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The organisation of worker activities in manufacturing shops have been differently conceived depending on political, societal, environmental and economic circumstances affecting industrial development. From Taylorism and Fordism through Lean Manufacturing to the innovative Cell Production system, the level and quality of abilities and competencies of workers have increasingly become the kernel of factory management models. Sustainability has increasingly become a crucial factor for product success. The design and manufacture of industrial products are conceived in circular loops within the 6R framework. The digitalisation of information has allowed significant advancements. Qualified and skilled operators have accompanied and led these evolutions, and their abilities and creativity have grown relevant, despite the continuous increase in automation.This work investigates the contribution of craftsmanship abilities in the industrial environment. For this purpose, the Craftsmanship Index has been proposed to assign a quantitative value to the craftsmanship skills contributing to the manufacturing activities. A customised questionnaire to be administered to workers is used to calculate this index, which is helpful to analyse worker abilities and the way they are learned and developed, being part of effective management and decision-making tools. A case study in the Japanese manufacturing environment expands on previous results achieved in Italy.The Craftsmanship Index allowed us to give a quantitative relevance to the level of abilities of operators depending on the analysed department. Some cultural differences have also emerged thanks to the comparison between the Japanese and the Italian culture.

Numerical simulations involving detailed kinetic combustion reaction mechanisms for long chain fuels are associated with prohibitive computational costs. Thus, there is the need for reduced kinetic mechanisms for the effective numerical simulation of these fuels. The objective of this work is the development of a skeletal mechanism of moderate stiffness for the methyl formate (MF). MF is not indicated as a biodiesel surrogate due to its very short chain, but its study allows to understand its role in the combustion process. Then, based on a detailed mechanism composed of 950 reactions and 176 species, Directed Relation Graph, Depth First Search and a model of Artificial Neural Networks are employed to obtain a skeletal mechanism with 43 reactions and 23 species. The results obtained are satisfactory.

Computational aeroacoustic analyses of a premixed swirled combustor are performed. The Large Eddy Simulation is used to compute the flow and the acoustic pressure is solved through the Acoustic Perturbation Equations for Reacting Flows method (APE-RF). The numerical solution is based on a finite difference scheme for a 3D grid with temporal integration by the Simplified Runge–Kutta multi-step method. Simulations are performed for two fuels, for methane and for propane. To verify the numerical procedure comparisons are made with experimental results and the discretization error is obtained by the Richardson estimator. The solver runs with low computational cost and good overall agreement has been observed between simulation results and the literature data.

Many mathematical models for fuel cells are presented in the literature, however, few studies of numerical analysis of these models are found. The novelty of this work is the proof of stability and convergence of the equation of chemical species, providing greater reliability to the mathematical model. In this work, a mathematical model is proposed that calculates the flow and concentration of species for proton exchange membrane fuel cells using the finite element method for spatial discretization and the Crank–Nicolson method for temporal discretization. The model takes into account the losses overpotentials at the anode and at the cathode. The numerical results confirm the proof of convergence which is demonstrated in this work. Finally, a numerical result is shown for the fuel cell power relative to current density, and the result has good relation with the experimental data.

The computational treatment of detailed kinetic reaction mechanisms for combustion is expensive, especially in the case of biodiesel fuels. In this way, great efforts in the search of techniques for the development of reduced kinetic mechanisms have been observed. As Methyl Butanoate (MB, $$C_3H_7COOCH_3$$ ) is an essential model frequently used to represent the ester group of reactions in saturated methyl esters of large chain, this paper proposes a reduction strategy and uses it to obtain a reduced kinetic mechanism for the MB. The reduction strategy consists in the use of artificial intelligence to define the main chain and produce a skeletal mechanism, apply the traditional hypotheses of steady-state and partial equilibrium, and justify these assumptions through an asymptotic analysis. The main advantage of the strategy employed here is to reduce the work required to solve the system of chemical equations by two orders of magnitude for MB, since the number of reactions is decreased in the same order.

The processes of conversion of energy by combustion tend to increasingly consider the economic and environmental constraints, making it necessary to understand the interaction between combustion and turbulence. This work aims to develop a new mechanism for a jet diffusion flame of ethanol considering NO x formation. As a result, a reduced mechanism of 43 steps was achieved for combustion of ethanol by applying an Artificial Neural Network (ANN) for chemical kinetics. The results obtained agree satisfactorily with data found in the literature.

