Semi-analytical model for thermal response of anhydrite radiant slab

The choice of heating systems in buildings is primarily guided by the desired comfort level and energy saving concerns. Radiant floor heating systems are suitable for satisfying these requirements by considering the trade-off between minimizing the thermal inertia of the radiant slab and maintaining the surface temperature below a certain value. In this study, a new simplified model based on an analytical correlation is proposed to evaluate the heating radiant slab surface temperature and examine its thermal behavior under dynamic conditions. A full-scale test cell, monitored by a set of sensors, was used to obtain measurements under transient conditions. In addition, numerical models based on the finite difference method and the finite volume method were developed and validated under transient conditions. The design of experiments method is used to derive meta-models for the time constant and the delay time in order to compute the surface temperature. The sensitivity analysis indicated that the specific heat capacity of the slab material and the heating water flowrate significantly affect the time constant as opposed to the insignificant effect of the thermal conductivity and the heating water pipe inner diameter. In addition, it was found that all of these parameters, except for the heating water flowrate, have a significant impact on the delay time. Compared to the experimental results, the maximum relative deviations on the computed surface temperature were within 2% for the numerical model and 4% for the semi-analytical model.