IllI. J. t/WI .\lo.u Inrm/cr. Vol. 36. No. X. pp. 2135-2145. I’JYI Pnntcd in Great Brilam 0017-9310193S6.W+&oa c 1993 Pcrgamon Press Ltd Steady-state heat transfer from horizontally insulated slabs MONCEF KRARTI Joint Center for Energy Management, CEAE Department, University of Colorado, Boulder, CO 80309-0428, U.S.A. (Receicecl I3 Fcbruq~ 1992 md injitdfornr 28 Aqusl 1992) Abstract-A general solution for the steady-state heat conduction problem under a slab-on-grade floor with horizontal insulation is presented. The soil temperature field, the heat flux along the slab, and the total slab heat loss are obtained and analyzed using the Interzone Temperature Profile Estimation (ITPE) technique. The derived solution addresses all the common configurations for horizontal insulation of slab- on-grade floors. The elfect of the outer inner edge insulation on heat flux variation along the slab floor surface and on total slab heat loss is discussed and analyzed. Finally, the influence of water table level on total slab heat loss is ittustrated for various inner edge insulation configurations. 1. INTRODUCTION THE THERMAL performance of the above-grade portion of buildings has been significantly improved after the energy crisis of the 1970s. As a consequence, the proportional foundation contribution to a building’s total heating load has increased. To improve the energy efficiency of slab-on-ground foundations, two insulation configurations are primarily used : (1) ver- tical insulation placed on the interior or on the exterior of the foundation walls, and (2) horizontal insulation placed under either the slab perimeter or the soil sur- face outside the slab. Several models exist for calculating heat losses from uninsulated or uniformly insulated slabs [l-3]. How- ever, very few models have addressed the heat transfer from .partially insulated slabs, especially when the insulation extends outside the building. Mitalas [4] provided correlations based on a finite element model for a comprehensive set of slab-on-grade insulation configurations. Unfortunately, the Mitalas cor- relations are restricted to certain insulation values and limited to particular geometric dimensions. Hagentoft [5] developed a semi-analytical model based on con- formal mapping and Fourier series to calculate heat losses from a house with variable thermal insulation thickness along the ground surface. The model did not allow for the existence of a water table underneath the slab. This paper presents a steady-state solution to the heat conduction problem under slab-on-grade floor with horizontal insulation. The insulation can be placed (i) uniformly under the slab as shown in Fig. l(a), (ii) a short distance inward from the perimeter of the slab (Fig. 1(b)), or (iii) extending outward from the edge of the slab is indicated in Fig. I(c). The proposed model can handle any combination of the above mentioned horizontal insulation configur- ations. A water table effect is considered in this model. The soil temperature field and the heat flux along the slab are obtained and analyzed using the Interzone Temperature Profile Estimation (ITPE) technique [6-IO]. The model developed in this paper extends the method for treating slabs developed by Krarti [8]. A parametric discussion is presented on the effect of the outer/inner edge insulation and of the water table level on total slab heat losses. A companion paper will deal with heat loss calculation from a slab-on-grade floor with vertical insulation [ 1 I]. 2. FORMULATION OF THE PROBLEM Figure 2 shows a model of a slab-on-grade floor with horizontal insulation. The insulation is placed along the perimeter of the slab and can extend along the soil surface. To account for thermal resistance between soil and room air or ambient air, an equi- valent air-insulation-slab (if any)-soil conductance, /I, is introduced : h = (/I, ’ + u; ’ + CJ- ’ + h- ’ ) - ’ where l h, is a convective heat transfer coefficient above the slab or the soil surface. l Ui is the insulation conductance. l Us is the slab material (or soil layer above insu- lation extending outward) conductance. l hi is the interface contact conductance (slab-to- earth or insulation-to-earth). The steady-state temperature distribution 7&y) in the soil beneath the horizontally insulated slab-on- grade floor model of Fig. 2 is subject to the Laplace equation : d’T a2T gp+‘==o ay - (1) with the boundary conditions : 2135