Thermal Exchanges Research Articles

Thermomagnetoelastic Stability of Ferromagnetic Cylindrical Shell Carrying Constant Electric Current

The modeling and study of the instability behavior of a magnetically active ferromagnetic cylindrical shell exposed to thermal and magnetic fields with a constant electric current is considered in this paper. It is assumed that the internal surface area of the shell is covered by the thin conductive cylindrical strip. The thickness of this metallic strip is small as compared to the total thickness of the shell and therefore its contribution to the elastic properties of the overall cylindrical shell can be considered negligible. The thermal and magnetic fields of the undisturbed state of the shell are determined assuming that the edges of the shell are thermo-isolated. Undisturbed state coincides with the equilibrium which was generated under the action of thermal field (in equilibrium the forces of magnetic origin are equal to zero). It is also assumed that the thermal exchanges shell-to-strip and shell-to-external media follow Newton-Rickman's law. Using the theory of thermo-magneto-elasticity of undisturbed state in conjunction with the predetermined thermal and magnetic fields the stresses of the undisturbed state are determined under the assumption that the deflection along the generators of the shell equals to zero. The solutions of the homogeneous boundary value problems are carried out and the buckling analysis of the shell is investigated. In particular, a close-form solution for the critical value of electric current for which the shell becomes statically unstable is presented.

Improvement in Thixoforging of 7075 Aluminium Alloys at High Solid Fraction

Thixoforging is a type of semi-solid metal processing at high solid fraction (0.5<fs<1). 7075 aluminium alloys have been used as a feedstock for thixoforging in order to investigate thixoformability of a high performance aluminium alloy at high solid fraction. Higher solid fraction of 7075 alloy is less sensitive to temperature, avoids metal splash at high speed and allows laminar flow at high speed. Hot tool combined with lubricant tool coating are used to slow down the solidification rate of the high solid fraction metal by decreasing thermal exchanges with the tool. Improved thermal and forming parameters [1-2] will be applied to produce an automotive component by thixoforging and mechanical properties have been measured from tensile samples. High mechanical properties are obtained after T6 thermal treatment.

Measurements of projected areas of seated and standing people of southern Italy based on a statistical analysis

One of the most important components affecting the human thermal balance is represented by its radiative exchange with the surrounding surfaces. The projected area of the human body is an important parameter of these thermal exchanges. Unfortunately, although the anthropometric measures of people are characterized by significant differences among various populations, the experimental data currently available in the literature refers to a small group of people. Moreover, measurements are generally performed regardless of the statistical significance of the involved subjects with respect to the population to which they belong. In this study, a statistical study is introduced that is based on a large analysis of the anthropometric characteristics of the analysed population. Moreover, a new experimental procedure is applied to evaluate the projected area factor and the effective radiating area of a sample of people belonging to the population of southern Italy. The calculated projected area factors are fairly in accordance with those originally proposed by Fanger for standing people. For seated people, however, the experimental values of the present study show some differences from those of the literature. This study provided a tentative explanation for these discrepancies.

Influence of non-reactive particles on the microstructure of NiAl and NiAl–ZrO 2 processed by thermal explosion

Nickel aluminide intermetallic alloy and NiAl–ZrO 2 composites were synthesized in a hot press by sintering reaction and thermal explosion (or Self-propagating High temperature Synthesis, SHS). The addition of a post-SHS heat treatment allows a control of the microstructure and an enhancement of the mechanical characteristics. Thus, NiAl properties processed by self-combustion are above those obtained by reactive sintering (RS). For all these syntheses, the role played by the non-reactive particles is determining. Indeed, the product granulometry is a function of the diluent size distribution since this latter acts as nucleation sites during the reactive processes. These particles can also enhance mechanical properties by specific reinforcement mechanisms and exercise an influence on SHS reaction parameters by controlling its reactivity and the thermal exchanges during self-combustion.

Steel thixoforming, influence of forming parameters on the microstructure

Forming of parts in the semi-solid state is quite a complex process, especially for high melting point alloys such as steel. A reason for this complexity is the amount of parameters involved in the process. Among these we could quote liquid fraction, shear rate, shape factor, contiguity, tool temperature, agglomeration level, heating rate, protecting gas, temperature distribution, lubricant. Of course all of these parameters don’t have the same order of importance. In this paper we show the influence of a set of chosen parameters and we highlight their effects on the microstructure and so, on the deformation behavior. The studied parameters are the heating conditions, the tool temperature, the part temperature, the thermal exchanges between the part and the dies and the forming rate.

