting of pedestrians who move from a volume to one or two exits. The living space has two variable aspect ratios, the floor shape and the profile shape (or the number of floors). First, the paper reports analytically the optimal floor and profile shapes for which the total evacuation time is minimum. Second, the analytical results are complemented and validated by numerical results obtained based on numerous simulations of pedestrian flow from volume to exits. The numerical results are further validated by performing the simulations of pedestrian movement with two different computational codes (Simulex and FDS + Evac). The fundamental relation presented in this paper can be used in the design of larger and more complex living spaces in modern urban settings.