Nous avons développé un modèle prédictif, utilisant le principe de contribution de groupes, pour prédire avec précision, le comportement des fluides pétroliers. Ce modèle baptisé PPR78 utilise l’équation d’état de Peng et Robinson et des règles de mélange de type Van der Waals avec un coefficient d’interaction binaire kij, dépendant de la température. De telles règles de mélange sont équivalentes à celles obtenues en combinant à compacité constante une fonction d’excès de type Van Laar et une équation d’état cubique.La première partie de cette étude a consisté à étendre le domaine d’application du modèle PPR78 aux systèmes contenant de l’eau, des alcènes et de l’hydrogène, en définissant six nouveaux groupes élémentaires. Une bonne précision du modèle est obtenue pour décrire les équilibres de phases de systèmes binaires impliquant ces constituants, notamment pour les systèmes présentant des diagrammes de phases de Type I et de Type II. Dans la deuxième partie l’ensemble des paramètres de groupes ont été réajustés, non seulement sur des données d’équilibres de phases mais également sur des données de grandeur de mélange. L’avantage de ce nouveau modèle E-PPR78 est qu’il permet de restituer les équilibres de phases avec une précision équivalente au modèle original et qu’il conduit à une très nette amélioration de la prédiction des enthalpies d’excès et des capacités calorifiques d’excès. / We have developed a predictive model, by means of a group contribution method, in order to predict with accuracy, the behavior of petroleum fluids. The model called PPR78 uses the Peng-Robinson equation of state and Van der Waals-type mixing rules with a temperature dependent binary interaction parameter kij. Such mixing rules are identical to those obtained by combining at constant packing fraction, a Van Laar-type excess function and a cubic equation of state.The first part of this study consisted in extending the application of the model PPR78 to systems containing water, alkenes and hydrogen, by defining six new elementary groups. The phase equilibria of binary systems involving these components are accurately described by the model, especially for the phase diagrams of Type I and Type II. In the second part, all the group parameters of the original model were re-fitted by using the phase equilibrium data, as well as the mixing property data. The advantage of this new model E-PPR78 is that it is capable to correlate the phase equilibria with an accuracy which is equivalent to the original model and it produces a very clear improvement in the prediction of excess enthalpies and excess heat capacities.

Made available in DSpace on 2017-07-21T18:53:18Z (GMT). No. of bitstreams: 1 Tiago Andre Denck Colman.pdf: 2275498 bytes, checksum: 7e32b023c4865edb06d349d33b4c809d (MD5) Previous issue date: 2013-05-07 / Samples of acid-modified and oxidised untreated cassava starch were exposed to microwave radiation for periods of five, ten and fifteen minutes. Immediately after these exposure periods the temperature of each starch sample was measured, which was at a maximum of 135 °C. All samples were analysed by thermogravimetry and derivative thermogravimetry (TG/DTG); differential scanning calorimetry (DSC); rapid viscoamylographic analysis (RVA); X-ray diffraction powder, and non-contact atomic force microscopy (NC-AFM). Colour characteristics were determined by reflectance spectrophotometry. Thermal behaviour, gelatinisation temperature, enthalpy, and paste and structural properties were determined. Viscosity gradually decreased with increasing exposure to microwaves for the samples of untreated and oxidised starch samples. The acid-modified starch failed to show pasting properties during all the periods of exposure to radiation. The relative degree of crystallinity (%) increased with the acid-modification and decreased with increasing exposure time to microwave radiation. The micro images obtained by NC-AFM showed a gradual increase in the diameter of the granules of the acid-modified and oxidised starches; for the samples of untreated starch no significant variation was observed in the granule diameter after exposure to microwaves. Reflectance spectrophotometry showed that there was a progressive change in colour due to the microwave action causing a trend mainly to yellow for all the studied samples. / Amostras de amido de mandioca nativo, ácido-modificado e oxidado foram expostas a radiação de micro-ondas pelos tempos de cinco, dez e quinze minutos. Imediatamente após a exposição, foi medida a temperatura de cada uma das amostras de amido, que foi de no máximo de 135 ºC. Todas as amostras foram analisadas por Termogravimetria e Termogravimetria Derivada (TG/DTG), Calorimetria Exploratória Diferencial (DSC), Análise Viscoamilográfica (RVA), Difração de raios X em pó, microscopia de força atômica, pelo método não-contato (NC-AFM) e as características de cor foram determinadas por espectrofotometria de refletância. O comportamento térmico, temperaturas de gelatinização, entalpia e propriedades de pasta e estruturais foram determinados. A viscosidade diminuiu gradualmente com o aumento a exposição as micro-ondas para as amostras de amido nativo e oxidado e as amostras de amido ácido-modificado deixaram de apresentar propriedades de pasta em todos os tempos de exposição a radiação. O grau de cristalinidade relativa (%) aumentou com a modificação ácida e diminuiu proporcionalmente ao aumento de tempo de exposição as micro-ondas. As microimagens obtidas através da NC-AFM revelaram um aumento gradual no diâmetro dos grânulos dos amidos ácido-modificado e oxidado e para as amostras de amido nativo não foi observada variação significativa no diâmetro dos grânulos com a exposição as micro-ondas. A espectrofotometria de reflectância demonstra que ocorreu uma alteração na cor pela ação das micro-ondas progressivamente causando principalmente a tendências para amarelo para todas as amostras estudadas.