Extrusion tests of 7075 aluminium alloy at high solid fraction

Thixoforging is a type of semi-solid metal processing at high solid fraction (0.5 < fs < 1). 7075 aluminium alloy has been used as a feedstock for thixoforging in order to investigate thixoformability of a high performance aluminium alloy at high solid fraction. Higher solid fraction of 7075 alloy is less sensitive to a drop in temperature, avoids metal splash at high speed, allows laminar flow at high speed. Hot tool is used to slow down the solidification rate of the high solid fraction metal by decreasing thermal exchanges. To determine the best parameters to achieve maximum mechanical properties in thixoforging of 7075 aluminum alloy, we need to consider the impact of some parameters such as tool temperature, shear rate. For this, we use extrusion tests with constant speed [1] where these parameters are known. The result of this study is that each parameter has its level of impact on the thixoforging: the temperature of the tool and the deformation rate shouldn’t be high to avoid cracks. Thermal exchanges between the material flow and the tool have to be reduced to avoid high solidification rate [2].

Thermal Exchanges and Thermomechanical Couplings in Amorphous Polymers

During mechanical loading, the strain process can be accompanied by thermal effects generated by thermomechanical couplings. The aim of this work was the determination of energy (heat sources, mechanical energy, internal dissipated energy) during a mechanical test on polymer materials by observing strain and thermal data fields. Heat sources were calculated by establishing the heat equation using concepts of the classical thermodynamics of irreversible processes and applied to polymer materials. With a simple experimental set-up, we show that the thermal exchanges and the thermal losses in polymer samples are mainly induced by conduction and convective. The temperature at the surface was assumed to be equal to the average temperature in the thickness. We show that it is possible to obtain heat source values quantitatively without knowing their position and dimension along the thickness. It can also be difficult to calculate heat sources correctly because of lack of knowledge of the polymer property values involved in the heat equation (thermal conductivity, specific heat and heat transfer coefficient). So we present a procedure to determine these thermal parameters easily in our environmental conditions of work without making a mechanical hypothesis, and without knowing the heat source distribution because we analyse thermal data as soon as the heat source is switched off. In conclusion, we show an application involving a large strain mechanical test on a specimen of PC. The strain field is obtained by a mark tracking method. The energy balance has been calculated and associated with the volumetric deformation, showing the macroscopic and microscopic behaviour.

Modelling and experimental validation of a fluidized-bed reactor freeboard region: Application to natural gas combustion

A theoretical and experimental study of natural gas–air mixture combustion in a fluidized bed of sand particles is presented. The operating temperatures are lower than a critical temperature of 800 °C above which the combustion occurs in the vicinity of the fluidized bed. Our study focusses on the freeboard zone where most of the methane combustion takes place at such temperatures. Experimental results show the essential role of the projection zone in determining the global thermal efficiency of the reactor. The dense bed temperature, the fluidizing velocity and the mean particle diameter significantly affect the thermal behaviours. A model for natural gas–air mixture combustion in fluidized beds is proposed, counting for interactions between dense and dilute regions of the reactor [P. Pré, M. Hemati, B. Marchand, Study of natural gas combustion in fluidised beds: modelling and experimental validation, Chem. Eng. Sci. 53 (1998) (16), 2871] supplemented with the freeboard region modelling of Kunii–Levenspiel [D. Kunii, O. Levenspiel, Fluidized reactor models: 1. For bubbling beds of fines, intermediate and large particles. 2. For the lean phase: freeboard and fast fluidization, Ind. Eng. Chem. Res. 29 (1990) 1226–1234]. Thermal exchanges due to the convection between gas and particles, and due to the conduction and radiation phenomena between the gas-particle suspension and the reactor walls are counted. The kinetic scheme for the methane conversion is that proposed by Dryer and Glassman [F.L. Dryer, I. Glassman, High-temperature oxidation of CO and CH4, Proceedings of the 14th International Symposium on Combustion, The Combustion Institute, Pittsburg (1973) 987]. Model predictions are in good agreement with the measurements.

