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COB288 TWO-DIMENSIONAL SIMULATION OF HEAT CONDUCTION IN ORDERED COMPOSITES WITH A THERMALLY-CONDUCTING DISPERSED PHASE

Manuel Ernani de Carvalho Cruz

Department of Mechanical Engineering, EE/COPPE/UFRJ, CP 68503, CEP 21945--970 Rio de Janeiro, RJ, Brazil

In this paper we extend a finite--element--based methodology to simulate two--dimensional heat conduction in ordered composites with a thermally--conducting dispersed phase. The method of homogenization is employed to derive the continuous cell problem and an expression for the effective thermal conductivity. Finite elements are used for numerical solution of the cell problem. Our formulation is applicable to both ordered and random composites; however, here we only compute the effective conductivity of the former, and validate our results against well--known analytical solutions to the same problem. Future research will extend the current implementation to random composites, which model real composite materials more closely.

Keywords: Heat Conduction; Finite Elements; Thermal Composites; Ordered Media; Numerical Methods /

Condução de Calor; Elementos Finitos; Compósitos Térmicos; Meios Ordenados; Métodos Numéricos

COB298 FORMULAÇÃO BIDIMENSIONAL GERAL PARA PROBLEMAS INVERSOS DE CONDUÇÃO DE CALOR / A GENERAL TWO-DIMENSIONAL FORMULATION FOR INVERSE HEAT CONDUCTION PROBLEMS

J. P. Alencar Jr. and H. R. B. Orlande

DEM/PEM-EE/COPPE - UFRJ, Cid. Universitária, Cx. Postal: 68503, Rio de Janeiro, RJ, 21945-970, Brasil

M. N. Ozisik

Dept. of Mechanical Engineering. - NCSU, PO. Box: 7910, Raleigh, NC 27695-7910, USA

In this paper we present a general solution for two-dimensional boundary inverse heat conduction problems, by using the conjugate gradient method of minimization together with an elliptic scheme of numerical grid generation. The direct problem, as well as other auxiliary problems, are formulated in terms of generalized coordinates in a computational domain, where they are solved by finite-differences over a rectangular region. Simulated measurements are used to illustrate the application of the present approach with a practical inverse problem of engineering interest.

Keywords: Boundary Inverse Problem, Conjugate Gradient Method, Function Estimation, Numerical Grid Generation, Generalized Coordinates.

COB299 SOLUÇÃO VIA TRANSFORMADA INTEGRAL PARA PROBLEMA DE CONDUÇÃO DE CALOR EM CHIPS COM ENCAPSULAMENTO PLÁSTICO / AN INTEGRAL TRANSFORM SOLUTION FOR THE HEAT CONDUCTION PROBLEM IN PLASTIC ENCAPSULATED CHIPS

L. B. Dantas, H. R. B. Orlande, R. M. Cotta and M. D. Mikhailov

PEM/COPPE/UFRJ, Cidade Universitária, Cx. Postal 68503, CEP 21.945-970 Rio de Janeiro, RJ – E-mail: helcio@serv.com.ufrj.br

In this paper we study the steady-state heat conduction problem involving a plastic encapsulated chip. The two-region problem is solved as a single-region one, by assuming perfect contact between the chip and the encapsulant. The Classical Integral Transform Technique is used for the solution of the present problem, by using a two-dimensional auxiliary eigenvalue problem. The Generalized Integral Transform Technique is then applied for the solution of such eigenvalue problem. Results are presented for a typical test-case.

Keywords: Integral Transform Technique, Plastic Encapsulated Chips, Heat Conduction / Técnica de Transformação Integral, Chips com Encapsulamento Plástico, Condução de Calor.

COB324 ESTIMADOR DE UMA FUNÇÃO OBJETIVO DE CORRELAÇÃO NA MEDIÇÃO SIMULTÂNEA DE PROPRIEDADES TÉRMICAS / SIMULTANEOUS THERMAL PROPERTIES ESTIMATION USING A CORRELATION OBJECTIVE FUNCTION ESTIMATOR

Sandro M. M. de L. e Silva, Gilmar Guimarães & Marcus A.V. Duarte

Departamento de Engenharia Mecânica, Universidade Federal de Uberlândia - UFU - Uberlândia

CEP 38400-902 Uberlândia, MG, Brasil - E-mail: gguima@ufu.br, metrevel@ufu.br

This paper describes an experimental technique to measure simultaneously the thermal diffusivity and thermal conductivity of nonmetallic materials. Thermal properties are estimated by using parameter estimation techniques with measured surface heat flux and temperature histories on only one surface of a perspex sample. In addition the golden section optimization technique is used with the parameter estimation for minimizing two different objective functions. Each of the thermal properties is estimated in a different way. The diffusivity estimation uses a correlation function estimator between the heat flux and temperature while a square function error of experimental and estimated temperatures is the objective function used for determining the conductivity. A comparison with the guarded hot plate method indicates a deviation of 2.1% of the thermal conductivity.