L'objectif de cette thèse est de développer un nouveau code pour prédire l'équilibre final d'un processus chimique complexe impliquant beaucoup de produits, plusieurs phases et plusieurs processus chimiques. Des méthodes numériques ont été développées au cours des dernières décennies pour prédire les équilibres chimiques finaux en utilisant le principe de minimisation de l'enthalpie libre du système. La plupart des méthodes utilisent la méthode des « multiplicateurs de Lagrange » et résolvent les équations en employant une approximation du problème de Lagrange et en utilisant un algorithme de convergence pas à pas de type Newton-Raphson. Les équations mathématiques correspondantes restent cependant fortement non linéaires, de sorte que la résolution, notamment de systèmes multiphasiques, peut être très aléatoire. Une méthode alternative de recherche du minimum de l’énergie de Gibbs (MCGE) est développée dans ce travail, basée sur une technique de Monte-Carlo associée à une technique de Pivot de Gauss pour sélectionner des vecteurs composition satisfaisant la conservation des atomes. L'enthalpie libre est calculée pour chaque vecteur et le minimum est recherché de manière très simple. Cette méthode ne présente a priori pas de limite d’application (y compris pour las mélanges multiphasiques) et l’équation permettant de calculer l’énergie de Gibbs n’a pas à être discrétisée. Il est en outre montré que la précision des prédictions dépend assez significativement des valeurs thermodynamiques d’entrée telles l'énergie de formation des produits et les paramètres d'interaction moléculaire. La valeur absolue de ces paramètres n'a pas autant d’importance que la précision de leur évolution en fonction des paramètres du process (pression, température, ...). Ainsi, une méthode d'estimation cohérente est requise. Pour cela, la théorie de la « contribution de groupe » est utilisée (ceux de UNIFAC) et a été étendue en dehors du domaine d'interaction moléculaire traditionnel, par exemple pour prédire l'énergie de formation d’enthalpie libre, la chaleur spécifique... Enfin, l'influence du choix de la liste finale des produits est discutée. On montre que la prédictibilité dépend du choix initial de la liste de produits et notamment de son exhaustivité. Une technique basée sur le travail de Brignole et Gani est proposée pour engendrer automatiquement la liste des produits stable possibles. Ces techniques ont été programmées dans un nouveau code : CIRCE. Les travaux de Brignole et de Gani sont mis en œuvre sur la base de la composition atomique des réactifs pour prédire toutes les molécules « réalisables ». La théorie de la « contribution du groupe » est mise en œuvre pour le calcul des propriétés de paramètres thermodynamiques. La méthode MCGE est enfin utilisée pour trouver le minimum absolu de la fonction d'enthalpie libre. Le code semble plus polyvalent que les codes traditionnels (CEA, ASPEN, ...) mais il est plus coûteux en termes de temps de calcul. Il peut aussi être plus prédictif. Des exemples de génie des procédés illustrent l'étendue des applications potentielles en génie chimique. / The objective of this work is to develop a new code to predict the final equilibrium of a complex chemical process with many species/reactions and several phases. Numerical methods were developed in the last decades to predict final chemical equilibria using the principle of minimizing the Gibbs free energy of the system. Most of them use the “Lagrange Multipliers” method and solve the resulting system of equations under the form of an approximate step by step convergence technique. Notwithstanding the potential complexity of the thermodynamic formulation of the “Gibbs problem,” the resulting mathematical formulation is always strongly non-linear so that solving multiphase systems may be very tricky and having the difficult to reach the absolute minimum. An alternative resolution method (MCGE) is developed in this work based on a Monte Carlo technique associated to a Gaussian elimination method to map the composition domain while satisfying the atom balance. The Gibbs energy is calculated at each point of the composition domain and the absolute minimum can be deduced very simply. In theory, the technique is not limited, the Gibbs function needs not be discretised and multiphase problem can be handled easily. It is further shown that the accuracy of the predictions depends to a significant extent on the “coherence” of the input thermodynamic data such the formation Gibbs energy of the species and molecular interaction parameters. The absolute value of such parameters does not matter as much as their evolution as function of the process parameters (pressure, temperature, …). So, a self-consistent estimation method is required. To achieve this, the group contribution theory is used (UNIFAC descriptors) and extended somewhat outside the traditional molecular interaction domain, for instance to predict the Gibbs energy of formation of the species, the specific heat capacity… Lastly the influence of the choice of the final list of products is discussed. It is shown that the relevancy of the prediction depends to a large extent on this initial choice. A first technique is proposed, based on Brignole and Gani‘s work, to avoid omitting species and another one to select, in this list, the products likely to appear given the process conditions. These techniques were programmed in a new code name CIRCE. Brignole and Gani-‘s method is implemented on the basis of the atomic composition of the reactants to predict all “realisable” molecules. The extended group contribution theory is implemented to calculate the thermodynamic parameters. The MCGE method is used to find the absolute minimum of the Gibbs energy function. The code seems to be more versatile than the traditional ones (CEA, ASPEN…) but more expensive in calculation costs. It can also be more predictive. Examples are shown illustrating the breadth of potential applications in chemical engineering.

Despite years of research in high speed boundary layer flow, there is still a need for insightful experiments to realize key features of the flow like boundary layer response to different conditions and related transition mechanisms. Volumes of data on the these problems point to the fact that there is still much to be understood about the nature of boundary layer instability causing transition and growth of boundary layer in different conditions. Boundary layer stability experiments have been found to be more useful, in which the boundary layer is perturbed and its behavior observed to infer useful conclusions. Also, apart from the stability part, the effect of various changes in boundary layer due to the perturbation makes interesting observation to gain more insight into the understood and the not so understood facets of the same. In view of the above, the effect of a steady axisymmetric thermal bump is investigated on a hypersonic boundary layer over a 60º sharp cone cylinder model. The thermal bump, placed near tip of the cone, perturbs the boundary layer, the behavior of which is observed by recording the wall heat flux on the cone and cylinder surface using platinum thin film sensors. The state of the boundary layer is qualitatively assessed by the wall heat flux comparisons between laminar and turbulent values. The same thermal bump also acts as a heat addition source to boundary layer in which case this recorded data provides a look into the effect of the heat addition to the wall heat flux. To gain a larger view of heat addition causing changes to the flow, effects of change in enthalpy are also considered. Experiments are performed in the IISc HST2 shock tunnel facility at 2MJkg−1 stag-nation enthalpy and Mach number of 8,with and without the thermal bump to form comparisons. Some experiments are also performed in the IISc HST3 free piston driven shock tunnel facility at 6MJkg−1, to investigate the effect of change in stagnation enthalpy on the wall heat flux. To support the experimental results theoretical comparisons and computational studies have also been carried out. The results of experiments show that the laminar boundary layer over the whole model remains laminar even when perturbed by the thermal bump. The wall heat flux measurements show change on the cone part where there seems to be fluctuation in the temperature gradients caused by the thermal bump, which decrease at first and then show an increase towards the base of the cone. The cylinder part remains the same with and without the thermal bump, indicating heavy damping effects by the expansion fan at cone cylinder junction. A local peak in wall heat flux is observed at the junction which is reduced by 64% by the action of the thermal bump. The possible reason for this is attributed to the increased temperature gradients at the wall due to delayed dissipation of heat that is accumulated in the boundary layer as a result of the thermal bump action. The comparison of data for enthalpies of 2MJkg−1 and 6MJkg−1 show that there are negligible real gas effects in the higher enthalpy case and they do not affect the wall heat flux much. Also it is found that the thermal bump fails to dump heat into the flow directly though it creates heat addition virtually by mere discontinuity in the surface temperature and causes temperature gradients fluctuation in the boundary layer. Considering the thermal bump action and the change in stagnation enthalpy of the flow, there seems to be no change in both cases that can be attributed to a common observation resulting from the factor of change in heat inside the boundary layer.

