Analytical solution for heat transfer in a multilayer floor of a radiant floor system

In radiant floor systems, the distribution of the floor surface temperature, which can be used to determine the mean temperature and the lowest/highest temperature of the floor surface, is an important parameter. The mean temperature of the floor surface determines cooling/heating capacity and indoor thermal comfort. The lowest surface temperature, which considers the dew point in an indoor environment, is a crucial factor in the prevention of condensation on a floor surface. The highest surface temperature is typically considered for local thermal comfort. In this paper, an analytical solution for heat transfer in a multilayer floor structure of a radiant floor system is proposed based on the analysis of the heat transfer process of a multilayer floor, equivalent thermal resistance and separation of variables method. The corresponding formulas are derived to estimate the distribution of floor surface temperature. The calculation results are validated by experiments. The calculation and experimental results show good accordance. The absolute error between the calculation and experimental results for floor surface temperature is within 0.3°C. A method for the calculation of the dimensionless temperature of the floor surface, which can be used for radiant heating and cooling systems, is provided. Using this proposed method, the distribution of floor surface temperature and the influence of floor structure parameters on the thermal performance of floors can be estimated and analyzed.