Development of a design procedure for radiant heating in slab-on-grade floors in a cold climate.(Report)

INTRODUCTION

Radiant floor heating is a method of heating residential or commercial buildings by running a hot fluid through pipes underneath the floor. In the case of a slab foundation, pipes are often embedded in the concrete slab. A heated fluid flows through the piping circuit embedded in the concrete and transfers energy to the concrete. An overview of radiant floor heating was given by Olesen (2002). A schematic diagram showing the details of a portion of a typical slab-on-grade foundation with embedded heating tubes is shown in Figure 1. This figure shows the region of the slab (concrete panel) near the footing, including a floor covering and the layers of insulation, gravel, and soil below the slab. Some of the energy provided by the circulating hot fluid is transferred to the indoors (indicated by the heat flux q"(up)) to maintain the up inside temperature at the desired setting, and some of it is lost to the ground and the outdoors via the bottom surface of the panel ( q"(down) ) and the footing-side edge of the panel (q"(edge)). Figure 1 also includes nomenclature used later in discussing previous work and the present numerical model.

There exists a simple calculation procedure for designing in-floor-heating systems (ASHRAE 2008). The ASHRAE design procedure provides a means of calculating panel surface temperature [T.sub.(p,t)], heating tube outer wall temperature [T.sub.d], downward and edge heat losses q"(de) (note that q"(de)=q"(down)+q"edge using the nomenclature in Figure 1) and heating tube water average temperature [T.sub.w]for heated slab, foundations. The equation recommended by ASHRAE for calculating [T.sub.d] was taken from Kilkis et al. (1994) in which a panel embedded with heating tubes is modeled as a fin that transfers heat from its surface by radiation and convection. The equation recommended by ASHRAE for calculating the downward and edge heat losses was taken from Maher et al. (1957), which was developed for an unheated slab and is only valid for very specific insulation configurations.

In earlier experimental work, Sartain and Harris (1954) studied an in-floor-heating system installed in the Floor Slab Laboratory at the University of Illinois. Tests were performed on four different test rooms measuring 17 [m.sup.2] (183 [ft.sup.2]) each. The test rooms were heated using in-floor-heating tubes embedded in a concrete slab floor. The four rooms each had a different insulation configuration to study the effects of insulation placements on heat losses. Sartain and Harris found that insulating underneath the entire floor did not save enough energy (compared to perimeter insulation) to make it worth-while. They also found that extending the internal edge insulation vertically along the inside edge of the footing was as effective as providing perimeter insulation beneath the floor.

Several two-dimensional numerical models have been developed for in-floor-heated slab-on-grade buildings with heating tubes embedded in a concrete slab; these models had edge insulation and either complete or perimeter bottom insulation resting on gravel and soil. In some of these studies, the heating tubes were modeled as point sources in the slab (Youcef 1991; Laouadi 2004), while other studies applied a uniform temperature along the entire middle layer (Chuang-chid and Krarti 2001) or along a horizontal line through the center of the slab (Rantala and Leivo 2006). Weitzmann et al. (2005) modeled the tubes as squares and approximated the round geometry by introducing a thermal resistance between the four sides of the pipe and the surrounding concrete. Ho et al. (1995) used finite difference and finite element methods to compute steady-state and transient temperature variation in a concrete panel with ten embedded tubes, each with a specified surface temperature. The temperatures of the tubes varied across the panel. Hogan and Blackwell (1986) employed a steady-state approach and modeled the heating tubes as isothermal holes in the concrete and approximated the round holes by hexagonal holes of equal circumference. Hogan and Blackwell compared the results from their two-dimensional numerical model with the design procedure recommended by ASHRAE (1984) for panel surface temperature, downward and edge heat losses qs, and heating tube water average [q.sub.de] temperature [T.sub.w]. The comparisons were based on a single geometry and various outdoor air temperatures. Their conclusion was that the ASHRAE design recommendations overestimated both downward and edge-wise heat losses.

[FIGURE 1 OMITTED]

There have been very few three-dimensional numerical models developed for in-floor-heating systems. Adjali et al. (2000) developed a three-dimensional model of an in-floor-heated office building concrete slab which was for a very specific geometry with alternating sections of in-floor-heated areas and unheated areas. The heating tubes were modeled as a distributed heat source with a magnitude specified as an area-weighted fraction of the total slab heating energy that was measured in their experimental study. Sattari and Farhanieh (2006) developed a three-dimensional model of an in-floor-heating system but did not include the ground beneath the floor in their model and assumed no heat losses through the bottom of the panel.

Although several experimental and numerical studies have been made of in-floor-heating systems, the only simple calculation procedure that exists for slab-on-grade in-floor-heating systems is the ASHRAE design procedure. The equations used in the ASHRAE design procedure are based on many simplifying assumptions. In addition, this design procedure was not developed for concrete panels with full bottom insulation, as is often appropriate for a cold climate. The objectives of the present work are as follows:

1. Develop a validated steady-state two-dimensional numerical model for in-floor-heated slab-on-grade foundations with insulation placements suitable for a cold climate. The model is to be capable of predicting the temperature and heat transfer rates in the foundation and adjoining soil.

2. Use the numerical model to develop a simple design procedure for calculating the heat losses and the heating tube water average temperature necessary to provide a specified amount of heating. The design procedure is to be valid for a wide range of values of outdoor air temperature, heating tube center-to-center spacing, heating tube outside diameter, concrete thickness, and soil and concrete properties; it should also apply for different insulation placements.

MATHEMATICAL MODEL

The model assumes two-dimensional steady-state heat conduction in a composite domain made up of concrete, gravel, insulation, and soil regions. Within each region, the thermal conductivity is assumed uniform and constant, and contact resistance between materials is neglected. The model domain used in this study is the half region under a building structure with an in-floor-heated slab, as shown in Figure 2. Heating tubes with a constant, uniform outer wall temperature of [T.sub.d] are embedded vertically centered in a concrete floor panel. The heating tubes provide energy to the indoors with a flux [q".sub.up]. The fluxes of energy lost through the edge and up bottom surfaces of the floor panel are [q".sub.edge] and [q".sub.edge] down respectively, and their sum is referred to here as the downward and edge heat losses, [q".sub.de]. The flux of the total energy supplied de by the heating tubes, [q.sub.total] is equal to the sum of [q".sub.up]and [q".sub.de]. All the heat fluxes are per unit floor (panel top) area. The heating tubes have an outside diameter [D.sub.o], are spaced with a center-to-center distance m, and are vertically centered in the concrete panel with the tops of the heating tubes a distance [x.sub.c] from the top of the concrete panel, as shown in Figure 1. The …