Interzone Temperature Profile Estimation Research Articles

Impact of Above-Grade Walls on Three-Dimensional Building Foundation Heat Transfer From Slab-On Grade Floors

This paper presents a new three-dimensional analytical solution for transient ground-coupled heat transfer associated with slab-on-grade floor building foundations. The impact of above-grade walls on ground-coupled heat transfer is accounted for in the presented solution. The interzone temperature profile estimation (ITPE) technique is utilized to obtain the 3D solution suitable to determine soil temperature distributions and to estimate foundation heat loss/gain from slab-on-grade floors. The ITPE results are validated against results obtained from a closed-form solution in the case of steady-state conditions. It is found that that the above-grade walls can significantly affect the foundation heat losses especially for uninsulated slabs. Moreover, a simplified approach is proposed to obtain three-dimensional foundation heat losses from a two-dimensional solution.

A frequency-domain regression method for estimating building foundation heat transfer

In this article, the Interzone Temperature Profile Estimation solutions are first utilized to carry out a frequency analysis for the foundation heat transfer to determine the effect of indoor air and ambient air temperature fluctuations on the variation of the foundation heat loss/gain. Then, a frequency-domain regression-based method is used to develop transfer functions for ground-coupled surfaces. The regression frequency-domain method is tested and validated using one-dimensional heat transfer for above-grade walls. It is found that the proposed method provides a more effective alternative than numerical methods to estimate conduction transfer function coefficients for building foundations and thus can be easily implemented in whole-building simulation programs.

Heat transfer beneath ice-rink floors

This paper presents two models to determine ground-coupled heat gains for ice rinks. The first model is based on an analytical method: the Interzone Temperature Profile Estimation (ITPE) technique while the second model utilized implicit finite difference scheme. Using both models, time-varying heat transfer within the ice medium as well as the ground is investigated. The predictions of both models have been compared and are found to be within good agreement. Moreover, the results from the transient numerical model are compared against measurements obtained for a small-scale ice-rink model operated under laboratory conditions. The measurements provide the time period required to freeze the ice-rink surface as well as the ice temperatures at different locations of the ice-rink floor. The results of the numerical model are then utilized to investigate the impact of various design and operating conditions on the thermal performance of a typical ice rink.

Semi-analytical solution for steady-periodic heat transfer of attached underground engineering envelope

The solution for steady-periodic heat transfer of attached underground engineering can be expressed by complex temperature. The solution involves two parts: steady temperature and complex amplitude of the annual temperature fluctuations. Using a mathematical model of heat transfer of attached underground engineering, the calculation area is divided into eight rectangular blocks according to the interzone temperature profile estimation (ITPE) technology, and the solutions are obtained for all the parts using the separation of variables method. During the solution, the Fourier coefficients are determined based on the continuity of the heat flux and boundary conditions; as a result, a system of 14 N linear equations with 14 N unknowns is obtained, where N is the truncation point of the Fourier series. The linear equations can be easily solved with a standard method (e.g. Gauss–Jordan elimination). The semi-analytical solution obtained by the ITPE can provide rapid and accurate solution for calculation of heat transfer as well as the basis for analysis of the influential factors of the heat transfer.

Semi-analytical solution of roof-on-grade attached underground engineering envelope

Using a mathematical model of heat transfer of attached underground Engineering Envelope, the calculation area is divided into 13 rectangular blocks according to the Interzone Temperature Profile Estimation (ITPE) technology, and the solutions are obtained for all the parts using the technique of variable separation. During the solution, the Fourier coefficients are determined based on the continuity of the heat flux and boundary conditions. The influences of the temperature of earth surface and the heat transfer coefficient between air and wall on heat flow through the envelope has been quantitatively analyzed. The results show that the heat flux through the envelope is no longer monotonously increase or decrease with increase of the influencing factors. By analyzing the curve of r-value (the ratio of the flux through the roof to the overall flux through the engineering section including the floor and walls), it can be concluded that the heat flow between the first floor of the building and the engineering is the major reason and the shape of the engineering is another one.