Modeling the transformation of biomass into biogas is complex, because it involves a nonlinear and coupled set of ordinary differential equations. Thus, obtaining an analytical-numerical solution becomes attractive for this problem. In this paper, five chemical reactions are used to model the chemical kinetics of the anaerobic digestion process. The rate of production of each reaction is estimated by Gibbs free energy value. The equation system of the model is solved by the Modified Adomian Decomposition Method, applied to the time variable. The results obtained agree with the expected solution.

In this article, the first-order sensitivity coefficients for a system of stiff nonlinear differential equations from the anaerobic digestion model are calculated. In this approach, the auxiliary equations used to calculate the sensitivity coefficients are solved separately from the model equations, using the same time steps and numerical approximations used in the calculation of the model solution by the Rosenbrock method of order four. The results show the importance of each reaction for each species involved in the model.

In this paper, we use a three-dimensional mathematical model to analyze the flow in a direct ethanol fuel cell (DEFC). The overpotential losses are estimated based on the operating parameters of the cell, and based on the reactive flow within the channels, in the diffusion layer, and on the electrocatalyst surface. The model includes fuel consumption and the formation of acetic acid and acetaldehyde, and the rate of ethanol crossover through the membrane. The numerical simulation of the reactive flow was made based on the central finite difference method. The equations were discretized in time using the Crank–Nicolson method. The model calculates the flow velocity and species concentration along the inlet channel, the diffusion layer and the catalyst surface. The molar fraction of the species is calculated according to the current density in the DEFC. The results for the cell voltage versus current density were obtained for different catalysts on the anode side, for three temperatures and two initial concentrations of ethanol. The results obtained are consistent with the experimental data found in the literature.

The fuel cell is an electrochemical device that converts chemical energy directly into electricity and is more efficient than traditional power generators. In this work, we developed a mathematical model for a direct ethanol fuel cell (DEFC), which considers the flow and concentration of species dependent on time and space for the calculation of losses overpotentials. In addition, the concentration of each species is modeled according to the current density of the DEFC. The finite element method is used to calculate the flow and concentration of the species in different layers of the cell (inlet and outlet channels, diffusion layer and catalyst layer). The model takes into account the losses overpotentials at the anode and at the cathode and the passage of ethanol through the membrane. The voltage and power density of the cell are calculated with different catalysts, temperatures and concentrations of ethanol. A result is shown for limiting current density for low ethanol concentrations. The results obtained compare favourably with the data found in the literature.

The purpose of this article is to show the improvement of the mixture of a turbulent jet diffusion flame of methane by means of linear quadratic regulator control. The model is based on low Mach and high Damkohler numbers. Large eddy simulation is used to simulate a turbulent flow with the Smagorinsky submodel for turbulent viscosity. The control employs a pair of actuators that act transversally to the flow direction on the walls of the burner. They consist of rectangular openings added along the depth of the duct. Numerical tests were performed by changing the position of one of these actuators. The results show that the controllers alter the jet diffusion flame, generating vortices of different sizes and dispersion patterns, which quickly leads to highly complex flow patterns.

Numerical simulations involving detailed kinetic reaction mechanisms of combustion for conventional fuels are associated with computational costs prohibitive and, therefore, a lot of effort for obtaining reduced kinetic mechanisms has been observed. Among the known strategies, the Directed relation graph (DRG) method and the sensitivity analysis have proven to be very powerful tools, in addition to the traditional and efficient assumptions of steady-state and of partial equilibrium. The present work proposes a reduction strategy with these techniques for reduction of a mechanism for ethanol. Based on a mechanism of 377 reactions among 56 reactive species a skeletal mechanism, consisting of 24 species and 26 reactions, was obtained through the application of the DRG method and performing a sensitivity analysis. Using the assumptions of partial equilibrium and steady-state, which are justified by an asymptotic analysis, an additional reduction leads to a reduced mechanism of ten steps. Results of the new mechanism for a jet diffusion flame compare favorably with data found in the literature. The computational cost for simulation of jet diffusion flames with the reduced model is one order of magnitude less than necessary in the complete model, which is the principal contribution of this work.

