A mathematical model for the thermal behaviour of a ventilated floor slab

The passive cooling system of a large, multi-storied, commercial complex is considered, where the building mass is used for storing night time coolness. Fan driven air is forced through an air gap separating the concrete floors and ceiling slabs in order to achieve storage. A mathematical model is proposed for the air and slabs. Three numerical methods are considered: two using the traditional electrical analogy to heatflow, and finite elements for the other. The methods are compared through test examples and a choice is made. The resulting computer code allows for time varying air velocity in the ceiling/floor gap and, as a consequence, time varying convection. Measured input air temperatures at the entrance to the slab are used to drive the model. Investigations by sensitivity studies for forced air velocity, drift air velocity and convection, are described. Modelled slab outlet temperatures, using suitable parameter values, are compared with measurements and reproduce the trends and, to a reasonable extent, the details.