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COB186 Integral Transform Technique in 2D Drying Problems João Batista Furlan Duarte & Júlio Wilson Ribeiro

Departaments of Physics and Computer Science – UFC.

Rua Carolina Sucupira, 62, apto. 603 – Aldeota CEP 60140-120 – Fortaleza/CE, Brazil

E-mail: jwilson@lia.ufc.br and furlan@fisica.ufc.br

Multidimensional drying in capillary porous media is analytically solved for the associated temperature and moisture content distributions. Luikov's model with linear transport coefficients and two-dimensional plate geometry is adopted for description of the simultaneous heat and mass transfer phenomena. The generalised integral transform technique (G.I.T.T.) is imployed in the automatically global error-controlled solution of the coupled partial differential equations, and the convergence behaviour of the proposed eigenfunction expansions is illustrated.

Keywords: Integral Transform Method. Simultaneous Heat and Mass Transfer. Porous Media. Thermophysics. Drying. Luikov Problem. Método da Transformada Integral Transferência Simultânea de Calor e Massa Meios Porosos Termodinâmica Problema de Secagem de Luikov.

COB210 OPTIMIZATION OF FORCED DYNAMIC SYSTEM RESPONSE:THE MINIMUM VIBRATION PROBLEM / OTIMIZAÇÃO DA RESPOSTA FORÇADA DE UM SISTEMA DINÂMICO: O PROBLEMA DA VIBRAÇÃO MÍNIMA.

David Mauricio & Julio Maciel Treiguer

Sciences and Technology Center - State University of Norte Fluminense - CCT /UENF

Av. Alberto Lamego, 2000, 28015-620 - Campos, RJ - Brazil - E-mail:{mauricio,treiguer}@uenf.br

We introduce an optimization model and an approximation method to minimize the maximum vibration amplitude of multi-degree-of-freedom dynamic system. This system is discrete, linear and time-invariant. It is represented by the motion equation in the state-space form and characterized by modes. The presented optimization model corresponds to a global optimization problem. We develop simulated tests involving forced 3-dof-system response. At the end we present the results, discuss applications and next developments.

Keywords: Dynamic system, the minimum vibration problem, global optimization, heuristic algorithm, vibration analysis.

Sistemas dinâmicos,o problema da vibração mínima, otimização global, algoritmo heurístico, análise de vibração.

COB211 STOCHASTIC GRADIENT PROJECTION METHOD APPLIED TO AN EARTH MARS ORBIT TRANSFER PROBLEM

Atair Rios Neto & Fernando Madeira

Instituto de Pesquisa e Desenvolvimento- IP&D, Univesidade do Vale do Paraíba-UNIVAP - 12245-720 São Jose dos Campos, SP, Brasil E-mail: atair@univap.br

Embraer - 12227-901 São Jose dos Campos, SP, Brasil

A reviewed version of a stochastic gradient projection method is applied to an Earth Mars orbit transfer problem. Suboptimal open loop solutions are obtained by parameterization of the control and reduction of the dynamic optimization problem to one of nonlinear programming in each iteration of the numerical solution. A typical iteration is done by direct search and treated as a stochastic optimal linear parameter estimation problem. Random errors model the level of accuracy expected in the satisfaction of boundary constraints. Search increment determination is then done using a Gauss-Markov estimator in Kalman form. The resulting method is a stochastic version of the projection of the gradient that has the feature of inherently and automatically taking in account different specified errors in satisfaction of constraints. Numerical tests indicate that the method can produce results of quality comparable to that of an indirect numerical method.

Keywords: Suboptimal control, Stochastic projection of the gradient, Orbit transfer, Earth Mars orbit transfer.

COB312 MODELO DE LOCALIZAÇÃO INTEGRADA DE TÉRMICAS COM OBJETIVOS MÚLTIPLOS / MODELLING OF INTEGRATED THERMAL POWER PLANTS SITING WITH MULTIPLE OBJECTIVES

Antônio J. Silva Neto¹, Jean C. Negri², Mario V. Pereira³ & Silas Vieira²

¹Promon Engenharia, Av. Pres. Juscelino Kubitschek 1830, São Paulo, SP, 04543-900

Atualmente: Instituto Politécnico / UERJ, Av. Alberto Rangel s/No., Vila Nova, Nova Friburgo, RJ, 28630-050, E-mail: ajsneto@iprj.uerj.br

²Companhia Energética de São Paulo, CESP

³Power Systems Research, PSR

The software LITOM was developed as a tool for the selection of appropriate alternatives for thermal power generation. Both qualitative and quantitative information are taken into account for the identification of the combination of site, fuel and technology. The software furnishes several alternatives sorted according to the criteria established by the user. A brief description of the software is presented in this work along with some results.