In this paper, we develop a mathematical model to analyze a direct ethanol fuel cell (DEFC). The three-dimensional model is able to predict the flow on all layers of the fuel cell and allow a better analysis of physical and chemical phenomena that occur inside it. In addition, the calculation of mole fraction of species allows one to observe that the diffusion layer has great influence on mass transfer of fuel between the input channel and the catalyst layer. Numerical simulation of reactive flow was made based on the central finite difference method. The equations were integrated in time using the simplified Runge-Kutta multistage scheme. The results obtained are in agreement with the experimental data found in the literature, for different feed concentrations of ethanol and for different operating temperatures of the cell. In this way, the paper contributes to the development of a model for direct ethanol fuel cells, taking into account all losses overpotentials at the anode and the cathode, providing a better understanding of the physical and chemical behavior inside the cell, and on the conversion of chemical energy into electrical energy.

Major efforts in the search for techniques for the development of reduced kinetic mechanisms for biodiesel have been observed, since these mechanisms may have thousands of species. This paper proposes a reduction strategy and presents the development of a reduced kinetic mechanism for piloted jet diffusion flame of methyl decanoate (MD). The strategy consists of applying the DRG, Directed Relation Graph, technique for initial reduction, and the use of Layerless Neural Network (LNN) to define the main chain and obtain a skeletal mechanism. Hence the hypotheses of steady-state and partial equilibrium are applied, and the assumptions are justified by an asymptotic analysis. The main advantage of the strategy is to reduce the work required to solve the system of chemical equations by at least two orders of magnitude for MD, since the number of species is decreased in the same order.

The hydrogen fuel is considered to be an ideal source of energy, because its complete combustion generates no pollutants, only water vapor. Therefore, the hydrogen has been suggested as a clean fuel. A detailed kinetic mechanism for the combustion of hydrogen that comprises eight species ( H 2 , O 2 , O , OH , H 2 O , H , HO 2 and H 2 O 2 ) and 20 elementary reactions, was reduced to two-step mechanism for nonpremixed flames involving four reactive species ( H 2 , O 2 , H , H 2 O ). We performed, for this mechanism, a numerical analysis of the equations, including the velocity, mixture fraction, mass fractions and temperature. To quantify the components of intermediary reactions, the mixture fraction is decomposed into three parts, each part directly related to the mass fraction of each species. The results compare favorably with data in the literature for a jet diffusion flame of 50/50% in volume of H 2 - N 2 . The main advantage of the strategy employed here is to decrease the work needed to solve the system of equations of the reactive flow.

Bioethanol is a fuel additive or a fuel substitute that has the benefit of being cleaner and price competitive with gasoline. Therefore, we develop a reduced kinetic mechanism capable of modeling the ethanol combustion and the generation of the combustion products $$\text{H}_{2}\text{O},~\text{CO}_{2},~\text{CO},~ \text{H}_{2},~ \text{C}_{2}\text{H}_{4}$$ and OH. Based on a mechanism composed by 372 reversible elementary reactions among 56 reactive species, we propose a reduction strategy to obtain an eight-step mechanism for the ethanol. The reduction strategy consists in estimating the order of magnitude of the reaction rate coefficients, defining the main chain, applying the steady-state and partial equilibrium hypotheses, and justifying the assumptions through an asymptotic analysis. The main advantage of the obtained reduced mechanism is the decrease of the work needed to solve the system of chemical equations proportionally to the number of elementary reactions present in the complete mechanism. Numerical tests are carried out for a jet diffusion flame of ethanol and the results compare well with available data in the literature.

The hydrogen fuel seems to be a good candidate to replace the energy obtained from some fossil fuels. Therefore this work explains the process of obtaining a two-step reduced chemical kinetic mechanism for the hydrogen combustion. The development of a reduced mechanism consists in eliminating reactions that produce negligible influence on the combustion process. Moreover, for this mechanism, we obtain an analytical-numerical solution for a turbulent jet diffusion flame. To quantify the intermediate species, the mixture fraction is decomposed into three parts, each part directly related to the mass fraction of a species. The governing equations are discretized using the second order finite-difference approach and are integrated in time using the second order simplified three-step Runge-Kutta scheme. Obtained results compare favorably with data in the literature for a 50/50 % volume H2−N2 jet diffusion flame. The main advantage of this strategy is the decrease of the work needed to solve the system of governing equations, by one order of magnitude for the hydrogen.

The aim of this work is the numerical simulation of the formation of hydrogen-bonded base pairs between adenine, thymine, guanine and cytosine. We use a Monte Carlo diffusion simulation with geometric (molecular distances and orientation) and energetic (acceptance proportional to the Boltzmann factor) criteria. Our results show that the occurrence of the different types of base pairs is strongly influenced by base geometry. Such results can help to understand some mechanisms, which occur at processes related to mutation.