Mittels spontaner Raman-Streuung im Überschallstrahl wurden kleine Moleküle und Molekülaggregate untersucht. Es wird gezeigt wie Schwingungs- und Rotationstemperaturen im Jet mittels des Stokes/Anti-Stokes-Intensitätsverhältnisses bestimmt werden können. In Studien kleiner Wassercluster konnten Kopplungskonstanten der gebundenen OH-Oszillatoren verschiedener Ringcluster von Trimeren bis Pentameren bestimmt werden, die auch zum Verständnis der Dynamik in kondensierten Phasen relevant sind. Außerdem wird die experimentelle Ermittlung von Enthalpiedifferenzen verschiedener Monomerkonformere zweier isomerisierungsdynamisch sehr unterschiedlicher Systeme vorgestellt. Des Weiteren wurde die Weiterentwicklung der bestehenden Raman-Technik durch Kopplung mit einer IR-Laseranregung realisiert und erste Tests des neuen Aufbaus durch Studien des Methanol-Dimers durchgeführt.

This thesis describes the measurement of rate constants for gas phase reactions as a function of temperature (285 ≤ T/K ≤ 850) and pressure (48 ≤ P/Torr ≤ 700). One or both reactants was monitored directly in real time, using time–resolved resonance fluorescence (for atoms) and u.v. absorption (for radicals). Reactants were produced by exciplex laser flash photolysis. The technique was used to measure rate constants to high precision for the following reactions under the stated conditions: • H+O2+He->HO2+He and H+O2−→OH+O, for 800 ≤ T/K ≤ 850 and 100 ≤ P/Torr ≤ 259. A time–resolved study was performed at conditions close to criticality in the H2–O2 system. The competition between the two reactions affected the behaviour of the system after photolysis, and the rate constants were inferred from this behaviour. • H+C2H4+He<-->C2H5+He (T = 800 K, 97 ≤ P/Torr ≤ 600). The reactions were well into the fall–off region at all conditions studied. At 800 K, the system was studied under equilibrating conditions. The study provided values of the forward and reverse rate constants at high temperatures and enabled a test of a new theory of reversible unimolecular reactions. The controversial standard enthalpy of formation of ethyl, DH0f,298 (C2H5), was determined to be 120.2±0.8 kJ mol−1. Master Equation calculations showed that reversible and irreversible treatments of an equilibrating system should yield the same value for both thermal rate constants. • H+C3H5+He->C3H6+He (T = 291 K, 98 ≤ P/Torr ≤ 600) and O+C3H5 −→ products (286 ≤ T/K ≤ 500, 48 ≤ P/Torr ≤ 348). Both reactions were pressure–independent, and the latter was also independent of temperature with a value of (2.0±0.2) ×10−10 cm3 molecule−1 s−1. • H+C2H2+He<-->C2H3+He (298 ≤ T/K ≤ 845, 50 ≤ P/Torr ≤ 600). At 845 K, both reactions were in the fall–off region; rate constants were used to determine the standard enthalpy of formation of vinyl, ¢H0f,298 (C2H3), as 293±7 kJ mol−1. The value of this quantity has until recently been very controversial. • H+CH4 <--> CH3+H2. The standard enthalpy of formation of methyl, DH0 f,298 (CH3), was determined by re–analysing existing kinetic data at T = 825 K and 875 K. A value of 144.7±1.1 kJ mol−1 was determined. Preliminary models were examined to describe the loss of reactants from the observation region by diffusion and pump–out. Such models, including diffusion and drift, should prove useful in describing the loss of reactive species in many slow–flow systems, enabling more accurate rate constants to be determined.