Temperature dependence of de Gennes narrowing and transport properties of liquid rubidium: Experimental and simulation results

Recent neutron scattering results [F. Demmel et al., Phys. Rev. B 73, 104207 (2006)] on the temperature dependence of de Gennes narrowing in liquid rubidium have stimulated a molecular dynamics (MD) study in the same temperature and density range. At the $k$ value of the first peak of $S(k)$, the MD results agree very well with experimental data of $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{S}({k}_{\mathrm{max}},\ensuremath{\omega}=0)$, $F({k}_{\mathrm{max}},t=0)$, and longitudinal viscosity ${\ensuremath{\eta}}_{L}({k}_{\mathrm{max}},\ensuremath{\omega}=0)$. Other transport properties, such as self-diffusion and shear viscosity, are also accurately reproduced. At $k=0$, on the other hand, the MD results significantly underestimate the experimental values of bulk viscosity and thermal conductivity. For the latter, this is a well known deficiency of models which do not explicitly take into account the electronic contribution to thermal exchanges. However, the large difference between MD and macroscopic experimental data for bulk viscosity casts some doubts on its indirect calculation from sound absorption data. This contradictory result, which presumably extends to all alkali metals, is discussed in the light of various theoretical models.

Multicriteria-oriented preliminary design of a flash evaporation process for cooling in the wine-making process

The flash evaporation process uses pressure differences to cause instantaneous fluid cooling and concentration. It is thus used for shortened cooling time in the wine-making process. Although promising since it allows grape cooling and concentration in addition to improving wine quality with one single device, the development of this process remains limited because of the poor efficiency of the thermal exchanges and the important size of the installations. The preliminary design stage is one of the first steps of the design process. Often neglected, this stage is nevertheless important since decisions taken at this point, like gauging and choosing components, are of major importance in relation to global development costs. In order to improve the system compactness and thermal efficiency and, to support the decision-making process, a multicriteria and multiphysics-oriented preliminary design of an innovative two-stage flash evaporation process for cooling in wine-making process was performed. Using a specific formalisation methodology that uses Constraint Satisfaction Problem techniques to enable taking into consideration different types of data, constraints related to the physical behaviour of the system and to manufacturing, encumbrance, eco-design and cost criteria are simultaneously included in the design model. The entire physical model, considering multiple coupled phenomena, was validated through an experimental analysis carried out on an instrumented pilot unit. Results are presented and discussed. Global results, considering physics, gauging, mass, costs and eco-design constraints are also presented and discussed. A detailed design flash evaporator specifically for industrial use is briefly described.

A Monte Carlo implementation to solve radiation heat transfer in non-uniform media with spectrally dependent properties

This paper presents the application of the Monte Carlo method to solve the radiative heat exchange in non-homogeneous, non-isothermal gases with spectrally dependent properties. Among others models, the absorption-line blackbody (ALB) distribution function, originally defined and derived for the spectral line-based weighted-sum-of-gray-gases (SLW) model, allows an immediate, simple implementation of the Monte Carlo method to account the spectral dependence of the radiative properties. This work shows how the Monte Carlo method can be combined to the ALB distribution function, and provides results for heat transfer in a mixture of water vapor, carbon dioxide and nitrogen that have satisfactory agreement with the SLW method and with line-by-line integration. Finally, the solution technique is employed to solve two examples aiming at demonstrating the effect of the absorbing species concentration on the thermal radiative exchanges. The method is of great interest for the computation of radiative transfer in combustion systems where the chemical species concentration and the temperature are not uniform.

