Energy and Buildings 36 (2004) 1107–1115 Reduced linear state model of hollow blocks walls, validation using hot box measurements Y. Gao a,b , J.J. Roux b,∗ , C. Teodosiu b , L.H. Zhao a a School of Municipal and Environmental Engineering, Harbin Institute of Technology, 92 West Da-Zhi Street, Harbin 150001, China b Thermal Sciences Center—Building Physics, National Institute of Applied Sciences Lyon, INSA—Bˆ at FREYSSINET, 20 Av. A. Einstein, 69621 Villeurbanne Cedex, France Accepted 30 March 2004 Abstract It is not obvious to accurately determine the heat loss under dynamic conditions for building envelopes made of hollow blocks using classical one-dimensional heat flow computations. Consequently, complex three-dimensional heat transfers analyses are necessary to cor- rectly assess their thermal behaviour. This latter approach is characterised by linear state models with high-order matrixes. Therefore, this method is not very practical since it requires cautious numerical implementation and intensive computation time. One way to ob- tain important decrease of the computation time with no significant losses of precision is to use model size reduction techniques. This study presents such an approach based on Moore’s balanced method for two kinds of small-size concrete hollow blocks. The low-order models obtained after reduction for these two hollow blocks configurations are five-order state models (their complete state models had 680 modes and 973 modes, respectively). To estimate the accuracy and the efficiency of each reduction, the results are compared to those issued from the original complete models. The confrontations show that the proposed reduced models provide excellent predic- tion of hollow blocks thermal behaviour for excitation periods higher than 4min. Moreover, the numerical results were very satisfactory comparing to experimental data obtained by means of classical calibrated hot box measurements. Finally, it must be noted that the ap- proach developed in this study can be extrapolated to all kinds of heterogeneous walls. This can lead to simple “model libraries” within building simulation codes, based on “tabulated values” according to data issued by small matrixes set for each type of hollow blocks envelopes. © 2004 Elsevier B.V. All rights reserved. Keywords: Model reduction; Hollow blocks numerical model; Experimental validation 1. Introduction Nowadays, hollow concrete blocks and bricks are becoming very popular as they are extremely versatile and durable. These construction elements are being widely used in structure of residential buildings, factories and multi-storey buildings as they allow to bringing down their cost very considerably thanks to important savings in mate- rials and masonry work. Moreover, hallow blocks envelopes are characterised by light weight, improved thermal and acoustic insulation, as well as ease of ventilation. All these qualities make hollow blocks walls an attractive construc- tion technique as we can currently notice a growing interest in energy, environment and sustainable development con- ∗ Corresponding author. Tel.: +33-472-438-460; fax: +33-472-438-522. E-mail address: roux@etb.insa-lyon.fr (J.J. Roux). cerns. As a result, numerous theoretical, experimental and numerical studies have been focused on hollow blocks properties. With regard to the thermal behaviour of hollow blocks, we can quote here several works [1–5]. Among the thermal parameters of hollow blocks, the thermal transmit- tance (U-value, W/m 2 K) is the most important one since it allows simple (classical) buildings heat loss computations for engineers. Nevertheless, accurate prediction of thermal transmittance for different hollow blocks is not a trivial task as its value cannot be simply acquired by one-dimensional thermal transfer models. This is the result of hollow blocks particular geometry which leads to three-dimensional heat transfers between blocks cavities and blocks ribs (thermal bridge phenomena). Consequently, there are strict rules in order to determine the thermal transmittance (i.e. the U-value) or the thermal resistance (i.e. R-value, m 2 K/W) of hollow blocks walls. For example, these values are gen- erally obtained in Europe following classical standards [6] 0378-7788/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2004.03.008