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COB256 Convecção Natural em Cavidade Vertical com Fontes de Calor Discretas Montadas em uma das Paredes / natural Convection on a Vertical Cavity with Flush Mounted Heat Sources on a Lateral Side
Tito Dias Jr., Eduardo Yoshinori Honda, Ricardo Alan Verdú Ramos
Departamento de Engenharia Mecânica - Faculdade de Engenharia de Ilha Solteira - UNESP
CEP 15385-000 - Ilha Solteira-SP, Brasil - E-mail: titodias@feis.unesp.br; ramos@feis.unesp.br
In this work, the natural convection effect on the flow and the heat transfer in a vertical cavity with two discrete heat sources located on the left adiabatic wall is numerically studied. Laminar, two-dimensional and steady flow has been assumed. It has been used the Boussinesq approximation and the physical properties have been considered constant. The finite volumes method has been used to discrete the governing elliptical equations. The numerical solution has been obtained by the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm. A grid test was carried out and a more refined mesh was used near the heat sources region and with smooth space progression after that. The influence of the power distribution, spacing between the heat sources and cavity aspect ratio have been investigated. An analysis of the average Nusselt number of the two heat sources was realized to verify the improvement of the heat transfer coefficient.
Keywords: Convecção Natural, fontes de calor discretas, cavidade vertical, método de volumes finitos.
Natural convection, discrete heat sources, vertical cavity, finite volumes method.
COB532 ANÁLISE TEÓRICA E EXPERIMENTAL DA TRANSFERÊNCIA DE CALOR EM PLACAS DE CIRCUITO IMPRESSO FORMANDO CANAIS VERTICAIS ABERTOS / THEORETICAL AND EXPERIMENTAL ANALYSIS OF THE HEAT TRANSFER IN PRINTED CIRCUIT BOARDS FORMING OPEN VERTICAL CHANNELS
Ana Cistina Avelar & Marcelo Moreira Ganzarolli
Departamento de Energia, Faculdade de Engenharia Mecânica - UNICAMP - Campinas
CEP 13083-970, Campinas, Brasil - E-mail: ganza@fem.unicamp.br
This study analyses both theoretically and experimentally heat transfer in an array of vertical parallel printed circuit boards, cooled off by natural convection and proposes a modeling which tries to predict temperature distribution in significant places in the channels and boards. Due to its small thickness, the temperature gradient across the board was neglected, and the heat diffusion equation in two-dimensional Cartesian coordinates and steady state conditions was numerically solved. Energy balances for the componentes were formulated, and the problem was solved iterativelly. The concept of "buoyancy induced forced convection" was applied to the resistor where forced convection heat transfer coefficientes were employed. The printed circuit board has 25 resistors discretely distributed on its surface. Uniform heating tests with variation of power and distance among the printed circuit boards were performed. Good agreement between numerical and experimental results was observed.
Keywords: Transferência de calor, Canais verticais, Convecção natural, Convecção forçada, Placa de circuito impresso / Heat transfer, Vertical channels, Natural convection, Forced convection, Printed circuit board.
COB709 CONVECÇÃO NATURAL EM REGIME TRANSITÓRIO NO INTERIOR DE CAVIDADE POROSA / TRANSIENT NATURAL CONVECTION IN A POROUS CAVITY
Paulo Maria & Jorge Llagostera
Departamento de Energia, Faculdade de Engenharia Mecânica - Unicamp - Caixa Postal 6122, CEP 13083-970 Campinas, SP, Brasil.
E-mail: paulom@fem.unicamp.br, llagost@fem.unicamp.br
A numerical simulation on transient natural convection occurring in a square porous cavity is reported. The bottom wall of the bidimensional cavity is heated while the upper wall is cooled, both maintained at constant temperatures. The finite volume method was applied. The applicability of the Darcy model was assumed. The transient regime is examined for several intensities of the buoyancy effects due to fluid temperature variations. The transient fluid flow and heat transfer characteristics are studied and compared to other results. Global Nusselt numbers are reported for the heated and cooled walls. Aspects of the fluid flow and temperature fields are illustrated by contour maps.
Keywords: Convecção natural, regime transitório, cavidade porosa, modelo de Darcy / Natural convection, transient analysis, porous cavity, Darcy model.
