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The reliability of mathematical models for heat and mass transfer in building porous
material is of capital importance. A reliable model permits to carry predictions of the physical phenomenon with sufficient confidence in the results. Among the physical phenomena, the hysteresis effects on moisture sorption and moisture capacity need to be integrated in the mathematical model of transfer. This article proposes to explore the use of an smooth Bang-Bang model to simulate the hysteresis effects coupled with heat and mass transfer in porous material. This model adds two supplementary differential equations to the two classical ones for heat and mass transfer. The solution of these equations ensures smooth transitions between the main sorption and desorption curves. Two parameters are required to control the
speed of transition through the intermediary curves. After the mathematical description of the model, an efficient numerical model is proposed to compute the fields with accuracy and reduced computational efforts. It is based on the DuFort-Frankel scheme for the heat and mass balance equations. For the hysteresis numerical model, an innovative implici-explicit approach is proposed. Then, the predictions of the numerical model are compared with experimental observations from literature for two case studies. The first one corresponds to a slow cycle of adsorption and desorption while the second is based on a fast cycling case
with alternative increase and decrease of moisture content. The comparisons highlight a very satisfactory agreement between the numerical predictions and the observations. In the last Section, the reliability and efficiency of the proposed model is investigated for long term simulation cases. The importance of considering hysteresis effects in the reliability of the predictions are enhanced by comparison with classical approaches from literature.

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... We assume the room volume to be V = 2000 m 3 . Outside air is supplied at flow rate Q v = 2000 [m 3 /h] at the outdoor concentration C e , while C s is the concentration of the filtered supply air. The filter characteristics depending on clogging (pressure drop ∆p and efficiency η) are taken from the manufacturer's technical sheet, and plotted below on Figure The questions we will address in the next pages are the following: ...

... Given the non-linearity of transfer coefficients, the implicit method presented above has the drawback of requiring small time steps plus sub-iterations to ensure a proper solving of equations. In recent years, the explicit Du Fort-Frankel scheme [9], became increasingly popular in our field of interest [3,4,12] and is recognised as a state-of-the-art method to solve heat and mass transfer problems. ...

On one end of the scientific literature, profusion of works about solving partial differential equations exist, however often with a somewhat unfamiliar mathematical formalism. On the other end, volumes dealing with building physics may be either technical about HVAC or rather generic about the equations to be used.
Having struggled quite a bit in the past years with the practical implementation of numerical methods in this field, it appeared that putting together the recipes used in a modern programming language could be of interest.
Hence the parti pris in this book is to show the link between the governing equations and how to solve them, aiming at a practical use (i.e. ”how to make things work”). It can be seen as a toolbox for simulation engineering, a basis for the illustration of theory or a kick-start for the study of more complex problems.
This manual is composed of three chapters, with gradual increase in difficulty:
• Chapter 1 succinctly explains the fundamentals of the numerical methods used.
• Chapter 2 shows applications of these methods to heat transfer in phase change materials, PID control, indoor air quality and geothermal heat pumps.
• Chapter 3 deals with coupled problems and minimisation. Applications to polydispersed aerosols in enclosures, heat and mass transfer in walls and parameter fitting for transient problems are proposed.

... Secondly, mathematical modeling is being developed. These investigations consist of obtaining new mathematical formulas describing physic process of moisture transport, creating computer programs which give an opportunity to calculate moisture regime and finding new approaches helping to solve moisture transfer equations [20][21][22][23][24]. Finally, scientists have to assess the impact of the moisture regime on building life cycle and mode of heating and ventilation systems [25,26]. ...

... Thus, several studies have been carried out to investigate the behaviour of such material, regarding heat and mass transfer [8,15]. Recent studies have been aimed at integrating the hysteresis effects on the moisture content, to accurately predict the hygrothermal behaviour of hemp concrete [16][17][18][19]. More precisely [17,18], results showed that the predictions are very sensitive to the model input parameters, such as the moisture capacity, main adsorption and desorption curves, and the vapour diffusion resistance factor. ...

... Thus, several studies have been carried out to investigate the behaviour of such material, regarding heat and mass transfer [8,15]. Recent studies have been aimed at integrating the hysteresis effects on the moisture content, to accurately predict the hygrothermal behaviour of hemp concrete [16][17][18][19]. More precisely [17,18], results showed that the predictions are very sensitive to the model input parameters, such as the moisture capacity, main adsorption and desorption curves, and the vapour diffusion resistance factor. ...