Effect of the thermal conductivity of building materials on the steady-state thermal behaviour of underground building envelopes

Using a mathematical model of heat transfer of basement, the calculation area is divided into eight rectangles according to the interzone temperature profile estimation (ITPE) technology, and the solution obtained for all the parts by the separation of variables technique. During the solution, the Fourier coefficients are determined by the continuity of the heat flux and boundary conditions, as a result, a system of linear equation group including 14 N equations has been obtained. The effect of building materials on the temperature and heat flux for the building envelope has been evaluated by calculating the temperature and heat flux for three buildings built with different building materials. The results show that the highest relative error in heat flux among the three envelopes built with various non-insulation material is 27.8%, which indicates the thermal conductivity of the building materials is an important factor of the heat transfer of the envelope.

Foundation heat loss from heated concrete slab-on-grade floors

In recent years, there has been a renewed interest in heated concrete slab floors to provide for space heating in both residential and commercial buildings. The existing design procedures for these heating systems are based on simplified thermal models with several assumptions. In particular, the simplified models assume that both the upper and the lower concrete slab surface are isothermal and that the heat transfer through the bottom of the slab surfaces is uniformly distributed over the entire surface. In this paper, a more realistic and flexible model for heated or cooled concrete slab floors is considered to determine the heat transfer between the concrete slab and the ground. In particular, steady-state and steady-periodic semi-analytical solutions are developed to determine the temperature field within the ground medium and within the concrete slab-on-grade floor where hot or chilled water pipes are embedded. The solution presented in this paper is applied to determine the ground heat loss/gain for a heated or cooled floor under various design conditions including the level of floor insulation, and the temperature of the water pipes. These solutions are obtained using the interzone temperature profile estimation (ITPE) procedure. Detailed analysis is presented to determine the effect of the slab insulation configuration on soil and slab temperature field and on the monthly variation of the total slab heat loss.

Steady-State Component of Three-Dimensional Slab-on-Grade Foundation Heat Transfer

General semi-analytical solutions for the steady-state heat conduction problems for circular and three-dimensional rectangular slab-on-grade floors with uniform insulation are presented. The soil temperature field, and the total slab heat loss are presented and analyzed using the Interzone Temperature Profile Estimation (ITPE) technique. A parametric analysis is conducted to determine the effect of thermal insulation U-value, slab size, and water table depth on the total slab heat loss. In particular, it was found that the total slab heat loss is independent of its shape but is strongly affected by the slab size and thermal characteristics.

Thermally optimal insulation distribution for underground structures

This paper provides an analytical solution of the optimal distribution of thermal insulation along the surfaces of underground structures to minimize the annual heat transfer through the ground-coupled surfaces. The analytical solution is obtained using the Interzone Temperature Profile Estimation (ITPE) technique. Two underground structures are considered in this paper: a fully earth-sheltered structure and a partially bermed structure with a shaft that opens to an above-grade interior space. The results of a parametric analysis are summarized to determine the effects of the amount of heat flux imposed on each surface on the optimum insulation distribution along the underground surfaces.

Heat transfer for slab-on-grade floor with stepped ground

A general solution is developed to calculate foundation heat transfer for a slab-on-grade floor with lifted ground. The Interzone Temperature Profile Estimation (ITPE) technique is applied to determine the steady state variation of temperature within the ground. A water table at constant temperature is assumed to exist at a given depth below the soil surface. The derived solution addresses all the common horizontal insulation configurations for slab-on-grade floor foundations. The effect of various insulation configurations and the height of the lifted ground on foundation heat loss are discussed in detail.

Time-varying heat transfer from adjacent slab-on-grade floors

A steady-periodic solution for the heat conduction problem under a slab-on-grade floor adjacent to another slab is presented. The two slabs can be uninsulated or uniformally insulated. A water table is assumed to exist at finite depth from the soil surface. The interzone temperature profile estimation technique is used to develop a semi-analytical solution for the heat conduction equation in the ground medium. The soil temperature field, and the total slab heat loss are obtained and analysed in detail. The effect of the distance that separates the adjacent slabs on the mean and amplitude of total slab heat loss is discussed.