COB718 CONVECÇÃO NATURAL TRANSITÓRIA TURBULENTA NUM RECIPIENTE CILÍNDRICO VERTICAL / TRANSIENT TURBULENT NATURAL CONVECTION INSIDE A VERTICAL CYLINDER
Paulo Vatavuk & Marcos M. Pimenta
Departamento de Engenharia Mecânica, Escola Politécnica - Universidade de São Paulo
CEP: 005508-900, São Paulo, Brasil E-mail: pvatavuk@usp.br
Natural convection of a liquid inside a vertical cylinder is solved numerically. The flow is caused by the uniform heating of the lateral wall. In spite of the practical importance of this problem very few results are available for the turbulent flow, which is the subject of this work. The turbulence model previously used by Ince & Launder, to study the problem of natural convection inside a rectangular cavity, was transformed into cylindrical coordinates and applied to the problem. This low Reynolds number model accepts a laminar as well as a turbulent solution. So, as the flow is initially laminar, it would be necessary in some instance to cause the transition. This difficulty was avoided by considering that in the initial condition the fluid was static but had a high turbulence intensity. This technique was not completely successful because the initial turbulent intensity had a phase effect in the solution.
Keywords: Convecção Natural - Modelos de Turbulência - Dinâmica dos Fluidos Computacional
Natural Convection - Turbulence Models - Computational Fluid Dynamics.
COB719 CONVECÇÃO NATURAL TURBULENTA DE METAIS LÍQUIDOS EM CAVIDADES FECHADAS / natural convection of liquid metal inside a closed cavity
Luiz Joaquim Cardoso Rocha & Angela Ourivio Nieckele
Departamento de Engenharia Mecânica - Pontifícia Universidade Católica do Rio de Janeiro
CEP 22453-900 - Rio de Janeiro/RJ - Brasil - E-mail: nieckele@mec.puc-rio.br
At the present work, natural convection of liquid metal inside a closed cavity is examined, based on the Boussinesq approximation. The upper and lower cavity walls are adiabatic, while the vertical walls are at uniform and different temperatures. When the Prandtl number is low, the transition from the laminar to the turbulent regime occurs for a Rayleigh number approximately equal to 105. Therefore, the laminar and turbulent regimes are examined. The turbulence model selected was the two differential equation low Reynolds number LRN k -e model. The problem was numerically solved by the finite volume method, based on the Power-law interpolating scheme. The pressure-velocity coupling was solved with the algorithm SIMPLEC. The solution obtained was validated comparing with some experimental and numerical results available in the literature. The effect of the Rayleigh and Prandtl number in the flow field was examined.
Keywords: Convecção Natural - Metal Líquido - Escoamento Laminar/Turbulento / Natural Convection - Liquid Metal - Laminar/Turbulent Flow
COB775 LOCALLY-COUPLED NUMERICAL SOLUTION OF THERMALLY-DRIVEN CAVITY FLOWS
Marcelo J.S. de Lemos
Departamento de Energia, Instituto Tecnológico de Aeronáutica-CTA
12228-900 - São José dos Campos, SP, Brasil - E-mail: mlemos@tecsat.com.br
This work reports a numerical investigation on buoyancy-induced flows occurring in enclosures of small aspect ratio. The numerical method used consists of the control-volume approach and a new block-implicit smoothing operator. Governing equations are written in terms of the so-called primitive variables and are recast into a general form. In the proposed method all governing equation are relaxed locally, at the same time, in contrast with commonly used segregated schemes. The effect of the Rayleigh number and aspect ratio on temperature and velocity patterns are presented.
Keywords: Coupled Solvers, Laminar Flow, Numerical Methods
COB797 ANALYSIS OF AXIAL FLUID CONDUCTION EFFECTS IN THERMALLY DEVELOPING FLOW IN TUBES
Ana Cristina Rocha de Castro, F. Scofano Neto & R. O. C. Guedes
Departamento de Engenharia Mecânica e de Materiais. Instituto Militar de Engenharia
Praça General Tibúrcio 80, CEP 22290-270 Rio de Janeiro, RJ, Brasil. E-Mail:imes4fsn@epq.ime.eb.br
This contribution addresses the internal forced convection problem in a circular duct including axial fluid conduction effects. The problem is modeled by taking under consideration the "two-region" model which avoids the prescription of the inlet temperature profile. The mathematical formulation is handled by the Generalized Integral Transform Technique and special consideration is given to the slug flow condition. The results are focused on the axial distribution of bulk and wall temperatures and Nusselt numbers over a range of suitable Peclet and external Biot numbers.
Keywords: Forced Convection, Eigenfuction Expansion, Analytical Solution, Slug Flow.