In this article, both numerical and experimental investigations were carried out on the durability of hemp concrete. For this, an accelerated aging process was performed using cycles of immersion, freezing and drying. Then, an experimental campaign was enabled to determine heat and mass transfer properties, as well as the microstructure for both aged and reference materials. Observations using a digital microscope showed the appearance of cracks at the interfaces and an increase of the porosity of about 6%. These microstructural modifications imply a non-negligible evolution of heat and mass transfer properties. Thus, a numerical model for the prediction of heat and mass transfer was developed. The prediction of physical phenomena was computed using both aged and reference material properties. It highlights the aging effects on the behaviour of the hemp concrete. The numerical simulation results showed significant discrepancies between the predicted relative humidity values for the two configurations (aged and reference) of about 18% and a maximum phase shift of 40 min, due to the amplification of the mass transfer kinetics after aging. Nevertheless, few deviations in temperature values were found. Thus, after aging, sensible heat fluxes were overestimated compared to the reference case, unlike latent heat fluxes, where an underestimation was shown.

... Compression of main electrocardiography signals using a new genetic programming-based mathematical modelling algorithm has been studied by Feli and Abdali-Mohammadi [7]. With the aim of assessing the Bang-Bang model related to hysteresis influences on heat and mass transmit in spongy building material, another important article has been proposed by Berger et al. [8]. ...

This paper applies a powerful scheme, namely Bernoulli sub-equation function method, to some partial differential equations with high non-linearity. Many new travelling wave solutions, such as mixed dark-bright soliton, exponential and complex domain, are reported. Under a suitable choice of the values of parameters, wave behaviours of the results obtained in the paper – in terms of 2D, 3D and contour surfaces – are observed.

... Therefore, adequate material parameters and their characterization are currently an important factor tor identifying the reliability of the development and verification of theoretical models, such as the numerical prediction of heat, air and moisture transport (HAM) in porous building materials [14,15]. The effects of hysteresis on the sorption and moisture capacity-the key physical phenomena-need to be included in the mathematical model of transfer. ...

Autoclaved aerated concrete (AAC) and its hygric parameters are a highly important issue in the field of building physics. There are several methods currently available to determine the equilibrium moisture content of building materials. Beside the conventional ones, new methods are constantly being introduced. This study explores the sorption/desorption properties of of three types of commercially produced AACs with three different bulk densities and demonstrates the application of the relevant methods available to characterize these parameters. The reliable characterization of the studied material was done through the conventional static approach, using the desiccator and an environmental chamber, and a new automated method of dynamic vapor sorption is implemented. The goal is to compare and identify the reliability of all methods used with respect to the efficiency of the data measurement process. Sound consistency between the results of the conventional methods and the experimental data obtained indicates the dynamic vapor sorption technique is highly reliable when measuring the equilibrium moisture content—particularly exemplified during the AAC sample testing. Therefore, the methodology developed in this study is expected to provide the reference for measuring the sorption/desorption isotherms of building materials with both static and automated techniques.

Comparisons of experimental observation of heat and moisture transfer through porous building materials with numerical results have been presented in numerous studies reported in the literature. However, some discrepancies have been observed, highlighting underestimation of sorption process and overestimation of desorption process. Some studies intend to explain the discrepancies by analysing the importance of hysteresis effects as well as carrying out the sensitivity analysis on the input parameters as convective transfer coefficients. This article intends to investigate the accuracy and efficiency of the coupled solution by adding advective transfer of both heat and moisture in the physical model. The efficient Scharfetter-Gummel numerical scheme is proposed to solve the system of advection-diffusion equations, which has the advantages of being well-balanced and asymptotically preserving. Moreover, the scheme is particularly efficient in terms of accuracy and reduction of computational time when using large spatial discretization parameters. Several linear and nonlinear cases are studied to validate the method and highlight its specific features. At the end, an experimental benchmark from the literature is considered. The numerical results are compared with the experimental data for a purely diffusive model and also for the proposed model. The latter presents better agreement with the experimental data. The influence of the hysteresis effects on the moisture capacity is also studied, by adding a third differential equation.