Keywords: Usinas Termoelétricas; Localização; Seleção; Software para Seleção e Localização de Termoelétricas; LITOM / Thermal Power Plants; Siting; Selection; Software for Selection and Siting; LITOM

COB314 HOW TO CHOOSE EIGENVALUE PROBLEMS WHEN USING GENERALIZED INTEGRAL TRANSFORMS TO SOLVE THERMAL CONVECTION-DIFFUSION PROBLEMS.

João Batista Aparecido

Departamento de Engenharia Mecânica, Faculdade de Engenharia-UNESP - Ilha Solteira, CEP 15385-000 Ilha Solteira-SP-Brasil

This work presents mathematical aspects of the theory of Generalized Integral Transforms. The main focus is directed toward on how to choose the auxiliary eigenvalue problems when solving thermal convection-diffusion type problems using such integral transforms. A class of problem considered here is mathematically modeled by a linear second order partial differential equation having general boundary conditions of first, second and third kind; and initial condition. Basic ideas are given why is feasible truncate the infinite system in a sufficient large finite system. Once the analysis is performed, a sample problem is solved using two kinds of auxiliary eigenvalue problems. The Graetz convective-diffusive problem is considered as sample problem. It is solved in the classical manner using an auxiliary eigenvalue problem that leads to degenerate hypergeometric type eigenfunctions. It is also solved using a second auxiliary eigenvalue problem that leads to trigonometric type eigenfunctions. Among physical variables of interest are bulk fluid temperature, local axial Nusselt Number, and average Nusselt Number. Results for bulk fluid temperature and heat transfer are compared each other as well with data found in open literature.

Keywords: Integral Transform, Eigenvalue Problem, Convection, Diffusion, Heat Transfer

COB721 OTIMIZAÇÃO DE UMA SUPERFÍCIE ALETADA UTILIZANDO UM ALGORITMO GENÉTICO / COOLING FINS OPTIMIZATION USING A GENETIC ALGORITHM

Ricardo Poley Martins Ferreira & Ricardo Luiz Utsch de Freitas Pinto

Departamento de Engenharia Mecânica, Escola de Engenharia - UFMG, Av. Antônio Carlos, 6627 - Pampulha, Belo Horizonte, Minas Gerais, CEP 31270-901, E-mail: poley@demec.ufmg.br & utsch@vesper.ufmg.br

Cooling fins have been usually used to guarantee a suitable heat transfer through a thermal surface. On the other hand, when cooling fins are used, increase the weight and costs of the equipments. It is very hard to obtain the optimal geometry with traditional optimization methods (linear and nonlinear programming). Genetic algorithms have been sucessfully used to find global solutions in complex spaces without derivative knowledge. This paper presents how a genetic algorithm can be used to find the optimum cooling fin geometry to maximize the heat transfer through a surface. The model is composed by a system of nonlinear equations with implicit boundary conditions.

Keywords: Aletas ótimas, algoritmos genéticos, transferência de calor, otimização, métodos numéricos

Optimal cooling fins, genetic algorithms, heat transfer, optimization, numerical methods.

COB768 TRANSIENT LAMINAR FORCED CONVECTION HEAT TRANSFER IN CIRCULAR AND PARALLEL-PLATES DUCTS OF HERSCHEL-BULKLEY FLUIDS

E. N. Macêdo and J. N. N. Quaresma

Chemical Engineering Department – CT/UFPA, Campus Universitário do Guamá, Rua Augusto Corrêa, 01, 66075-900 – Belém-PA-Brasil, E-mail: quaresma@marajo.ufpa.br

The transient analysis of the thermal entry region in laminar forced convection heat transfer of Herschel-Bulkley fluids, within both circular and parallel-plates ducts, is analytically studied through the so-called Generalized Integral Transform Technique (GITT). A prescribed constant uniform wall temperature is considered for the boundary condition. Benchmark results for the local Nusselt numbers in regions very close to the duct inlet are established, for various rheological behavior parameters, such as power-law exponents and yield numbers, which are then confronted with the previous results in the recent literature.

Keywords: Generalized Integral Transform Technique, Transient internal forced convection, Herschel-Bulkley fluids, Parallel-plates channel and circular tube.

COB898 ANÁLISE DE CONVECÇÃO NATURAL NO ESPAÇO ANULAR DE DOIS CILINDROS CONCÊNTRICOS VERTICAIS / NATURAL CONVECTION ANALYSIS IN ANNULAR CAVITY BETWEEN TWO CONCENTRIC VERTICAL CYLINDERS

Marcelo Assato, Genésio José Menon & Dênio Lemos Panissi

Departamento de Engenharia Mecânica - EFEI, Av. BPS n^o1303-Bairro Pinheirinho - CEP 37.500-000 - Itajubá-MG-Brasil,

e-mail:genesio@iem.rmg.efei

This work deals with the study of heat transfer by natural convection, two-dimensional, laminar in annular cavity between two concentric vertical cylinders with the inner wall maintained at a higher temperature than the outer wall. The top and bottom wall are insulated. The finite element method is used for the solution of the conservation equations, in order to find the local and average Nusselt number together with the distributions of the stream function y , dimensionless temperature q and vorticity w , as function of the thermal and geometrical parameters. Numerical results are obtained for Rayleigh numbers range from 10⁴ to 10⁵, radius ratios from 2 to 10, and aspect ratios from 1 to 5. Prandt number is kept constant at 0.7 in this study.