From cold dialysis to isothermic dialysis: a twenty-five year voyage

Twenty-five years have passed since our groupdescribed for the first time the role played byTemperature (T) in cardiovascular stability. ‘Cold’treatments prevented the hypotension induced by‘warm’ treatments, whether in haemodialysis (HD) orin isolated ultrafiltration [1] or in haemofiltration [2,3].Though some notes of caution were sounded [4],all researchers studying the problem in the years thatfollowed confirmed the role played by T in short-term[5–9] as well as in long-term studies [10,11]. Ascompared to standard HD or ‘warm’ HD, that iswith dialysate T of 37–37.58C, ‘cold’ HD, that is withdialysate T of 35–35.58C, ensures better cardiovascularstability. In 1997, reduction of dialysate T wasrecommended by the DOQI Guidelines as a meansto prevent intradialytic hypotension [12]. A systematicreview recently published found that ‘intradialytichypotension occurred 7.1 (95% CI, 5.3–8.9) times lessfrequently with cool-temperature dialysis. A total of 22studies comprising 408 patients were included, all studieswere of crossover design and relatively short duration’[13]. Lastly, the European Best Practice Guidelinesson cardiovascular instability, announced at the 2006ERA-EDTA Congress, scored only cold dialysis withevidence level I, among the different dialysis techniquesusually adopted to prevent intradialytic hypotension.The terms ‘warm’ and ‘cold’ HD, though immedi-ately understandable, are in reality too simplistic todescribe the complex interrelations between the ther-mal profile of the dialytic treatment and its impact onthe patient’s body T and cardiocirculatory function.Since 1984a good correlation (r¼0.75) betweenvariations in dialysate T in the 34–388C range andconcomitant changes in patients’ body T has beenfound [14]. However, in standard HD with a dialysateT of 378C no thermal exchanges, on average, took placein the extracorporeal circuit, in that the T of the bloodin the venous line was equal to or slightly lower thanthat of the arterial line [14]. Despite this thermoneutralbehaviour however, an average rise in patient’s body Tof 0.5–0.78C takes place [14,15], and this is the reasonfor defining standard HD as a ‘warm’ treatment.However, further analysing the behaviour of individualpatients, differentiated responses (with some subjectswho tended to warm up and others to cool down), forthe same T of the dialysate were described [15].To better understand the physio-pathologicalmechanisms and the clinical implications underlyingdialytic hyperthermia, it is useful to review thephysiology of the relations between T and arterialpressure, to evaluate whether the haemodynamicprofile during HD is in accordance with physiologyand finally, to study what determines thermal balancein the course of HD.

Determination of the inlet temperature profile of an extrusion die in unsteady flow

The aim of this study is to determine the temperature profile at the inlet of an extrusion die by measurements in unsteady flow. Temperature measurements are collected by thermocouples installed along the die, in walls, at the borders of the extrusion channel. Measured temperatures are function of the inlet temperature profile, which we are looking for, of the heat generated by the viscous dissipation and of thermal transfers inside the walls and inside the extrudated polymer. Sensitivity to all those phenomena is thus a crucial problem. Our model describes flow, heat generation, thermal exchanges, and their coupling by thermal rheological laws. Experimental validation of numerical results is provided thanks to real measurements from an instrumented die. The adjoint method is used to solve the inverse problem. First results are shown and analyzed.

Thixoforming of Steel – Influence of Thermal Parameters

This paper presents experimental results on steel thixoforming. The influence of thermal effects on the semi-solid response is analysed through the influence of thermal exchanges with tools and environment. Several rheological experiments such as compression, extrusion or radial filling test were developed to understand the semi-solid steel behaviour and determine the parameters that have a major influence on thixoforming. Actually, in our experiments, the temperature of the slug and consequently the solid fraction were found first order parameters while; the morphology of the solid phase plays a minor role.

A multi-scale approach to urban thermal analysis

An environmental consequence of urbanization is the urban heat island effect, a situation where urban areas are warmer than surrounding rural areas. The urban heat island phenomenon results from the replacement of natural landscapes with impervious surfaces such as concrete and asphalt and is linked to adverse economic and environmental impacts. In order to better understand the urban microclimate, a greater assessment of the overall urban thermal pattern, including an analysis of the thermal properties of individual land covers, is needed. This study examines the surface thermal pattern by means of thermal land cover response for the Salt Lake City, Utah, study area at two scales: 1) the community level, and 2) the regional or valleywide level. Airborne ATLAS (Advanced Thermal and Land Applications Sensor) data, a high spatial resolution (10-meter) dataset appropriate for an environment containing a concentration of diverse land covers, are used for both land cover and thermal analysis at the community level. The ATLAS data consist of 15 channels covering the visible, near-IR, mid-IR and thermal-IR wavelengths. At the regional level Landsat TM data are used for land cover analysis while the ATLAS channel 13 data are used for the thermal analysis. Results show that a ground-level heat island is evident at both the community and the valleywide level where there is an abundance of impervious surfaces. ATLAS data perform well in community level studies in terms of land cover and thermal exchanges, but other, more coarse-resolution data sets are more appropriate for large-area thermal studies. Thermal response per land cover is consistent at both levels, which suggests potential for comparison with more coarse spatial resolution studies.

