Session 6: Convective Heat and Mass Transfer

Chair:

Carlos Alberto Carrasco Altemani
UNICAMP - FEM

Genésio Menon
Escola Federal de Engenharia de Itajubá

Jurandir Itizo Yanagihara
Departamento de Engenharia Mecânica Escola Politécnica Universidade de São Paulo

Renato Machado Cotta
Programa de Engenharia Mecanica, COPPE/UFRJ








s06p01

A SECOND-ORDER IN TIME SCHEME FOR EVOLUTION EQUATIONS MODELLING BENARD CONVECTION

C. I. