New transient simplified model for radiant heating slab surface temperature and heat transfer rate calculation

A new simplified model based on a semi-analytical correlation is proposed in this paper to evaluate the heating radiant slab surface temperature and to examine its thermal behavior under dynamic solicitations. In fact, the surface temperature is a normative design parameter and shall be kept under an upper limit whatever are the running conditions. Experimental measurements and a two-dimensional finite difference model (2D FDM) were carried out to validate the developed simplified model based on two characteristic parameters that are the time constant and the delay time. A Design of Experiments (DoE) method is employed to derive meta-models for the time constant and the delay time in order to compute the surface temperature. The sensitivity analysis shows that the specific heat capacity of the slab material and the heating water flow rate affect significantly the time constant compared to the thermal conductivity and the heating water pipe inner diameter. Moreover, it was found that all these parameters, except the heating water flow rate, have a substantial impact on the delay time. Compared to the experimental results, the maximum relative deviations from the computed surface temperature are within 2.4% for the numerical model and 1.75% for the simplified semi-analytical model. Consequently, the proposed simplified model may be utilized by engineers and designers to quickly estimate the radiant slab surface temperature and heat flux as well as to study its thermal behavior under dynamic running conditions. This model may also be integrated in the thermal building simulation software.