Heat Transfer for Slab-on-Grade Floors With Prescribed Heat Flux

The general solution of soil temperature distribution is developed for a slab-on-grade floor with a known heat flux distribution at the slab surface. The Interzone Temperature Profile Estimation (ITPE) technique is applied to determine the steady-state variation of temperature within the ground. A water table at constant temperature is assumed to exist at a given depth below the soil surface. As a first application of the general solution, the optimum thermal insulation distribution is obtained for a slabon-grade floor. A second application of the solution developed in this paper consists of a diagnostic method to determine the configuration and the R-value for the thermal insulation of the slabon-grade floor based on measured data for the heat flux at the slab surface. A parametric analysis is conducted to determine the effects of heat flux profiles and water table depths on the required insulation distribution at the slab surface.

Slab heat loss calculation with non-uniform inside air temperature profiles

The general solution of soil temperature variation is developed for a slab-on-grade floor with a varying inside air temperature distribution. The Interzone Temperature Profile Estimation (or ITPE) technique is applied to determine the steady-state variation of temperature within the ground. A water table at constant temperature is assumed to exist at a given depth below the soil surface. The effect of the indoor air temperature profile on the total slab-on-grade heat loss is analyzed.

Effect of spatial variation of soil thermal properties on slab-on-ground heat transfer

A time-varying solution is developed to determine the heat transfer between an insulated slab-on-grade floor and non-homogeneous ground. The soil just beneath the slab has thermal properties that are different from those of the ground surrounding the slab foundation. Using the Interzone Temperature Profile Estimation (ITPE) technique, the soil temperature field and the total slab heat loss are presented and analyzed for both winter and summer conditions. In particular, the effect of soil thermal conductivity on the total slab heat loss is discussed in detail.

Optimum insulation for rectangular basements

The general solution of soil temperature variation is developed for a rectangular basement with a known heat flux distribution along the walls and the floor. The Interzone Temperature Profile Estimation (or ITPE) technique is applied to determine the steady-state variation of temperature within the ground. A water table at constant temperature is assumed to exist at a given depth below the soil surface. As an application of the general solution, the optimum thermal insulation distribution is determined for various basement configurations. A parametric analysis is conducted to determine the effect of basement depth and amount of heat flux required on the optimum insulation distribution along the surfaces of a rectangular basement.

Heat loss and moisture condensation for wall corners

In this paper, a detailed, analytical, two-dimensional steady-state thermal analysis of insulated square corners is presented. The Interzone Temperature Profile Estimation (or ITPE) technique is employed to obtain heat flow and temperature distributions for configurations of square structures with an insulation layer placed at the inside surface of the structure envelope. The problem of moisture condensation at the inner surface of the envelope is quantified by determining the extent of the envelope area that is susceptible to condensation. The results showed that, even though corner heat loss is reduced with increasing insulation thermal resistance, the risk of moisture damage increases.

Time-varying heat transfer from partially insulated basements

The Interzone Temperature Profile Estimation (or ITPE) technique is applied to determine the steady-periodic temperature distribution within earth in contact with a partially insulated rectangular basement. A water table is assumed to exist at a given depth below the soil surface. The solution derived addresses all the common insulation configurations for basements and crawl spaces. The effect of basement depth and of partial insulation length and U-value on the mean, amplitude, and phase lag of total heat loss from the basement floor and walls is investigated through a parametric analysis.

Time-varying heat transfer from slab-on-grade floors with vertical insulation

The steady-periodic temperature field distribution beneath a vertically insulated slab is derived using the Interzone Temperature Profile Estimation (ITPE) technique. A water table is considered at a finite depth below the soil surface. The temperature variation within the ground is discussed as well as the effect of vertical insulation length and thermal resistance on the total heat losses from the slab-on-grade floor. It is shown that when the depth and/or the R- value of the vertical insulation increases, the annual mean and amplitude of total slab heat loss decreases while the phase lag generally increases following the law of diminishing returns.

Time-varying heat transfer from horizontally insulated slab-on-grade floors

A general solution for the steady-periodic heat conduction problem under a slab-on-grade floor with horizontal insulation is presented. The soil temperature field, 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. A parametric analysis is conducted to determine the effect of thermal insulation U-value and length on the mean, amplitude, and phase lag of total slab heat loss.

Steady-state heat transfer from horizontally insulated slabs

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 effect 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 illustrated for various inner edge insulation configurations.