scope:

INTRODUCTION

Simulation and analysis of the thermal fluxes in a building help the developer to choose the best materials for the local climatic characteristics and consequently to improve the envelope thermal performance and the inner thermal conditions. Many thermal processes are relevant in the assessment of building thermal behavior. These include the following:

• heat conduction through exterior walls, roofs, ceilings, floors and interior partitions;

• solar radiation through transparent surfaces;

• latent or sensible heat generated in the space by occupants, lights, and appliances; and

• heat transfer through ventilation and infiltration of outdoor air and other miscellaneous heat gains. (ASHRAE Handbook 2005)

One of the most important items in the above process is the thermal conduction through a multilayered wall which can be calculated in several ways, including:

• Numerical finite differences;

• Numerical finite elements;

• Transform methods; and

• Time series methods

Many software packages for the thermal dynamic simulation of buildings employ the Transfer Function Method (TFM) or Conduction Transfer Functions (CTFs) to provide a set of coefficients to relate the conductive heat fluxes to the current and past surface temperatures and past heat fluxes. TFM has been selected for the procedure recommended by ASHRAE, and called the Heat Balance Method (HB) (ASHRAE Handbook 2005), mainly because of the following:

• computational time advantage; and

• inputs or outputs data are discrete in the time domain such as climatic data

Accurate simulations of thermal systems in the built environment can be performed using complicated modeling techniques and are available in many software packages. Some of the most used software, as DOE-2, TRNSYS, and ENERGY PLUS, which are employed to perform design cooling load calculations, use mathematical models based on transform methods, such as:

• the response factor method; and

• TFM or z-transfer function method

The TFM developed by Stephenson and Mitalas (Stephenson and Mitalas 1971) uses CTFs to calculate the transient one-dimensional heat conduction through the building wall and roof elements.

As presented in the following section some researchers have shown that the earlier methods can lead to unreliable evaluations especially when the walls have high thermal inertia. CTFs represent an efficient method to compute surface heat fluxes because they do not require the knowledge of temperatures and fluxes within the boundary surfaces of the thermal elements. Unfortunately, conduction transfer function series become progressively more unstable as the time step decreases, and eventually this instability can lead the entire simulation to diverge.

In this paper, the authors focus on these issues and also assess the numerical stability and sensitivity analyses of the time step and of the thermal inertia on the prediction of thermal performance of walls.