Keywords: Estimação de Parâmetros, Medição de Propriedades Térmicas, Condução, Problemas Inversos, Otimização. Parameter Estimation, Thermal Properties Measurements, Heat Conduction, Inverse Problems, Optimization.

COB905 APLICAÇÃO DO MÉTODO DE ELEMENTOS FINITOS EM PROBLEMAS DE MUDANÇA DE FASE COM PROPRIEDADES FÍSICAS DEPENDENTES DA TEMPERATURA / FINITE ELEMENT METHOD APLICATION IN PHASE CHANGE PROBLEMS WITH TEMPERATURE DEPENDENT PHYSICAL PROPERTIES

Scalon, V.L.¹ , Padilha, A.² & Ismail, K.A.R.³

1 Depto de Engenharia Mecânica - FET-UNESP-Bauru. Email: scalon@bauru.unesp.br

2 Depto de Engenharia Mecânica - FET-UNESP-Bauru. Email: padilha@bauru.unesp.br

3 Depto de Eng. Térmica e de Fluidos - FEM-UNICAMP. Email: kamal@fem.unicamp.br

This work studies a solidification process with temperature-dependent physical properties for the solid region. Is developed a numerical unsteady model based upon an enthalpic approach and the finite element method. The obtained numerical results compare well with an analytical solution for a semi-infinite body and obtained experimental results.

Keywords: Mudança de Fase/Phase Change; Elementos Finitos/Finite Element; Método Entálpico/Enthalpic Method

COB1228 ESTUDO DE TÉCNICA PARA SOLUÇÃO DE PROBLEMA INVERSO DE CONDUÇÃO DE CALOR BIDIMENSIONAL /STUDING OF TWO-DIMENSIONAL IHCP TECHNIQUES

Frederico Romagnoli Silveira Lima & Gilmar Guimarães

Departamento de Engenharia Mecânica, Universidade Federal de Uberlândia, Bloco 1M, Campus Santa Mônica CEP 38-400 089 Uberlândia M. G. - E-mail: gguima@ufu.br;romagnol@ufu.br.

This work treats techniques for solving inverse heat conduction problems (IHCP) related to tools used in machining. The surface heat flux can be estimated from experimental and calculated temperature data. An evaluation of boundary conditions of metal cutting indicates the complexity of the thermal problem and a 3-D analysis is necessary. However, in a first study, the use of a simplified hypothesis enables two-dimensional (2D) analysis initially. The heat source due the machining process was simulated numerically to permit a great flexibility in the analysis of the technique used. The results of the 2D analysis are presented in several graphics. In this case, the linear imposed heat transfer history varies with time and position and the heat appeared to be lost laterally. The evaluation of results indicates the cases that the methods can be applied successfully.

Keywords: Inverse problems – parameter estimation – heat conduction – two-dimensional – cutting.

Problemas inversos – estimação de parâmetros – condução de calor – bidimensional – usinagem.

COB1503 MACRO-TO MICROESCALE HEAT TRANSFER: THE LAGGING BEHAVIOR

Da Yu Tzou

Department of Mechanical and Aerospace Engineering

University of Missouri-Columbia, Columbia, MO65211, USA – E-mail: tzou@riscl.ecn.missouri.edu

Thermal lagging is a physical phenomenon in heat transport becomes pronounced as the physical scale and/or transient time shorten. The resulting phase-lag concept extends the macroscopic approach that is familiar, and probably more palatable, to practicing engineers to accommodate the thermalization and relaxation behavior in small-scale heat transport. Several sets of experimental results, including femtosecond ultrafast laser heating on metal films, fast-transient heat transport in amorphous materials, heat propagation in superfluid liquid helium, and energy dissipation in sand are revisited to reveal the insufficiencies in the existing models and the need for a more refined approach. The dual-phase-lag model then follows, aiming at accurate descriptions of the salient features that reflect the interweaving behavior of thermalization and relaxation in these experiments. Physical meanings of phase lags are summarized, with emphasis on the interrelations with the existing macroscopic and microscopic models. Lagging behavior in rapid thermal oxidation in silicon dielectrics is demonstrated, which appears as the counterpart of thermal lagging, but occurs in mass transport with time delays due to species diffusion and chemical reactions.

Keywords: Thermal lagging, relaxation, thermalization, phase lags, microscale.