We consider the behaviour of mixing reacting compressible flows with inflow–outflow boundary conditions corresponding to the injection of reactants, fuel and oxidizer in a bounded region. Analytical results on the existence of solutions for small time and data are given in the two-dimensional case, using extensions of the techniques of Valli and Zajaczowski [Navier–Stokes equations for compressible fluids: global existence and qualitative properties of the solutions in the general case, Commun. Math. Phys. 103 (1986), 259–296]. As well, computational results are presented using finite difference methods.

The present work develops a low cost numerical method for the solution of nonpremixed piloted methane jet flames. This method is based on the mixture fraction for fluid flow and on unsteady flamelet models, combined with the presumed probability density function, for the chemistry. Numerical tests, for the governing equations discretized by the finite difference and solved by the Gauss-Seidel scheme, were carried out for turbulent, nonpremixed, nonreacting propane-jet flow and for confined Sandia C and D flames for reasonable values of gaseous hydrocarbon chemistry. The methodology, developed for low Mach number flows and based on a density approximation, allows to decrease considerably the computational time while obtaining results which contributes to a better understanding of the complexity involved in the numerical solution of piloted methane jet diffusion flames.

This chapter shows the potential of the techniques discussed in the previous chapters when employed for the solution of diffusion flames of hydrocarbons, reactive flows in porous media, and premixed combustion in porous media. It is noted that the same techniques presented for solving problems of combustion at high temperatures are also useful in the analysis of the precipitation and/or dissolution of minerals in aqueous solution, which can be understood as a reaction process at low temperatures.

In this chapter, some techniques are presented for obtaining reduced kinetic mechanisms as the Direct Relation Graph (DRG) the sensitivity analysis based on the eigenvalues and eigenvectors of the Jacobian matrix of the chemical system, and techniques such as Intrinsic Low Dimensional manifolds (ILDM), Reaction Diffusion manifolds (REDIM), and flamelet. For premixed flames, laminar burning velocity and the basic equations are obtained, and the length and time scales are discussed. In order to represent the flame front, the G equation is discussed. For diffusion flames, flamelet equations are presented with the introduction of the probability density function and the scalar dissipation rate. The Burke-Schumann solution and an analytical solution for jet diffusion flames and for plumes are also illustrated. Then, models are presented for reactive flows in porous media. Initially, we discuss the model of Darcy and appropriate equations for precipitation and dissociation of minerals without combustion. Finally, the equations are presented for combustion in porous media and a discussion about ion precipitation is made.

This chapter presents the basics of mixing in turbulent flow, starting with the notion of mixture fraction. This formulation can be extended to flows with various mixture fractions, when the number of reactions is small. Following is presented the basics of turbulent flows, such as turbulence scales, and the averages of Reynolds and Favre, which are useful for writing the reactive Navier equations. Notions of turbulence and models for the turbulent viscosity to be used with large-eddy simulation (LES) are presented. LES is the preferred technique, because there are no conditions for solving realistic Reynolds numbers, encountered in practice, using direct numerical simulation techniques.

First, the Cartesian and generalized coordinate systems and the coordinate transformation are introduced. We also discuss the method of virtual boundaries and the need to introduce a forcing term to represent the geometry. Next, we present the formulation for low Mach number, valid for most cases of reactive flows. Then the large-eddy simulations formulation is discussed as an improvement of Reynolds averaged Navier-Stokes (RANS) formulation, which is less expensive than direct numerical simulations (DNS) formulation. Subsequently, for a reactive flow model, the equations of momentum, energy, enthalpy, and chemical species are written as a general equation, which is approximated by methods of finite difference, finite volume, and finite element, to be integrated by Runge-Kutta methods. After that, approximations of order 3 and 4 are given, as well as some compact schemes of order of approximation 6. Then, we discuss some of the main methods used in the flow solution such as Gauss-Seidel, simplified Runge-Kutta, tridiagonal matrix algorithm (TDMA), Newton, strongly modified implicit procedure (MSI), and LU-SSOR, which is an LU decomposition with the introduction of dissipation. Then, we indicate some methods for solving stiff systems of equations, such as Newton’s method and Rosenbrock’s method, which can be seen as a combination of the methods of Newton and Runge-Kutta. After that, the principal boundary conditions, such as permeable and impermeable wall, symmetry and cut, far field and periodic are given, which are common in jet diffusion flames, and in reactive flows in porous media. Finally, some techniques for the acceleration of convergence as local time-stepping, residual smoothing, and the multigrid technique are introduced. Moreover, some numerical implementation details and the analysis of uncertainties for the solution of reactive flows is discussed.