Hygroscopic materials such as wood and wood based materials have been widely used as insulation and surface moisture buffering materials due to their low thermal conductivity and high moisture capacity. And their hygrothermal performance is mainly dependent on the moisture properties, such as sorption isotherm and water vapor permeability etc. Instead of a univalued function of relative humidity, sorption isotherm of wood materials is not only affected by sorption history, but also temperature dependent. A heat and moisture transport model is formulated based on local thermodynamic equilibrium assumption, which includes thermal moisture capacity and a hysteresis model in [1]. To validate this model, sorption isotherms at 23 °C were measured using the static gravimetric method; and a moisture response test under dynamic boundary conditions was carried out in a climatic chamber. The simulation results show that the hygrothermal model with temperature dependency and sorption hysteresis can capture the dynamic moisture response to variable boundary conditions very well. Therefore, this model could be used to further analyze the individual and combined effects of sorption hysteresis and its temperature dependency through hygrothermal modeling in a companion paper.

In natural environment, the cover layer of reinforced concrete structures is affected by periodic variations of external relative humidity (RH). However, most moisture transport models in the literature only focus on drying of materials. In this study, a method coupling a moisture transport model with any kind of hysteresis modelling is presented. Two hysteresis models (conceptual and empirical) have been implemented and compared. The scope of the study is limited to cyclic variations of RH with no direct contact with liquid water during the wetting steps. Experimental data verifications show that the conceptual approach yields better results than the empirical one. Comparisons of non-hysteresis and hysteresis modellings have been carried out for different cycle durations, RH amplitudes and initial moisture states. All comparisons and investigations enhance the necessity of considering hysteresis to quantify moisture transport under repeated drying–wetting boundary conditions.

Hysteretic behavior of water vapor sorption isotherms (WVSIs) has been widely recognized as one of the main factors which can significantly affect moisture transport within building materials exposed to natural weather conditions. Due to the lack of experimental data for validation, there are few studies about hysteresis models in the field of cementitious materials. In this paper, a detailed review of hysteresis models has been presented. Models which have been initially developed for water transport in soils and sands have been selected, including the conceptual and empirical models. The comprehensive comparisons with experimental data have been performed for cement pastes and concretes. It enables to conclude a set of best models for prediction of WVSIs and their hysteresis. Comparison results show that for the prediction of the first scanning curves, available hysteresis models (either conceptual or empirical) perform similarly. However, studied empirical models yield pumping errors for the secondary or higher order scanning loops. A multi-level hysteresis modeling has been proposed as well. Evaluations and recommendations for use of this multi-level modeling method have been provided for an application purpose of compared models.

This paper presents both experimental and theoretical works concerning the evaluation of the thermal conductivity and thermal diffusivity of hemp concrete. Experimental measurements of thermal properties are performed using a hot-strip technique for temperatures ranging from -3 °C to 30 °C and relative humidities ranging from 0 % to 95 %, thus creating a large database for this material. These experimental thermal conductivities are then compared with the results from the Krischer theoretical predictive model. The comparison shows good agreement, and a predictive analytical relation between the hemp concrete thermal conductivity, temperature, and relative humidity is determined.

A new and relatively simple equation for the soil-water content-pressure head curve is described. The particular form of the equation enables one to derive closed-form analytical expressions for the relative hydraulic conductivity, when substituted in the predictive conductivity models of N. T. Burdine or Y. Mualem. The resulting expressions contain three independent parameters which may be obtained by fitting the proposed soil-water retention model to experimental data. Results obtained with the closed-form analytical expressions based on the Mualem theory are compared with observed hydraulic conductivity data for five soils with a wide range of hydraulic properties.

Hemp concrete is a sustainable lightweight concrete that became popular in the field of building construction because of its thermal and environmental properties. However; available experimental data on its hygrothermal behavior are rather scarce in the literature. This paper describes the design of a large-scale experiment developed to investigate the hygrothermal behavior of hemp concrete cast around a timber frame through a spraying process; and then coated with lime-based plaster. The equipment is composed of two climatic chambers surrounding the tested wall. The experiment consists of maintaining the indoor climate at constant values and applying incremental steps of temperature; relative humidity or vapor pressure in the outdoor chamber. Temperature and relative humidity of the room air and on various depths inside the wall are continuously registered during the experiments and evaporation phenomena are observed. The influence of the plaster on the hygrothermal behavior of hemp concrete is investigated. Moreover; a comparison of experimental temperatures with numerical results obtained from a purely conductive thermal model is proposed. Comparing the model with the measured data gave satisfactory agreement.