COB798 CONJUGATED HEAT TRANSFER IN PARALLEL PLATE CHANNELS SUBJECTED TO A PRESCRIBED FLUX AT THE WALL
R. C. de Araújo, R. O. C. Guedes & F. Scofano Neto
Departamento de Engenharia Mecânica e de Materiais, Instituto Militar de Engenharia - IME
Praça General Tibúrcio 80, Rio de Janeiro, RJ, 22290-270 - E-mail: d4guedes@epq.ime.eb.br
Conjugated convective-conductive heat transfer in laminar flow inside a parallel-plates channel subjected to prescribed wall heat flux is investigated . The Generalized Integral Transform Technique is used to handle the mathematical formulation and results are presented in terms of the dimensionless parameters governing the problem.
Keywords: Forced Convection, Thermal Entrance, Eigenfuction Expansion, Conjugate Problems
COB904 CONJUGATE HEAT TRANSFER TO NEWTONIAN FLUIDS IN DUCTS BY FINITE ELEMENTS
José Karam Filho1 & Nisio C. Lobo Brum2
1 Laboratório Nacional de Computação Científica (LNCC/CNPq-Brazil)
Rua Lauro Muller 455, Botafogo, Rio de Janeiro, RJ, 22290-160, Brazil, e-mail: jkfi@alpha.lncc.br
2 Programa de Eng. Mecânica - COPPE/UFRJ, Cidade Universitária, C. P. 68503, Rio de Janeiro, RJ, 21945-970, Brazil
In this work, we analyse conjugate heat transfer problems to Newtonian fluids in ducts by an SUPG finite element method. The case of prescribed temperature at the outside surface wall is considered, as well as radial and axial conduction effects in both fluid and solid. Heat fluxes are calculated by a post-processing technique and numerical results are presented.
Keywords: Conjugate convection-diffusion heat transfer, finite element, post-processing method, SUPG-methods.
Transferência conjugada de calor por convecção-difusão, elementos finitos, método de pós-processamento, métodos SUPG.
COB1124 CONVECÇÃO NATURAL TRANSIENTE EM CAVIDADES 3D / TRANSIENT NATURAL CONVECTION IN 3D CAVITIES
Paulo Martins Tollini & Antonio Cesar Pinho Brasil Junior
Departamento de Engenharia Mecânica, Faculdade de Tecnologia - UnB - Brasília
CEP 70.910-900 Brasília, Brasil - E-mail: brasil@enm.unb.br
The transient heat transfer by natural convection in a fluid confined into a completely filled 3D cavity (H = 165 mm, L = 95 mm, W = 65 mm) is analyzed here. The fluid is initially at a temperature T fi , and at a given time, all walls are heated to T b , greater than T fi . Heat is propagated by natural convection into the enclosure, until its complete thermal equilibrium. The problem is analyzed by numerical simulations and experimental measurements, for different values of the initial Rayleigh number. The numerical simulations are performed using the finite element method for 3D natural convection flow problems. Temperature profiles during the heating process, the flow visualization of the convective patterns, a discussion of the topology of the flow into the cavity and the mixing problem resulted from the natural convective effects, are presented. Practical relations for the Nusselt number into the cavity are proposed.
Keywords: Natural convection. Heat transfer. Convecção Natural. Transferência de Calor
COB1236 NATURAL CONVECTION IN THE EVAPORATOR REGION OF HOUSEHOLD REFRIGERATORS
Ricardo Hernandez Pereira e Angela Ourivio Nieckele
Department of Mechanical Engineering, Pontifícia Universidade Católica do Rio de Janeiro
CEP 22453-900 - Rio de Janeiro - RJ - Brazil - e-mail: nieckele@mec.puc-rio.br
The buoyancy induced convection of air in the evaporator region of household refrigerators is investigated numerically. The problem formulation accounts not only for body forces due to temperature gradients, but also to those due to moisture nonuniform concentration. In this way the whole problem is governed by two dimensionless and independent body force parameters, Grashof numbers, related to temperature and moisture concentration nonuniformity. Results were obtained for different combinations of thermal and concentration Grashof numbers, while the problem geometry remained unchanged. For a variety of operating conditions, that is, Grashof numbers, streamline pattern, temperature and moisture concentration fields are shown. Emphasis is given to overall values of Nusselt and Sherwood numbers, that allow for estimation of the sensible heat exchange and rate of air dehumidification between the evaporator and refrigerator cabinet.
Keywords: Natural Convection, Simulation, Refrigeration, Evaporator.