Le contexte de cette thèse est la production du vecteur énergétique hydrogène par thermolyse de la vapeur d’eau consistant en la dissociation de la molécule H2O en oxygène (O) et hydrogène (H). Le dispositif employé est une torche à plasma d’arc non transféré développée au LAEPT. Après l’exposition de la théorie sur la physique des plasmas et la spectrométrie d’émission atomique nécessaire à l’exploitation des mesures, cette thèse présente l’évolution de la torche à plasma ainsi que son environnement nécessitée par la présence de gaz instables et explosifs. Les mesures des différentes grandeurs électriques, hydrauliques et spéctrométriques ont permis la détermination des caractéristiques physique et chimique d’un plasma formé d’un mélange de vapeur d’eau – d’argon. La détermination de grandeurs telles que la température du jet plasma, la conductivité électrique, l’enthalpie massique et la densité électronique, est basée sur la comparaison entre expérimentation et théorie. / The context of this thesis is the production of hydrogen as an energy vector by steam thermolysis consisting in the dissociation of H2O molecule into oxygen (O) and hydrogen (H). The process used is a plasma torch device developed by the LAEPT. After presenting the theory of plasma physics and atomic emission spectroscopy which will help to make the most of the measured realized, this thesis will show the evolution of the plasma torch device and the experimental environment required to work with explosive and unstable gases. Some measurements like electrical, hydraulic and spectroscopy magnitudes made it possible to determine the chemical and physical characteristics of a water vapor – argon plasma. A comparison between experiments and theoretical knowledge will enable to determine the temperature of a flow of plasma, electrical conductivity, enthalpy and the electronic density.

Protein (mis)folding into highly ordered, fibrillar structures, amyloid fibrils, is a hallmark of several, mainly neurodegenerative, disorders. The mechanism of this supra-molecular self-assembly reaction, as well as its relationship to protein folding are not well understood. In particular, the molecular origin of the metastability of the soluble state of proteins with respect to the aggregated states has not been clearly established. In this dissertation, it is demonstrated, that highly accurate kinetic experiments, using a novel biosensing method, can yield fundamental insight into the dynamics of proteins in the region of the free energy landscape corresponding to protein aggregation. First, a section on Method development describes the extension and elaboration of the previously established kinetic assay relying on quartz crystal microbalance measurements for the study of amyloid fibril elongation (Chapter 3). This methodology is then applied in order to study in great detail the origin of the various contributions to the free energy barriers separating the soluble state of a protein from its aggregated state. In particular, the relative importance of residual structure, hydrophobicity (Chapter 4) and electrostatic interactions (Chapter 5) for the total free energy of activation are discussed. In the last part of this thesis (Chapter 6), it is demonstrated that this biosensing method can also be used to study the binding of small molecules to amyloid fibrils, a very useful feature in the framework of the quest for potential inhibitors of amyloid formation. In addition, it is shown that Thioflavin T, to-date the most frequently employed fluorescent label molecule for bulk solution kinetic studies, can in the presence of potential amyloid inhibitor candidates be highly unreliable as a means to quantify the effect of the inhibitor on amyloid formation kinetics. In summary, the work in this thesis contributes to both the fundamental and the applied aspects of the field of protein aggregation.

Submitted by LILIAN FACHIN LEONARDO BETIOL null (lilianfacleo@hotmail.com) on 2016-12-04T18:12:23Z No. of bitstreams: 1 Tese - Formatada (1) Corrigida.pdf: 1975637 bytes, checksum: a2ca74a2f726452b217e860e0c11c866 (MD5) / Approved for entry into archive by Felipe Augusto Arakaki (arakaki@reitoria.unesp.br) on 2016-12-06T13:52:01Z (GMT) No. of bitstreams: 1 betiol_lfl_me_sjrp.pdf: 1975637 bytes, checksum: a2ca74a2f726452b217e860e0c11c866 (MD5) / Made available in DSpace on 2016-12-06T13:52:01Z (GMT). No. of bitstreams: 1 betiol_lfl_me_sjrp.pdf: 1975637 bytes, checksum: a2ca74a2f726452b217e860e0c11c866 (MD5) Previous issue date: 2016-11-21 / As isotermas de sorção tornaram-se importantes para prever o comportamento da cinética de secagem e as condições de armazenamento de resíduos da indústria alimentícia. O conhecimento de tal propriedade é útil para projetar equipamentos ou operações para fins de armazenamento ou processamento. O bagaço quando é apenas descartado, representa um desperdício de matéria prima, de compostos orgânicos com categoria bioquímica definida (proteínas, açúcares, ceras, graxas, resinas), que poderia ser aproveitada. Dentro deste contexto, a presente pesquisa teve como objetivo caracterizar quimicamente o bagaço de mandioca e fazer a determinação experimental das isotermas de sorção