Because the behavior of semi-active devices is often highly nonlinear, one of the main challenges in the application of this technology is the development of appropriate control algorithms. In this paper, a number of recently proposed semi-active control algorithms are evaluated for use with the magnetorheological (MR) damper, an innovative semi-active control device that appears to be particularly promising for civil engineering applications. The performance of the resulting control systems are compared through simulation, and the advantages of each algorithm are discussed. The results demonstrate that the performance of the control system is highly dependent on the choice of algorithm employed

Models for the prediction of heat and mass transfers in building porous materials have been developed since the 90’s with simulation programs such as MATCH, UMIDUS, DELPHIN and Wufi. These models are used to analyze the physical phenomena occurring and particularly the impact of moisture on buildings’ energy performance and durability. With this goal in mind, it is important to validate the representation of the physical phenomena made by the numerical models. This article reviews recent studies comparing the results obtained with numerical models and experimental data. An overall trend can be observed for most of these studies, highlighting that the experimental front always rushes faster than the simulation results. Therefore, this study analyses theses comparisons to explain these discrepancies based on the effects of (i) the type of materials, (ii) the boundary conditions, (iii) the scale of the design facility, (iv) the model used to describe the physical phenomena and (v) the influence of the model input parameter. The general trend shows that discrepancies are observed most particularly for highly hygroscopic or bio-based materials. These discrepancies are also greater for time dynamic boundary conditions, particularly at the scale of the wall. Moreover, some of the assumptions on the properties of the materials used as input in the models are questioned. Indeed, the models considering the hysteresis effects and temperature dependency of the moisture storage capacity show better agreement with experimental data. Finally, the physical phenomena used in the models only consider diffusive transport while it appears that the advective of moisture through the porous material may play an important role.

This book is the second edition of Numerical methods for diffusion phenomena in building physics: a practical introduction originally published by PUCPRESS (2016). It intends to stimulate research in simulation of diffusion problems in building physics, by providing an overview of mathematical models and numerical techniques such as the finite difference and finite-element methods traditionally used in building simulation tools. Nonconventional methods such as reduced order models, boundary integral approaches and spectral methods are presented, which might be considered in the next generation of building-energy-simulation tools. In this reviewed edition, an innovative way to simulate energy and hydrothermal performance are presented, bringing some light on innovative approaches in the field.

A new formulation is proposed for describing the moisture sorption hysteresis in lignocellulosic products. This model introduces the concept of gripped-box. This concept allows complex experimental pathways to be fitted with only two adjustable parameters, including the closure of scanning loops without any pumping effect. The product history is embedded in a unique internal variable, which defined the actual window of interest. The formulation proposed in the present work can be easily implemented in existing computational softwares. Based on comprehensive experiments, the model parameters were defined for five lignocellulosic materials largely used in the building construction.

This work presents an alternative view on the numerical simulation of diffusion processes applied to the heat and moisture transfer through multilayered porous building materials. Traditionally, by using the finite-difference approach, the discretization follows the Method Of Lines (MOL), when the problem is first discretized in space to obtain a large system of coupled Ordinary Differential Equations (ODEs). This paper proposes to change this
viewpoint. First, we discretize in time to obtain a small system of coupled ODEs, which means instead of having a Cauchy (Initial Value) Problem (IVP), we have a Boundary Value Problem (BVP). Fortunately, BVPs can be solved efficiently today using adaptive collocation finite-difference methods of high order. To demonstrate the benefits of this new approach, three case studies are presented. The first one considers nonlinear heat and moisture transfer through one material layer. The second case includes the rain effect, while the last one considers two material layers. Results show how the nonlinearities and the interface between materials are easily treated, by reasonably using a fourth-order adaptative method. In our numerical simulations, we use adaptive methods of the fourth order which in most practical situations is more than enough.

