Session 12: Heat and Mass Diffusion and Analytical Methods
Chairs:
Helcio Rangel Barreto Orlande
Programa de Engenharia Mecanica, COPPE/UFRJ
Marco Túlio Mena Barreto de Vilhena
Departamento de Engenharia Nuclear
UFRGS
Vladimir V. Kulish - mvvkulish@ntu.edu.sg
School of Mechanical &
Production Engineering
Nanyang Technological University
50 Nanyang Ave., Singapore
639798
José L. Lage - JLL@SEAS.SMU.EDU
Pavel L. Komarov - pavel@seas.smu.edu
Peter E. Raad - praad@seas.smu.edu
Mechanical Engineering Department
Southern Methodist University
Dallas, Texas, 75275-0337
The thermoreflectance method,
suitable for determining the thermal properties of thin films, consists
of measuring changes in the reflectivity of a thin film under pulsed laser
heating, and relating these
changes to corresponding temperature variations. Analytical or numerical
solutions of the diffusion problem are then used to determine the thermal
property of the material following an iterative matching process between
the analytical and the experimental results. The existing analytical or
numerical solutions, valid when the laser energy is absorbed at the surface
or when it is absorbed volumetrically by the thin film, allow for the determination
of only one thermal property (thermal conductivity or diffusivity), with
the other one assumed to be equal to the bulk material property. A complete
solution to the non-homogeneous diffusion equation with surface and volumetric
heating, found using fractional calculus and presented in a semi-derivative
form, provides the means to determine the two thermal properties of thin
films (thermal conductivity and diffusivity) concomitantly. This can be
achieved by utilising a secondary laser for heating the material. The solution
component for surface heating is validated by comparison with experimental
data for a GaAs bulk sample using the classical thermoreflectance method.
Keywords: thermoreflectance,
thin films, fractional calculus
Jesús Salvador Pérez
Guerrero - jperez@cnen.gov.br
Marco Aurélio Leal
- maleal@cnen.gov.br
Comissão Nacional
de Energia Nuclear, Coordenação de Rejeitos Radioativos -
COREJ
Rua General Severiano, 90
- Botafogo - Rio de Janeiro - RJ - 22294.900- Brazil
The Generalized Integral Transform Technique (GITT) is employed in the solution of two-dimensional laminar natural convection within inclined enclosures filled by air (Prandtl number of 0.71), subjected to differentially heated walls and insulated horizontal surfaces. The hybrid nature of the GITT approach allows for the establishment of reference results in the solution of non-linear partial differential systems, as the coupled set of heat and fluid flow equations that govern the steady natural convection problem under consideration. The aim of the present work is to provide reference results to steady-state natural convection in square cavities with Rayleigh numbers equal to 10 4 and 10 5 for several different inclination angles, a = 40 0 , 60 0 , 120 0 and 140 0 . Numerical values of the mean Nusselt numbers and streamfunctions are presented to all examined situations.
Keywords: Natural convection,
Integral transform, Hybrid method
Sérgio Wortmann -
s_wortmann@hotmail.com
Angela B. D. Moura - angelabm@ufrgs.br
Marco T. M. B. Vilhena -
vilhena@cesup.ufrgs.br
PROMEC - Universidade Federal
do Rio Grande do Sul
Sarmento Leite, 425, 3 º
andar - 90035-972 - Porto Alegre, RS,Brasil
The objective of this work consists of presenting an analytical solution, being used the Generalized Integral Transform Technique (GITT) and Laplace Transform, for the vertical dispersion of polutants in a stable atmospheric boundary layer, with a diffusion coefficient derived from the local similarity and of the statistical diffusion theories. Numerical simulations are reported.
Keywords: GITT, Analitical
Solution, Atmospheric Dispersion, Laplace Transform.