Keywords: Natural Convection, Vertical Concentric Cylinder, Finite Element Analysis, Nusselt Number.

Convecção Natural, Cilindros Verticais Concêntricos, Método de Elementos Finitos, Número de Nusselt.

COB1019 PRECONDITIONED ITERATIVE TECHNIQUES FOR LINEAR SYSTEMS DERIVED TO SOLVE THE HEAT CONDUCTION PROBLEM IN VORONOI MESHES

Viviana Cocco Mariani & Sérgio Peters

Departamento de Informática e de Estatística, Universidade Federal de Santa Catarina - UFSC - Florianópolis

CEP 88040-900 Florianópolis, Brasil - E-mail: viviana@inf.ufsc.br, peters@inf.ufsc.br

When practical problems involving fluid mechanics, heat transfer, etc., are solved numerically, systems of linear equations are generated and their matrices of coefficients are generally sparse and large. The present work compares the performance of the conjugate gradient method using the general purpose preconditioners for solving the linear systems resulting from the discretization of the heat conduction equation in unstructured Voronoi meshes. We use the Finite Volume Method. Three preconditioners are tested: Diagonal Scaling, Symmetric Successive Over-relaxation and Incomplete Cholesky Factorization. We analyze them through their distribution of eigenvalues, number of iterations and CPU time.

Keywords: Preconditioning, Conjugate Gradient, Voronoi diagrams, linear systems, equation of heat conduction.

COB1138 COMPORTAMENTO DINÂMICO DE VÁLVULAS TIPO PALHETA EM ESCOAMENTOS PERIÓDICOS / DYNAMIC BEHAVIOR OF REED TYPE VALVES IN PERIODIC FLOWS

Mauricio Nath Lopes & Alvaro Toubes Prata

Departamento de Engenharia Mecânica, Universidade Federal de Santa Catarina - UFSC

CEP 88040-900 Florianópolis, Santa Catarina, Brasil - e-mail: prata@nrva.ufsc.br

In the present work a numerical methodology is developed to simulate the dynamic behavior of reed type valves of reciprocating compressors used in refrigeration. A one-degree freedom model is adopted for the valve motion, and a finite volume methodology is employed to obtain the flow field through the valve. The valve dynamics and the time dependent flow field are coupled and solved simultaneously. The flow through the valve is assumed laminar, compressible, adiabatic and axisymmetric. In presence of the valve motion a numerical methodology was developed to take into account the variation with time of the computation domain. Through a coordinate transformation a moving coordinate system was obtained; this new system was able to expand and compress according to the valve displacement. Results for the force acting on the valve were obtained for a prescribed periodic velocity at the valve entrance. The complex interaction between mass flow rate through the valve and the distance between the reed and the valve seat affected the force on the valve in a non-periodic manner. The present model has proved to be effective and accurate in exploring the valve motion in disc-type valves.

Keywords: Valve dynamics, compressor technology, none steady fluid flow, moving coordinate.

Dinâmica de válvulas, tecnologia de compressores, escoamento transiente, coordenadas móveis.

COB1381 análise dinâmica de estruturas engastadas no semi-espaço através do método dos elementos finitos incluindo o amortecimento geométrico / Dynamic analysis of structures embedDed In A half-space by the finite element method including geometric damping

Renato Marques de Barros, Euclides de Mesquita Neto

Deptartamento de Mecânica Computacional, Faculdade de Engenharia Mecânica - UNICAMP

CEP 13.083-970 Campinas, Sâo Paulo, Brasil - E-Mail: euclides@dmc.fem.unicamp.br

Pércio de Almeida Barros

Faculdade de Engenharia Civil - UNICAMP

The article compares the accuracy presented by the Finite Element Method using an infinite elements and Boundary Element procedures, based on influence functions to analyse the dynamic response of structures buried or embedded in a visco-elastic half-space. The infinite element shape functions were sinthesised to emcompass simultaneously the propagation of half-space body and surface waves. The numerical studies are conducted for a two-dimensional rigid rectangular foundation in the frequency domain. It is shown that the FE scheme produces good results , even for deeply buried foundations.

Keywords: Infinite elements, Soil-Structure Dynamic Interation, Finite Elements, Boundary Elements

Elementos Infinitos, Interação Dinâmica Solo-Estrutura, Elementos Finitos, Elementos de Contorno