This paper aims at estimating the sorption isotherm coefficients of a wood fiber material using experimental data. First, the mathematical model, based on convective transport of moisture, the Optimal Experiment Design (OED) and the experimental set-up are presented. Then, measurements of relative humidity within the material are carried out, after searching the OED using the computation of the sensitivity functions and a priori values of the unknown parameters. It enables to plan the experimental conditions in terms of sensor positioning and boundary conditions out of 20 possible designs, ensuring the best accuracy for the identification method and, thus, for the estimated parameter. After the measurements, the parameter estimation problem is solved. The determined sorption isotherm coefficients calibrate the numerical model to fit better the experimental data. However, some discrepancies still appear since the hysteresis effects on the sorption capacity are not included in the model. Therefore, the latter is improved proposing an additional differential equation for the sorption capacity to consider the hysteresis effects. The OED approach is developed for the estimation of five of the coefficients involved in the hysteresis model. To conclude, the prediction of the model with hysteresis have better reliability when compared to the experimental observations.

Implicit schemes require important sub-iterations when dealing with highly nonlinear problems such as the combined heat and moisture transfer through porous building elements. The computational cost rises significantly when the whole-building is simulated, especially when there is important coupling among the building elements themselves with neighbouring zones and with HVAC (Heating Ventilation and Air Conditioning) systems. On the other hand, the classical Euler explicit scheme is generally not used because its stability condition imposes very fine time discretisation. Hence, this paper explores the use of an improved explicit approach - the Dufort-Frankel scheme - to overcome the disadvantage of the classical explicit one and to bring benefits that cannot be obtained by implicit methods. The Dufort-Frankel approach is first compared to the classical Euler implicit and explicit schemes to compute the solution of nonlinear heat and moisture transfer through porous materials. Then, the analysis of the Dufort-Frankel unconditionally stable explicit scheme is extended to the coupled heat and moisture balances on the scale of a one- and a two-zone building models. The Dufort-Frankel scheme has the benefits of being unconditionally stable, second-order accurate in time O(dt^2) and to compute explicitly the solution at each time step, avoiding costly sub-iterations. This approach may reduce the computational cost by twenty, as well as it may enable perfect synchronism for whole-building simulation and co-simulation.

Implicit schemes have been extensively used in building physics to compute the solution of moisture diffusion problems in porous materials for improving stability conditions. Nevertheless, these schemes require important sub-iterations when treating nonlinear problems. To overcome this disadvantage, this paper explores the use of improved explicit schemes, such as Dufort–Frankel, Crank–Nicolson and hyperbolization approaches. A first case study has been considered with the hypothesis of linear transfer. The Dufort–Frankel, Crank–Nicolson and hyperbolization schemes were compared to the classical Euler explicit scheme and to a reference solution. Results have shown that the hyperbolization scheme has a stability condition higher than the standard Courant–Friedrichs–Lewy condition. The error of this schemes depends on the parameter τ representing the hyperbolicity magnitude added into the equation. The Dufort–Frankel scheme has the advantages of being unconditionally stable and is preferable for nonlinear transfer, which is the three others cases studies. Results have shown the error is proportional to O(dt). A modified Crank–Nicolson scheme has been also studied in order to avoid sub-iterations to treat the nonlinearities at each time step. The main advantages of the Dufort–Frankel scheme are (i) to be twice faster than the Crank–Nicolson approach; (ii) to compute explicitly the solution at each time step; (iii) to be unconditionally stable and (iv) easier to parallelize on high-performance computer systems. Although the approach is unconditionally stable, the choice of the time discretization remains an important issue to accurately represent the physical phenomena.

This sound introduction to classical and modern control theory concentrates on fundamental concepts. Employing the minimum of mathematical elaboration, it investigates the many applications of control theory to varied and important present-day problems, e.g. economic growth, resource depletion, disease epidemics, exploited population, and rocket trajectories. An original feature is the amount of space devoted to the important and fascinating subject of optimal control. The work is divided into two parts. Part one deals with the control of linear time-continuous systems, using both transfer function and state-space methods. The ideas of controllability, observability and minimality are discussed in comprehensible fashion. Part two introduces the calculus of variations, followed by analysis of continuous optimal control problems. Each topic is individually introduced and carefully explained with illustrative examples and exercises at the end of each chapter to help and test the reader's understanding. Solutions are provided at the end of the book. • Investigates the many applications of control theory to varied and important present-day problems • Deals with the control of linear time-continuous systems, using both transfer function and state-space methods • Introduces the calculus of variations, followed by analysis of continuous optimal control problems.

