A Mathematical Model of a Thermally Activated Roof (TAR) Cooling System Using a Simplified RC-Thermal Model with Time Dependent Supply Water Temperature

Abstract

This paper presents a computer simulation model of a thermally activated roof (TAR) to cool a room using cool water from a wet cooling tower. Modeling was achieved using a simplified 1-D resistance-capacitance thermal network (RC model) for an infinite slab. Heat transfer from the cooling pipe network was treated as 2-D heat flow. Only a limited number of nodes were required to obtain reliable results. The use of 6^th order RC-thermal model produced a set of ordinary differential equations that were solved using MATLAB - R2012a. The computer program was written to cover all possible initial conditions, material properties, TAR system geometry and hourly solar radiation. The cool water supply was considered time dependent with the variation of the ambient wet bulb temperature. Results from RC-thermal modeling were compared with experimental measurements for a second story room measuring 5.5 m x 4 m x 3 m at Amarah city/ Iraq (31.865 ˚N, 47.128 ˚E) for 21 July, 2013. The roof was constructed of 200 mm concrete slab, 150 mm turf and 50 mm insulation. Galvanized 13 mm steel pipe coils were buried in the roof slab with a pipe occupation ratio of 0.12. The walls were constructed of 240 mm common brick with 10mm cement plaster on the inside and outside surfaces and 20 mm Styrofoam insulation on the inside surface and covered with PVC panel. Thermistors were used to measure the indoor and outdoor temperatures, TAR system water inlet and outlet temperatures and temperature distribution inside the concrete slab. The effect of pipe spacing and water mass flow rate were evaluated. Agreement was good between the experimental and RC-thermal model. Concrete core temperature reaches the supply water temperature faster for lower pipe spacing. Heat extracted from the space increased with water mass flow rate to an optimum of 0.0088 kg/s.m².