destes resíduos da indústria de fécula, além de calcular a entalpia e entropia, temperatura media harmônica e calor isostérico de adsorção. Para isso, o teor de umidade de equilíbrio nas isotermas de sorção, de bagaço de mandioca, foi determinado utilizando o método gravimétrico estático nas temperaturas de 20 a 80 °C. Modelos teóricos e empíricos foram usados para representar os valores experimentais das isotermas de sorção, sendo que o modelo de GAB foi o que apresentou os melhores ajustes. Utilizando o modelo de GAB foi possível determinar o calor isostérico de adsorção como função do teor de umidade. A teoria da compensação foi confirmada pela relação linear entre entalpia e entropia. Maiores valores de temperatura isocinética do que a temperatura harmônica reforçam a teoria da compensação e sugeriram que a adsorção de água pelo bagaço de mandioca é considerado um processo conduzido pela entalpia. / The sorption isotherms become important to predict the drying kinetics behavior and waste storage conditions of the food industry. The knowledge of such property is useful for designing equipment or operations for storage or processing. The bagasse is only when discarded, is a waste of raw materials, organic compounds with defined biochemical category (proteins, sugars, waxes, greases, resins), which could be harnessed. Within this context, this study aimed to chemically characterize the Cassava Bagasse and make the experimental determination of the sorption isotherms of these starch industry waste and calculates the enthalpy and entropy, harmonic average temperature and isosteric heat of adsorption. For this, the equilibrium moisture content in the sorption isotherms of cassava bagasse was determined using the gravimetric static method in temperatures 20-80 ° C. Theoretical and empirical models were used to represent the experimental values of sorption isotherms, and the GAB model was the one that presented the best fit. Using the GAB model was possible to determine the isosteric heat of adsorption and moisture content of the function. The theory of compensation was confirmed by the linear relationship between enthalpy and entropy. Isokinetic higher temperature values than the harmonic temperature reinforce the theory of compensation and suggested that the adsorption of water by mancioca bagasse and considered one of enthalpy driven process.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-11-07T12:20:00Z No. of bitstreams: 1 gessicalacerdasiqueira.pdf: 2914379 bytes, checksum: 13b701ceac7f6562db4c0a3167e60c32 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-11-09T14:37:17Z (GMT) No. of bitstreams: 1 gessicalacerdasiqueira.pdf: 2914379 bytes, checksum: 13b701ceac7f6562db4c0a3167e60c32 (MD5) / Made available in DSpace on 2017-11-09T14:37:17Z (GMT). No. of bitstreams: 1 gessicalacerdasiqueira.pdf: 2914379 bytes, checksum: 13b701ceac7f6562db4c0a3167e60c32 (MD5) Previous issue date: 2017-07-13 / Processos de transferência de calor com mudança de fase são de interesse em várias áreas da ciência, engenharia e aplicações industriais. Em processos de solidificação, por exemplo, a ocorrência de trincas e formações de vazios causados por uma redução na capacidade de resistir a esforços mecânicos geralmente são observados, e é de grande importância prever esses comportamentos para que possam ser evitados. Uma das formas de se estudar esses fenômenos e suas aplicações é através do uso de modelos matemáticos que possibilitam, através do uso de métodos de discretização temporal e espacial a realização de simulações computacionais. Dessa forma, este trabalho estudou e comparou diferentes formulações numéricas do método dos elementos finitos para problemas de transferência de calor com mudança de fase levando em consideração a condução como mecanismo de transferência de calor. Na metodologia usada, os processos de solidificação ou fusão foram tratados por meio de métodos baseados em malhas fixas. Diversos experimentos numéricos foram realizados para se analisar a adequabilidade dos métodos estudados e propostos neste trabalho e os resultados obtidos foram satisfatórios. / Heat transfer processes with phase change are of great interest in several areas of science, engineering and industrial applications. In some of these applications, such as in solidification processes, the occurrence of cracks and void formation caused by a reduction in the ability of the material to resist mechanical loadings are generally observed, and it is of great importance to predict these behaviors so that they can be circumvented. One of the ways to study these phenomena and their applications is through the use of mathematical models and executing of computer simulations. Thus, this work studied and compared different numerical formulations of the finite element method for the heat transfer problems with phase change considering only conduction as the main mechanism of heat transfer. In the methodology used, the solidification or melting processes were treated by means of numerical methods based on fixed meshs. Several numerical experiments were performed to analyze the suitability of the methods studied and proposed in this work and the results were satisfactory.