The main objective of this work is to present the impact of atmospheric pressure gradient on the hygrothermal transfers in porous material. In this way, a mathematical model described by driving forces of temperature, moisture content and total pressure gradient has been addressed. The non-linear partial differential equations are defined through the balance equations of mass and energy development. After that, a numerical implementation focused on the wood drying behavior is treated for one dimensional Fourier boundary conditions. In order to evaluate the pressure sensitivity, temperature and moisture content profiles are presented and compared to the ones obtained by the classical models 15 and 16. Results show that the atmospheric pressure gradient may cause significant influence on the hygrothermal behavior of the porous materials especially for wood process. A significant effect, up to 15%, on moisture content profile distribution is observed.

This study deals with dynamic characterization of hydric behaviour of sprayed hemp concrete. The measurement of moisture buffer value (MBV) is held according to the NORDTEST protocol (Rode, 2005). Specimen are exposed to daily cyclic variation of relative humidity: 8 h at 75%RH and 16 h at 33%RH the test is held under isothermal conditions (23 °C). The experimental set-up is validated by comparison of moisture buffer value measured on cellular concrete with values given in the NORDTEST project for the same kind of material. Results show that sprayed hemp concrete has an excellent moisture buffer capacity (MBV = 2.15 g/(m2 %RH)). So, it is an excellent hydric regulator that improves hygrothermal comfort and reduces energy needs. Moisture effusivity is then calculated from sorption and water vapour permeability value and from dynamic test of MBV. The results (respectively 5.8 × 10−07 and 4.8 × 10−07 kg/(m2 Pa s1/2) show a slight discrepancy between values obtained from steady-state and from dynamic conditions. Finally, the penetration depth for daily cyclic variation is estimated about 5.8 cm for sprayed hemp concrete. Also, the experimental data set can be used for benchmarking buffering models.

Hemp concrete is a bio-based building material the main qualities of which are its low environmental impact and its hygrothermal behaviour. Even for one kind of application (for example: wall), several compositions and manufacturing methods are encountered in the market. This study compares the hygroscopic behaviour of three hemp concretes used for building walls to identify whether composition and manufacturing have an impact on hygric properties. The investigations are based on the measurement of the sorption curve, of the water vapour permeability versus humidity and of the moisture buffer value. Moisture diffusivity is calculated from the sorption curve and from the water vapour permeability. The results underline the high transfer and storage capacities of these materials; they are classified as excellent (or nearly excellent) hygric regulators. A slight effect of porosity, connected with composition and manufacturing method, is observed.

Phenomenological models are employed into composite structural systems for simulating passive devices aimed at vibration mitigation and the Bouc-Wen one subsists as a significant example. In recent years, the control systems progress has moved toward a more efficient and adaptable semi-active technology. Therefore the existent numerical procedures, which proved effective for the passive implementation, are expected to comprise such features as well.This paper deals with a method of controlling in real time the hysteresis component in simulated semi-active control systems through the Bouc-Wen model. An introductive discussion on the theoretical formulation of the original settlement allows to focus on a way for tuning the parameters which can be managed for hysteresis regulation. Proper algorithms, embedded into the analytical formulation of the model, are subsequently selected for implementing the semi-active characteristic. Finally, straightforward dynamic applications on a plane oscillator system point out the general capability of the proposed approach by seismic response simulation and mitigation of the induced structural effects.

Durability of reinforced concrete is crucial for civil and building infrastructures. Deterioration related to corrosion of the reinforcement can be caused by chloride diffusion or carbonation due to atmospheric CO2 ingress. Chlorides and CO2 transport coefficients are dependent on the saturation degree of the porous material. Thus, the durability of concrete elements submitted to cyclic atmospheric conditions could depend on the hysteretic moisture behavior of concrete. To assess this influence, an analytical model has been developed describing hysteretic moisture behavior based on the independent domain theory. This model is incorporated in a finite element code for coupled heat and mass transfer, allowing to calculate the concrete response to changing temperature and relative humidity conditions. A comparison is made between simulations using the hysteresis model and using either the main ad- or desorption curve. The results show that durability risks may be underestimated when omitting moisture hysteresis in the outer concrete layer.

The long-awaited new edition of this classic text with its well-known "train wreck" cover. With twice the number of problems in this second edition, it is a valuable text and reference work for any student or instructor in the sciences and engineering.