COB1286 ANÁLISE TEÓRICA DA CONVECÇÃO FORÇADA LAMINAR TRANSIENTE EM DESENVOLVIMENTO SIMULTÂNEO EM PLACAS PARALELAS / THEORICAL ANALYSIS OF THE TRANSIENT LAMINAR FORCED CONVECTION FOR SIMULTANEOUS DEVELOPING FLOW IN PARALLEL PLATE CHANNELS
M. J. Medeiros, C. A. C. Santos, S. Kakac* & S.Cheroto*
Coord. Pós-Graduação em Eng. Mecânica-CT / UFPB-João Pessoa - PB 58090-900 – Brasil
(*) Departament of Mechanical Engineering - University of Miami - Coral Glabes-Flórida 33124, USA
Transient laminar forced convection for simultaneous developing flow between parallel plates is studied by aplying the generalized integral transform technique. A fifth kind boundary condition for the energy equation is used and an auxiliar complex problem is generated. The results for the Nussselt number and bulk temperature are compared with other publications in order to validate the technique used in this work.
Keywords: Transient Forced Convection Generalized Integral Transform Technique Fifth Kind Boundary Condition
COB1289 ANÁLISE TEÓRICA DA CONVECÇÃO NATURAL LAMINAR NUMA CAVIDADE POROSA CONSIDERANDO O EFEITO DA POROSIDADE VARIÁVEL / THEORICAL ANALYSIS OF LAMINAR NATURAL CONVECTION INSIDE A RECTANGULAR CAVITY POROUS CONDIDERING THE EFFECT OF VARIABLE POROSITY
Jesus Marlinaldo Medeiros+*, Francisco Marcondes++ , Carlos Antônio C. Santos* & José Maurício Gurgel*
(+)Escola Técnica Federal de Sergipe/UNED - Aracaju - SE 49056-260
(++)Laboratório Computacional em Térmica e Fluidos - LCTF-DEM-CCT-UFPB - marconde@lctf.ufpb.br
(*)Laboratório de Energia Solar - LES-CPGEM-DTM-UFPB - cabral@les.ufpb.br - gurgel@les.ufpb.br
58059-900 João Pessoa - PB - Brasil
A numerical study is performed on steady two-dimensional natural convection inside a rectangular porous enclosure with uniform internal heat generation. The boundary conditions were: Two isothermal walls at same temperatures, two horizontal adiabatic walls. The effects of non-uniform porosity are taken into consideration in the momentum equation. The governing equations in terms of the primitive variables are solved by the finite volume method. The coupling velocity - pressure was treated by PRIME algorithm employing staggered grids. The results are presented in terms of the isotherms, stream functions and Nusselt number with and without uniform porosity.
Keywords: Natural Convection - Porous Medium - Non-Darcian Model - Variable Porosity - Convecção Natural – Meio Poroso – Modelo não Darciano – porosidade variável
COB1372 FORCED CONVECTION AIR COOLING OF A 1/2 ATR PROCESSOR BOX - AN EXPERIMENTAL STUDY
V. Srinivasa Rao*, R. Raghunathan*, K. Rajaiah* , K.S. Gautam** & K. Srinivasan**
* E-mail: raghu@ade.ernet.in
* Scientists, Aeronautical Development Establishment, Bangalore-560 075, India
** Dept of Mechanical Engg, Indian Institute of Science, Bangalore-560 012, India
Wind tunnel studies have been carried out to evaluate the forced convection air cooling requirements of a 1/2 ATR processor box designed for air-borne applications. Various levels of heat flux are simulated at the PCB level in the box using resistance element heating. Pressure drop, transient heating and cooling curves are analysed and a set of performance curves involving the time constants and steady state excess operating temperatures are obtained.
Keywords: Processors, Convection, Air cooling, Time constant, Steady state excess operating temperature.
COB1420 VERTICAL PLATE IN RELATIVE MOTION TO A PARALLEL AIR STREAM
M.V. A. Bianchi1 0. H. G. Branco2, J.V.C. Vargas2 & R. Viskanta1
1 Heat Transfer Laboratory, School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-1288 USA
2 Departamento de Engenharia Mecânica, Universidade Federal do Paraná
Heat transfer from a surface in motion relative to either a stationary or moving fluid occurs in many materials processing applications such as hot rolling, extrusion, drawing, and drying. In this study, an analysis has been carried out to predict convective transport occurring in the laminar air boundary layer on a continuous vertical surface which moves in parallel or in counterflow with respect to the free stream in the presence of gravity. Numerical results obtained with the local non-similarity method based on boundary layer assumptions are compared to numerical results from a complete formulation. Predictions for the local skin friction and heat transfer are made for different configurations of the relative position of the surface and the free stream. The comparison allows for the establishment of criteria on when the use of boundary layer assumptions is an acceptable approximation. New results are presented with the complete formulation using the finite element method.
Keywords: Moving plate, laminar regime, finite element method