This chapter presents the basic equations of fluid dynamics for reactive and nonreactive flows in Cartesian coordinates. The equations are based on the balance obtained for mass, momentum, and energy. It also presents the derivation of the equation for the mass fraction of the chemical species, and shows the terms to be added to the equations of momentum and energy. The reactive term is proportional to the species concentration and follows the Arrhenius kinetics. The set of equations is presented using Einstein notation, which allows simplification of writing the equations system, in order to facilitate the numerical implementation.

This chapter deals with the chemical equilibrium conditions in an aqueous system, directed to problems in geochemistry, and in the gas phase, directed to problems in combustion. The chemical equilibrium condition is often used when the chemical kinetics is fast. The chemical equilibrium is the state in which the forward and backward reactions have equal rates. The thermodynamic equilibrium occurs when a system reaches the chemical, thermal, and mechanical equilibrium.

This work develops a method to solve fluid–structure problems based on the arbitrary Lagrangian–Eulerian, ALE, formulation using the central finite difference, explicit Runge–Kutta time-stepping scheme. This model builds on earlier ones that involve ALE with finite elements instead of finite differences, in order to obtain higher-order space and time approximations which are necessary for some aeronautical applications. Numerical tests are carried out for an airfoil and a panel using the Euler equations with Mach numbers ranging from 0.2 to 2.0 and the results are shown to compare favourably with available data found in the literature.

The goal of this work is the numerical solution of incompressible laminar flows through a channel with 3:1 sudden expansion for power-law fluids. For such flows, above the critical Reynolds value, three solutions can appear: a symmetric and two non-symmetric. The simulations are performed using a finite difference explicit Runge–Kutta three-stages scheme for second-order time and space approximations. Results show that bifurcations occur for the range of power-law index n ϵ (0, 2]; for shear-thinning the bifurcation appears after that of the Newtonian situation, while the opposite occurs for shear-thickening. Moreover, the solution becomes time dependent for higher Reynolds numbers depending on the value of the power law exponent n. These results build on earlier ones found for sudden expansions because here higher Reynolds numbers and non-Newtonian behavior are considered.

Contributions to the aerodynamics development have to be involved to achieve an increase in quality, reducing time and computer costs. Therefore, this work develops an optimization method based on the finite volume explicit Runge–Kutta multi-stage scheme with central spatial discretization in combination with multigrid and preconditioning. The multigrid approach includes local time-stepping and residual smoothing. Such a method allows getting the goal of compressible and almost incompressible solution of fluid flows, having a rate of convergence almost independent from the Mach number. Numerical tests are carried out for the NACA 0012 and 0009 airfoils and three-dimensional wings based on NACA profiles for Mach-numbers ranging from 0.8 to 0.002 using the Euler equations. These calculations are found to compare favorably with experimental and numerical data available in the literature. Besides, it is worth pointing out that these results build on earlier ones when finding appropriate new three-dimensional aerodynamical geometries. Copyright © 2004 John Wiley & Sons, Ltd.

The aim of this work is the numerical solution of laminar flows inside a square cavity caused by temperature increase due to a chemical reaction. The model approximates the overall, single step, binary, irreversible reaction between two species, resulting in a third, which is taken to be a process of first order with respect to each of the reactants, where the specific reaction rate is controlled by temperature-dependent Arrhenius kinetics. The simulations are performed using the finite differences explicit Runge-Kutta three-stage scheme for second order time and space approximations. Consistent results, for reactant and product concentration fields, as well as for temperature of reaction, are obtained, showing that the model is able to follow nonlinear behavior of the mixing and reaction progress, for Schmidt and Prandtl numbers of order 1, Zel'dovich 5, Damkohler 300 and heat release parameter ranging from 300 to 1000, which are values for high temperature gaseous hydrocarbon chemistry. Besides, it is worth pointing out that these results build on earlier ones, which were obtained from thin-layer model approximations.