A standard for binary floating-point arithmetic is being proposed and there is a very real possibility that it will be adopted by many manufacturers and implemented on a wide range of computers. This development matters to all of us concerned with numerical software. One of the principal motivations for the standard is to distribute more evenly the burden of portability between hardware and software. At present, any program intended to be portable must be designed for a mythical computer that enjoys no capability not supported by every computer on which the program will be run. That mythical computer is so much grubbier than almost any real computer that a portable program will frequently be denigrated as "suboptimal" and then supplanted by another program supposedly "optimal" for the real computer in question but often inferior in critical respects like reliability. A standard --- almost any reasonable standard --- will surely improve the situation. A standard environment for numerical programs will promote fair comparisons and sharing of numerical codes, thereby lowering costs and prices. Furthermore, we have chosen repeatedly to enrich that environment in order that applications programs be simpler and more reliable. Thus will the onus of portability be shared among hardware manufacturers and software producers.

A distribution function is estimated by a kernel method with a poinrwise mean squared error criterion at a point x. Relation- ships between the mean squared error, the point x, the sample size and the required kernel smoothing parazeter are investigated for several distributions treated by Azzaiini (1981). In particular it is noted that at a centre of symmetry or near a mode of the distribution the kernei method breaks down. Point- wise estimation of a distribution function is motivated as a more useful technique than a reference range for preliminary medical diagnosis.

Based on the domain theory of hysteresis, the present study rigorously derives a unified scaling transformation for predicting the wetting scanning retention function, θw(ψ), following any sequence of wetting and drying processes, from the measured main wetting curve. It is proved theoretically that a shape-similarity exists among the different wetting curves of a given soil. Each wetting scanning curve and the main wetting curve are described by the same normalized equation, over the common interval of ψ values. This shape-similarity is a direct result of the Mualem domain theory. On this basis, a general unique equation is formulated for prediction of all wetting scanning curves, of all orders, which is compatible with the Mualem dependent, as well as independent, domain theory. On the same theoretical basis, it is proved that no similarity exists among the drying scanning curves. Thus, the use of the scaling transformation for prediction of the drying scans is subjected to inconsistency with the physical principles underlying the dependent domain theory. As a result, scaling in this case would inevitably lead to inaccuracies in the calculated drying curves. A significant step forward has been made in the present study, from Mualem’s dependent domain model (1984) with its implicit predictive formulae of the drying scanning curves. A unique explicit equation was theoretically derived, applicable for describing the drying scanning curves of all orders. This unique equation of the drying scanning curves, together with the general single equation of the wetting scanning curves, provided closure of all theoretical wetting and drying scans within the main hysteresis loop. Consequently, the retention function following any sequence of successive wetting and drying processes can be predicted by these two equations determined by the measured boundary curves.

In order to investigate the effects of sorption isotherm hysteresis on indoor climate and energy demand, a new module for precise representation of mass transfer in materials in contact with indoor air, called Humi-mur, was developed and implemented in the energy performance simulation tool, TRNSYS. This extended whole-building HAM (Heat–Air–Moisture) simulation tool was then used to investigate the impact of the moisture-buffering effect on indoor conditions in a room. Two modelling approaches were compared: including/excluding moisture-buffering effect and including/excluding hysteresis in sorption isotherm. In addition, two ventilation strategies were used: constant airflow ventilation (CAV) and relative humidity sensitive ventilation (RHS). The simulation showed that for the CAV system, the use of moisture-buffering materials did not change energy demand but improved the indoor conditions. For the RHS ventilation system, the use of the buffering materials led to a higher energy demand, but the indoor relative humidity comfort was significantly improved. The results also showed that hysteresis of the sorption isotherm impacts on indoor conditions, even if the effect is smaller for the studied material than the average moisture-buffering effect.

The flow of liquids in unsaturated porous mediums follows the ordinary laws of hydrodynamics, the motion being produced by gravity and the pressure gradient force acting in the liquid. By making use of Darcey's law, that flow is proportional to the forces producing flow, the equation K∇<sup>2</sup>ψ+∇K·∇ψ+g∂K/∂z=-ρ<sub>s</sub>A∂ψ/∂t may be derived for the capillary conduction of liquids in porous mediums. It is possible experimentally to determine the capillary potential ψ=∫dp/ρ, the capillary conductivity K, which is defined by the flow equation q=K(g-▿ψ), and the capillary capacity A, which is the rate of change of the liquid content of the medium with respect to ψ. These variables are analogous, respectively, to the temperature, thermal conductivity, and thermal capacity in the case of heat flow. Data are presented and application of the equations is made for the capillary conduction of water through soil and clay but the mathematical formulations and the experimental methods developed may be used to express capillary flow for other liquids and mediums. The possible existance of a hysteresis effect between the capillary potential and moisture content of a porous medium is considered.