Fernando P. Duda
Universidade Federal do
Rio de Janeiro, COPPE
Programa de Engenharia Mecânica,
C.P. 68503, 21945-970 - Rio de Janeiro, RJ, Brasil
Luiz C. G. Pimentel
Universidade Federal do
Rio de Janeiro
Departamento de Meteorologia,
RJ, Brasil
Jesús S. Perez Guerrero
Comissão Nacional
de Energia Nuclear CNEN/COREJ, RJ, Brasil
Resumo: Neste trabalho consideraremos aspectos relacionados com a formulação do modelo de Cattaneo visando a simulação do problema de condução hiperbólica. Obteremos a solução analítica para o problema de condução em uma placa finita, usando a Técnica da Transformada Integral e o Mathematica. A solução encontrada apresenta comportamento não realista do ponto de vista físico, o que pode estar relacionado com o fato do modelo de Cattaneo utilizado ser inconsistente com a segunda lei da termodinâmica. Finalmente, mostraremos como o arcabouço da termomecânica do contínuo pode ser utilizado para tornar o modelo de Cattaneo consistente com a segunda lei, resultando numa forma especial para a equaçaão constitutiva para a energia interna.
Palavras-chave: condução
de calor hiperbólica, termomecânica do contínuo, transformada
integral
Jiazheng Wang - jiazheng@iprj.uerj.br
Jian Su- sujian@lmn.con.ufrj.br
Antônio J. Silva Neto
- ajsneto@iprj.uerj.br, ajsneto@lmn.con.ufrj.br
Instituto Politécnico,
Universidade do Estado do Rio de Janeiro, CP 97282, CEP 28601-970, Nova
Friburgo, RJ, Brasil.
Programa de Engenharia Nuclear
- COPPE - Universidade Federal do Rio de Janeiro, CP 68509, CEP 21945-970,
Rio de Janeiro, RJ, Brasil.
In this work we consider the inverse problem of heat sources intensity estimation, with spatial and timewise dependency, in nonlinear heat conduction problems. The formulation and solution of the inverse problem with Alifanov's iterative regularization method is presented. A comparison is done between the results obtained with the non-linear formulation and those resulting from an approximation with a linear formulation.
Keywords: Inverse problems,
Nonlinear heat conduction, Conjugate gradient, Adjoint problem.
Romberg Rodrigues Gondim
- romberg@les.ufpb.br
Universidade Federal da
Paraíba - CT/DTM, Campus I, Laboratório de Energia Solar,
Caixa Postal 5115 - CEP 58051-970 - João Pessoa, PB, Brasil.
Renato Machado Cotta - cotta@serv.com.ufrj.br
Mechanical Engineering Department,
EE/COPPE/UFRJ - Universidade Federal do Rio de Janeiro, Caixa Postal 68503
- CEP 21945-970, Rio de Janeiro - RJ.
Transient forced convection within planar channels is solved for a thermally developing laminar flow situation, considering the presence of axial diffusion in the fluid energy equation. The analysis employs the generalized integral transform technique combined with a transient filtering solution, aimed at enhancing the convergence behavior of the associated eigenfunction expansions, and allowing for the inspection of the Peclet number influence on the final converged solution. The numerical results so obtained are critically compared against available results in the open literature for the infinite Peclet number situation. Finally, a computational cost analysis is performed among different possible filtering strategies for the same problem.
Keywords: Transient convection,
Integral transform, Axial
HIGHER ORDER LUMPED ANALYSIS OF TRANSIENT HEAT TRANSFER IN A NUCLEAR FUEL ROD
Jian Su - sujian@lmn.con.ufrj.br
Nuclear Engineering Department,
COPPE/UFRJ, CP 68509, Rio de Janeiro, 21945-970, Brazil
Renato M. Cotta - cotta@serv.com.ufrj.br
Mechanical Engineering Department,
COPPE/UFRJ
CP 68503, Rio de Janeiro,
21945-970, Brazil
Abstract. Transient heat transfer in a nuclear fuel rod is analyzed by an improved lumped parameter approach. The circunferential symmetry is assumed with the heat transfer through the gap modelled by a heat transfer coefficient. Higher order (H1,1) Hermite approximation for integration is used to obtain the average temperatures in the radial direction. A significant improvement over the classical lumped parameter formulation has been achieved. The proposed fuel rod heat conduction model can be used in stability analysis of BWR, simplified model of PWR or real-time simulator of nuclear power plants.