The present work develops a numerical method for the solution of rotating internal weakly viscoelastic flows in rectangular ducts for dimensionless parameters such as the Reynolds, Rossby and Weissenberg numbers, taken respectively in the intervals between 171 and 12000, 0.047 and 1/12 and up to 1/10000. It is shown that the usual counter-rotating double-vortex configuration of secondary flow breaks down with the increase of the Reynolds number (over the threshold of 171). For higher Reynolds numbers such as 7500 and 12000 the secondary flow diffuses to the interior of the duct where it assumes a fully developed configuration and the transition to the turbulence structure is observed. The Sobolev norms increase almost proportionally to the increase of the Reynolds number, and play an essential role for more complex problems involving transition to turbulence modelling. Copyright © 2002 John Wiley & Sons, Ltd.

The major considerations in the design of effective methods for computational aerodynamics are the capability to treat flows over complex geometrical shapes with proper representation of shock waves, discontinuities and viscous effects. The present work extends the numerical method used to solve compressible flows for the solution of almost incompressible fluid flow. The technique is based on the finite volume explicit Runge-Kutta multistage scheme with central spatial discretization in combination with multigrid and preconditioning. The discretization used follows the cell-centered arrangement of the control volume for the flow variables. Numerical tests are carried out for Mach numbers ranging from 0.8 to 0.002 and the results are found to compare well with analytical/experimental data available in the literature. A spectral radii comparison is also presented and helps to understand what the preconditioning really does with the characteristic variables. Besides, some solutions presented here were obtained for parameter values excluded from the range found in the literature (such as Mach 0.002 over the NACA 0012 airfoil) employing the same preconditioning technique.

The ever-widening applications of numerical calculations leads to a variety of new numerical methods, which are different in their solution algorithms as well as in the discretization of the governing equations. Despite this development, much work still remains in their improvement towards a fast, accurate and stable convergence. This work shows a numerical method for the solution of compressible and almost incompressible fluid flows using a finite volume, explicit Runge-Kutta multistage scheme, with central spatial discretization in combination with multigrid and preconditioning. Numerical tests are carried out for a vehicle launcher for Mach-number 3.75 and 2.0 using the Euler equations.

The aim of this work is the development of a numerical technique for the reduction of reaction mechanisms of common hydrocarbon and oxygenated fuels, such as methane, ethylene, propane, methanol and ethanol, using steady‐state and partial equilibrium assumptions. Numerical tests are carried to establish the basic chain for each fuel as well as to determine the amount of small products of combustion, whose concentration depends on the turbulent mixing and needs to be controlled due to environmental restrictions. The results are in agreement with data in the literature.

The present work develops a method for the solution of a nonpremixed jet flame based on the Reichardt’s equation for the mixture fraction and on the Burke‐Schumann for the chemistry. The developed method allows decreasing the complexity to obtain the solution of low and moderate Reynolds jet diffusion flames. Numerical tests are carried out for a 50‐50% H2/N2 flame and the results are in agreement with the experimental data.

This paper presents a non-linear friction compensation mechanism using a combination of neural network (NN) with fuzzy system (neuro-fuzzy compensator), applied to harmonic-drive robotic actuators. The friction compensation torque is constituted by NN output, which is trained off-line. Since the friction changes significantly over time, temperature and equipment operational conditions, the NN loses its performance. To recover this performance, a fuzzy algorithm is proposed to deal with the variation friction parameters. The output of the fuzzy algorithm is a gain that multiplied by the NN output will adjust the friction compensation torque. Experimental results have shown the efficiency of the proposed mechanism.

The development of controlled transition in a flat‐plate boundary layer is investigated using Large Eddy Simulations (LES) with the dynamic Smagorinsky model. The analysis of flow control with the objective to optimize the effects of Tollmien‐Schlichting waves on a flat plate by means of plasma actuators was studied. The plasma effect is modeled as a body force in the momentum equations. These equations are solved in a uniform grid using a 2nd‐order finite difference scheme in time and space. The response of plasma actuators operating in different time‐dependent conditions, produced by transient or periodic inputs at different frequencies, is also analyzed.

In many situations of engineering and applied mathematics interest we are confronted with heat and mass transfer problems in granular medium, as in the grains drying processes and in small load nuclear reactors safety, where the spheres are fuel elements. In the literature we have found several models that try to describe these two processes. Most of the models found in the literature are empiric or semi-empiric and valid, therefore, for a quite limited range of the involved parameters.

The improvement of combustor devices is very important especially for aeronautical applications; combustors or burners are mechanical equipments where the combustion takes place. New technologies, including mixture and reaction, instability, low cost and emission are helping the development of numerical codes employed in combustion problems. But, when the burners are improved, unexpected problems can appear.