Microclimates of l'Aven d'Orgnac and other French limestone caves (Chauvet, Esparros, Marsoulas)

AbstractWe assess the aerodynamics of the atmosphere in some limestone caves using a 5‐year monitoring of the Aven d'Orgnac system, shorter thermal vertical profiling experiments, and comparison with the time series from other French caves. In the first rooms, located under the Aven opening, our records indicate, for each year, a succession of a summer regime characterized by stable parameters (except for the perturbations introduced by tourist visits) and a winter regime, in which the inner air temperature drops and is highly correlated with that outside. Atmospheric composition suggests that during the winter regime the cave is ventilated by the outside air. We show that the onset of the winter regime is governed by a thermo‐convective instability involving the inflow of the outside cold and dense air. Atmospheric temperature and composition allow us to follow the stepwise progression of the winter regime toward the adjacent rooms.In the Salle Plane (SP), a far room of the Orgnac‐Issirac karstic system, in which the winter regime has never been observed, the air temperature is extremely homogeneous and steady, and is characterized by a half‐daily signal of amplitude less than 0.03 °C, which is correlated with the derivative of pressure versus time. This correlation, which is also observed in various other confined caves, may be explained by pressure‐induced temperature changes relaxed in less than 1 h by thermal exchanges with a large volume of rock whose temperature is assumed to be constant.The various microclimates of karstic cave systems should be taken into account for the conservation of the caves open to tourists and for the interpretation of growth laminae of speleothems. Copyright © 2006 Royal Meteorological Society.

The sources of thermal energy exchange accompanying microbial catabolism

Calculations are made of thermal energy exchanges from catabolic reactions in the aqueous state, using thermodynamic properties at 0.001 M, indicated by subscript “ B ”. Heats of reaction are calculated as Δ r H B , 298.15 o ′ = Δ r X B , 298.15 o ′ + Δ r Q ab , B , 298.15 o ′ (1), or as Δ r H B , 298.15 o ′ = Δ r G B , 298.15 o ′ + T Δ r S B , 298.15 o ′ (2), where Δ r X B , 298.15 o ′ and Δ r G B , 298.15 o ′ represent non-thermal, chemical energy converted into thermal energy during a reaction and where Δ r Q ab , B , 298.15 o ′ and T Δ r S B , 298.15 o ′ represent the exchange of absorbed thermal energy as reactants become converted into products. Percentages are tabulated of the thermal energy exchanges contributed to Δ r H B , 298.15 o ′ by Δ r X B , 298.15 o ′ and Δ r Q ab , B , 298.15 o ′ , and by Δ r G B , 298.15 o ′ and T Δ r S B , 298.15 o ′ . Aerobically, for substrates not containing nitrogen, the value of Δ r X B , 298.15 o ′ averages 4.21% more negative than that of Δ r G B , 298.15 o ′ . For substrates containing nitrogen this average drops to 1.80%. For substances not containing nitrogen, the thermal energy contributed by Δ r Q ab , B , 298.15 o ′ to Δ r H B , 298.15 o ′ averages 2.21%, whereas that contributed by T Δ r S B , 298.15 o ′ averages −1.95%. The difference is 4.16%, which is close to the average value of 4.21% that Δ r X B , 298.15 o ′ is more negative than Δ r G B , 298.15 o ′ . This observation indicates that the difference between Δ r X B , 298.15 o ′ and Δ r G B , 298.15 o ′ is due almost entirely to the manner in which exchanges in absorbed thermal energies are measured or calculated for the reaction systems studied. The same applies to the oxidation of substances containing nitrogen. Here, the thermal energy contributed to Δ r H B , 298.15 o ′ by Δ r Q ab , B , 298.15 o ′ averages 5.32%, whereas that contributed by T Δ r S B , 298.15 o ′ averages 3.50%. The difference between them is 1.82%, which is close to the average value of 1.80% that Δ r X B , 298.15 o ′ is more negative than Δ r G B , 298.15 o ′ . Anaerobically, for the processes tested fewer inferences could be drawn. The values of Δ r G B , 298.15 o ′ are much more negative than those of Δ r X B , 298.15 o ′ in three examples out of five and widely variable, quite the opposite of the data on the aerobic processes. One anaerobic Δ r X B , 298.15 o ′ value is positive, indicating that something other than the total free energy change must be driving this particular process.