Keywords: Transient Heat
Conduction, Lumped Parameter Analysis, Hermite Approximation, Nuclear Reactor
Thermohydraulics
Rubem Mário Figueiró
Vargas - rvargas@eq.pucrs.br
PUCRS - FEN G - DEQ
Porto Alegre - RS - Av Ipiranga
6681 CEP 90619.900 - Prédio 3 0 Bloco 6 Sala 216
Marco Tullio de Vilhena -
vilhena@cesup.ufrgs.br
Jacques Brancher
UFRGS - PROMEC
In this work is proposed
an analytica l solution for the nonlinear coupled conductive-radia tive
hea t p roblem. The solutio n is o b ta ined usin g the decomposition method.
This method is a powerful tool to solve nonlinear p roblems. Numerical
results a re a ttained a s for iso tropic med ium as anisotropic med ium.
These ones a re compared with results encountered in the literature. An
analyses is made comparing numerical and analytica l solutions.
SOLUTION OF THE TRANSIENT HEAT CONDUCTION EQUATION IN MULTICOMPONENT PLATES
Ivanilda B. Aseka - iaseka@vortex.ufrgs.br
Universidade Federal de
Santa Maria, Departamento de Matem_atica
Universidade Federal do
Rio Grande do Sul, Programa de Pos-Graduação em Minas, Metalurgica
e de Materiais - PPGEM
Osvaldo Aranha, 99/613 -
90035-190, Porto Alegre, RS, Brasil
Marco T. Vilhena - vilhena@cesup.ufrgs.br
Universidade Federal do
Rio Grande do Sul, Instituto de Matemática PPGEM
Paulo O. Beyer - pob@mecanica.ufrgs.br
Marcus V. A. Bianchi - bianchi@mecanica.ufrgs.br
Universidade Federal do
Rio Grande do Sul, Departamento de Engenharia Mecânica
Cx. P. 17819 - 90035-972
- Porto Alegre, RS, Brasil
In this work a semi-analytic method is presented for the solution of a two- dimensional transient heat conduction problems in a multicomponent plates. That method consists of the application of the nodal method combined with the Laplace transform technique, which allows to _nd expressions for the average temperatures and for the temperature in the boundary.
Keywords: semi-analytic,
transient conduction, plates multicomponent
SOLUÇÃO SEMI-ANALÍTICA DA EQUAÇÃO DE TRANSFERÊNCIA RADIATIVA NÃO-LINEAR
José V. P. de Oliveira
Universidade Federal de
Santa Maria, Departamento de Matemática
Av. Roraima, S/N - CCNE
- 97105-900 - Santa Maria, RS, Brasil.
Augusto V. Cardona - avcardona@pucrs.br
Pontifícia Universidade
Católica do Rio Grande do Sul, Faculdade de Matemática
Av. Ipiranga, 6681 - Prédio
15 - 90619-900 - Porto Alegre, RS, Brasil.
Marco T. M. B. de Vilhena
- vilhena@cesup.ufrgs.br
Universidade Federal do
Rio Grande do Sul, PPGEM
Av. Osvaldo Aranha, 99 -
6 o andar - 90046-900 - Porto Alegre, RS, Brasil.
Ricardo Barros - ricardob@iprj.uerj.br
Universidade do Estado do
Rio de Janeiro, Instituto Politécnico - IPRJ
Caixa Postal 97282 - 28630-050
- Nova Friburgo, RJ, Brasil.
Analytical Solution of the Non-Linear Radiative Transfer Equation. In this paper, we describe a new approach to solve the radiative transfer problem, combining the LTSN method and Spectral method. We use the essence of the spectral methods, where the intensity of radiation is expanded in time in a truncated series of Laguerre polynomials yielding a set of stationary one-dimensional transport problems, that we solve using the LTSN method. The material temperature and the intensity of radiation are determined by an iteration from the initial temperature. Numerical results and comparisons with the results found in the literature are also presented.