The processes of mass transfer in the material influence not only the conditions within the material but also inside the connected air spaces. A new module for precise representation of mass transfer in materials in contact with the indoor air, called Humi-mur, was elaborated and validated in this work. It allows for the precise representation of sorption isotherm and vapour permeability dependence on relative humidity. Also the sorption curve hysteresis has been implemented. The new module was then applied to estimate the sensitivity of the results to uncertainty in measured material properties and the impact of hysteresis effect. Reasonable estimation of experimental uncertainty resulted in the deviation of approximately 6% in the calculated results. Hysteresis quite strongly influences the dynamic behaviour of materials. Concerning hysteresis in the sorption isotherm, we showed that the average of the adsorption and desorption equations is a reasonable approximation of mean behaviour for coarse calculation. In case when precise results of the relative humidity (absolute humidity) are needed, the hysteresis effect should be taken into account.

This paper describes the coupling of a model for heat and moisture transport in porous materials to a commercial Computational Fluid Dynamics (CFD) package. The combination of CFD and the material model makes it possible to assess the risk of moisture related damage in valuable objects for cases with large temperature or humidity gradients in the air. To couple both models the choice was made to integrate the porous material model into the CFD package. This requires the heat and moisture transport equations in the air and the porous material to be written down in function of the same transported variables. Validation with benchmark experiments proved the good functionality of the coupled model. A simulation study of a microclimate vitrine for paintings shows that phenomena observed in these vitrines are well predicted by the model and that data generated by the model provides additional insights in the physical mechanisms behind these phenomena.

Existing methods available for practising designers and architects to calculate moisture transfer through building constructions are reviewed and a transient model on combined heat and moisture transfer in composite constructions is introduced. Results using the transient model on a particular case are compared with those obtained using the traditional methods. The consideration of hygroscopic inertia by the transient model significantly alters the prediction of how moisture migrates within and through a building construction.

The sustainable world's economic growth and people's life improvement greatly depend on the use of alternative products in the architecture and construction, such as industrial wastes conventionally called green materials. For this purpose, hemp concrete is more and more recommended by the eco-builders because hemp is a renewable plant, recyclable and does not degrade within time. It corresponds perfectly to the requirements of high environmental quality buildings. The objective of this article is to study transient hygrothermal behaviour of hemp concrete at whole building level. The physical model is one-dimensional and was implemented into the object-oriented simulation environment SPARK, using the finite difference technique with an implicit scheme. The numerical result showed that the use of hemp concrete wall in buildings can ensure good indoor air quality and energy savings in winter. Besides, the combined effect of moisture buffering with the adequate ventilation strategies increases hemp concrete building performance. Our results also suggest that taking into account the hygrothermal transfer at whole building level with heat and moisture production sources has significant effects on predictions.

It is shown that the Du Fort-Frankel method is unstable for the diffusion equation, if the usual central difference approximations are made to linear boundary conditions involving first order space derivatives. This is shown to be true even when the corresponding differential equation is stable. A modified boundary condition is presented which is proved to be stable provided the differential equation is stable.

Modelling of moisture transport in wood with hysteresis and temperature dependence sorption characteristics

- Rode

C. Rode, C.O. Clorius, Modelling of moisture transport in wood with hysteresis and
temperature dependence sorption characteristics, in: Proceedings of the
Conference Performance of Exterior Envelopes of Whole Buildings IX, 2004.
Florida.

Experimental and numerical analysis of the transient hygrothermal behavior of multilayered hemp concrete wall

- A Zaknoune
- P Glouannec
- P Salagnac

A. Zaknoune, P. Glouannec, P. Salagnac, Experimental and numerical analysis of
the transient hygrothermal behavior of multilayered hemp concrete wall, Heat
Mass Transf. 48 (2) (2016) 205-215.

Experimental and numerical analysis of the transient hygrothermal behavior of multilayered hemp concrete wall

- Zaknoune