DID EMBRYONIC RESPONSES TO INCUBATION CONDITIONS DRIVE THE EVOLUTION OF REPRODUCTIVE MODES IN SQUAMATE REPTILES?

Viviparity (live-bearing) has evolved from oviparity (egg-laying) more than 100 times within snakes and lizards, and thermal factors are thought to have driven this shift. However, other major features of reptilian reproduction may reflect selective pressures related to hydric rather than thermal exchanges between the egg and its incubation environment. Notably, why are intermediate stages of prolonged egg retention so rarely seen? Embryonic stages at oviposition in squamates are largely dichotomous: most oviparous species lay eggs with embryos about one-third developed, whereas viviparous taxa retain the eggs until development is complete. Why don't more species oviposit with embryos at either earlier or later stages? We suggest that the scarcity of squamates that lay eggs soon after ovulation (and thus, with very early-stage embryos) may reflect the need to delay oviposition until embryos have developed sufficient physiological control over water influx and efflux to survive in the challenging hydric environment of the nest. The scarcity of retention to later stages (intermediate between typical oviparity and viviparity), and the apparent lack of reversals from viviparity back to oviparity, may be due to a conflict between adaptations for water versus gas exchange; retention of larger embryos in utero requires eggshell thinning to allow gas exchange, but a thinner shell precludes effective hydric control after oviposition. Thus, although the transition from oviparity to viviparity in squamates has been driven largely by thermal advantages, the clustering of species at two main positions along the oviparity-viviparity continuum may be due to challenges of controlling embryonic water balance.

A comparative study of two large radiative dew water condensers

In order to improve the yield of dew condensation from atmospheric vapor, two large (30 m 2 in area) insulated plane radiative condensers, inclined at 30°, were installed in Ajaccio (Corsica island, France; latitude 41°55′N, longitude 8°48′E). Prototype P1 was elevated such that the underside was open and exposed. Prototype P2, however, was enclosed on all sides and closer to the ground. Both used a special radiative foil that enhances dew formation. The period of observation for P1 was July 22, 2000–November 11, 2001, and for P2 was December 10, 2001–December 10, 2003. All data were compared with respect to the same horizontal calibration plate of polymethylmethacrylate (Plexiglas) placed at 1 m above the ground on a sensitive recording balance. Water yield of both prototypes were compared and correlated against meteorological data (cloud cover, relative humidity, wind speed, condenser temperature and air temperature). Both prototypes exhibit improved performances when compared with the calibration plate: more dew days (+16% and +15% for P1 and P2, respectively); decrease of the humidity threshold (−3% and −4.4% for P1 and P2); increase of dew yields for wind speeds up to 3 m s −1. A model of the mass and thermal exchanges with the ambient air was used. Two adjustable parameters (heat and mass transfer coefficients) are used in the model. The values of these parameters were found larger than the values obtained in continental sites where dew forms with weak wind, thus emphasizing the peculiarities of dew formation in windy islands. When data are reduced with the calibration PMMA data, prototype P1 provided average water yields slightly larger than the enclosed prototype P2, a result that can be attributed to the influence of surface thermal radiation.

Dados climáticos para avaliação de desempenho térmico de edificações

O desempenho térmico de edificações é um fator importante em habitações, notadamente naquelas destinadas a pessoas de baixa renda. Uma edificação projetada para o clima no qual está inserida torna-se confortável, além de economizar energia. A avaliação do desempenho térmico de uma edificação engloba a resposta global do projeto arquitetônico proposto em relação às trocas térmicas entre o ambiente construído e o ambiente externo, onde a caracterização das condições climáticas locais é uma das etapas mais importantes. As condições de exposição da edificação ao clima são caracterizadas pelos valores locais horários da radiação solar, da temperatura e umidade relativa do ar e também pela velocidade predominante do vento. Nos métodos de avaliação do desempenho térmico, os dados climáticos são caracterizados pelos dias típicos de projeto, para os períodos de inverno e verão. Esses dias são determinados em função de sua freqüência de ocorrência e representam níveis de exigência na avaliação. Nesse trabalho, apresenta-se uma metodologia para se estimarem os dias típicos de projeto, por meio do tratamento estatístico dos dados climáticos.