Simplified calculation for cooling/heating capacity, surface temperature distribution of radiant floor
Highlights
► A simplified calculation method of cooling/heating capacity and surface temperature distribution of radiant floor are given. ► The simplified calculation results agree well with experimental and numerical data in literature. ► The simplified method can be used in actual design and application of radiant floor.
Introduction
Radiant floor is a low temperature heating and high temperature cooling system. A radiant floor cooling/heating system transports energy by water which is a more efficient way compared to an air system due to larger heat capacity of water [1]. Radiant floor exchanges heat with building envelope by radiation and exchanges heat with room air by convection. In real application of radiant floor, researchers and engineers pay close attention to three parameters: cooling/heating capacity of radiant floor, uniformity of surface temperature distribution, and the lowest temperature in surface.
In recent years there has been considerable amount of research in radiant floor and its applications in HVAC systems. Relevant research can be classified in several aspects as following: (1) solve heat transfer problem of radiant floor by analytical solution. Koschenz and Lehmann [2] present analytical solution of slab with embedded array of parallel circular pipes. Monte [3] studies the transient response of one-dimensional multilayered composite conducting slabs to sudden variations of the temperature of the surrounding fluid, applying the method of separation of variables to the heat conduction partial differential equation. Lu and Tervola [4] give a novel analytical approach to heat conduction in a composite slab subject to periodic temperature changes. Beck et al. [5] research on solutions for partial heating of rectangular solids. The methods of separation of variables and time-partitioning are analyzed. Laouadi [6] develops two-dimensional prediction model for radiant systems for integration in energy simulation software, and the model is validated using the numerical modeling approach. Weber and Johannesson [7] use both a simplified star network and a triangular network for the description of heat transfer in thermally activated building constructions. (2) Analyze radiant floor character by simulation and experiment. Holopainen et al. [8] examine the use of an uneven nodal network in floor heating simulation with finite difference heat balance method, and show the benefits of placing the densest gridding in steepest curvature of the temperature gradient. Koschenz and Dorer [9] propose model to illustrate the transient two-dimensional heat flow in hydronic concrete core systems. Results of simulations are compared with transient finite element analysis. Larsen et al. [10] develop 2-D transient solution of a slab with an embedded array of parallel circular pipes. Jin et al. [11] build a numerical model of radiant floor cooling system using finite volume method with composite grids, and show the pipe has effect on the performance when the thermal conductivity of the pipe is low and the effect of the water velocity on the performance is not great. (3) Apply radiant floor in HVAC system in building. Olesen [12], [13] researches on the possibility and limitation of application of radiant floor, and heat exchange of radiant floor with room air and envelope. Song et al. [14] propose a radiant floor cooling system integrated with dehumidified ventilation by physical experiment in a laboratory setting and TRNSYS simulation for an apartment. The proposed system is able to solve the problem of condensation on floor surface.
At present, cooling capacity of radiant floor is commonly provided by simulation, fitted equations or table lookup in engineering application [15]. There is not a simple way to obtain surface temperature distribution and the lowest surface temperature of radiant floor. This paper provides a method to calculate the above information of radiant floor based on basic heat transfer process of radiant floor. The results can be used for quick estimation of the important parameters in actual design and application of radiant floor.
Section snippets
Heat transfer process of radiant floor
Picture and schematic diagram of common hydronic radiant floor are shown in Fig. 1. Chilled water is supplied by embedded parallel circular pipes in concrete layer, above which there is a toweling layer of cement. Surface layer of radiant floor can be marble, tile floor, plastic floor and etc. Floor surface will exchange heat with indoor air by convection and with envelope by radiation. The heat transfer process from chilled water to indoor is analyzed in two parts: (1) heat transfer from floor
Surface temperature distribution of radiant floor
Apart from the mean surface temperature and heat flux, surface temperature distribution is also an important parameter of radiant floor, especially the lowest temperature of the floor surface in the cooling condition. The limitation of the lowest temperature on floor surface is the dew point of the air above the floor.
Considering the fact that the temperature distribution of the floor surface is more uniform than the temperature distribution at the bottom of the floor, an attenuation
Validation of cooling/heating capacity and surface temperature
For an actual case of radiant floor, simulation and experiment are conducted for radiant floor in literature [8], [11], [19]. As shown in Fig. 5, the structure of radiant floor is granite, cement mortar, gravel concrete, polystyrene board and floor slab respectively in Ref. [19]. The structures of radiant floor in Refs. [8], [11] are similar as Ref. [19], which are summarized in Table 2. In the case of simulation, finite difference method is used to discrete the heat conduction equation and
Utilization of simplified calculation to different types of radiant floor
Heat resistance Rs is the physical property of radiant floor, which remains the same both for heating and cooling condition, while convective heat exchange coefficient between floor surface and indoor air is different for cooling and heating condition. Table 1 shows recommended equations and values of convective heat exchange coefficient of radiant floor in literatures. Based on equations of heat resistance and heat transfer coefficient, the cooling and heating performance of radiant floor can
Conclusions
This paper analyzes the performance of radiant floor by solving heat transfer equation of slab with embedded circular pipes and uniform slab. The main conclusions of this paper are listed as:
- (1)
Cooling/heating capacity, surface temperature distribution and the lowest surface temperature are the three key parameters concerning application of radiant floor. A simplified calculation of these parameters is presented in this paper.
- (2)
The simplified calculation results agree well with the experimental
Acknowledgement
The research described in this paper was supported by National Natural Science Foundation of China (No. 51006058), Specialized Research Fund for the Doctoral Program of Higher Education in China (No. 20090002120022) and the foundation for the author of National Excellent Doctoral Dissertation of China.
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