Keywords: Radiative transfer,
Transient transport problem, Spectral method, LTSN method.
Angela B. D. Moura - angelabm@ufrgs.br
Marco T M. B. Vilhena -
vilhena@cesup.ufrgs.br
Universidade Federal do
Rio Grande do Sul , PROMEC
Sarmento Leite 425/ 3 andar-
Cx. P. 17819 - 90035.972 - Porto Alegre, RS, Brasil
Gervasio Degrazia - degrazia@super.ufsm.br
Universidade Federal de
Santa Maria, Departamento de Fisica.
Cyntia Segatto- cynthia@cesup.ufrgs.br
Universidade Federal do
Rio Grande do Sul, Depto. de Matematica.
O objetivo deste trabalho consiste na determinaçao de uma soluçao analitica para o problema de difusao e adveçao tridimensional estacionario que representa a dispersao de contaminantes em uma camada limite planetaria. Este modelo e valido para a dispersao de um contaminante passivo na camada limite atmosferica, emitido a partir de uma fonte pontual contnua, e sujeito a situaçoes de turbulencia homogenea e com velocidade de vento medio uniformes, ou seja, para abandonos elevados que ocorrem em condiçoes de estabilidade intermediaria e na ausencia de fortes empuxos. A soluçao e alcançada com o uso do metodo da Transformada Integral Generalizada e s~ ao analiticas no sentido de que nenhuma aproximaçao foi feita ao longo de sua derivaçao. Simulaçoes e comparaçoes com resultados experimentais disponveis na literatura sao apresentadas. Nestas simulaçoes os coeficientes de dispersao foram considerados dependentes da distancia da fonte.
Palavras-chave: soluçao
anaitica, GITT, dispersao atmosferica
Jader Lugon Junior 1 - lugon@iprj.uerj.br
Antônio J. Silva Neto
2 - ajsneto@iprj.uerj.br
Instituto Politécnico
- Universidade do Estado do Rio de Janeiro, CP 97282, CEP 28601-970, Nova
Friburgo, RJ, Brasil.
In this work is done the estimation of parameters related to the separation process of bio-molecules by adsorption in gas-liquid interfaces in bubble and foam columns. The results obtained with the Levenberg-Marquardt method and real experiment data of the concentration of the Bovine Serum Albumin (BSA) are presented.
Keywords: Inverse problems,
Gas-liquid adsorption, Fractionation, Bubble columns.
DISCRETE-ORDINATES SOLUTIONS TO SOME CLASSICAL FLOW PROBLEMS IN THE RAREFIED GAS DYNAMICS
M. Camargoy
P. Rodriguesy
Programa de Pos - Graduaçao
em Engenharia Mecanica
Universidade Federal do
Rio Grande do Sul
90050{170 Porto Alegre,
RS, Brasil,
E-mail: camargo@mecanica.ufrgs.br,
patricia@mecanica.ufrgs.br
L. B. Barichellozy
zInstituto de Matem_atica
Universidade Federal do
Rio Grande do Sul
91509{900 Porto Alegre,
RS, Brasil
E-mail: lbaric@mat.ufrgs.br
A recently developed version
of the discrete-ordinates method is used to solve in a uni_ed manner, for
plane and cylindrical geometry, some classical ow problems
based on the Bhatnagar,
Gross and Krook model in the theory of rare_ed-gas dynam- ics. In particular,
the thermal-creep problem for the case of a semi-in_nite medium and the
Poiseuille- ow problem, for a wide range of the Knudsen number, are solved.
Ana- lytical solutions for the discrete-ordinates problem are obtained
based on a \half-range" quadrature scheme which results in simpli_ed eigenvalue
problems. Numerical results are presented to show that the solutions are
specially accurate and easy to implement.
Key Words: Rare_ed Gas Dynamics,
BGK Model, Discrete-Ordinates