An analytical method to estimate temperature distribution of typical radiant floor cooling systems with internal heat radiation

Radiant floor cooling systems are increasingly used in practice. The temperature distribution on the floor surface and inside the floor structure, especially the minimum and average temperature of floor surface, determines the thermal performance of radiant floor systems. A good temperature distribution of the floor structure is very important to prevent occupant discomfort and avoid possible condensation in summer cooling. In this study, based on the heat transfer model of the single-layer homogeneous floor structure when there is no internal heat radiation in the room, this paper proposes a heat transfer model of single-layer floor radiant cooling systems when the room has internal heat radiation. Using separation variable methods, an analytical solution was developed to estimate temperature distribution of typical radiant floor cooling systems with internal heat radiation, which can be used to calculate the minimum temperature and the average temperature of typical composite floor structure. The analytical solution was validated by experiments. The values of the measured experiments are in a good agreement with the calculations. The absolute error between the calculated and the measured floor surface temperatures was within 0.45°C. The maximum relative error was within 2.31%. Prove that this model can be accepted. The proposed method can be utilized to calculate the cooling capacity of a typical multi-layer composite floor and will be developed in the future study for design of a typical radiant floor cooling system.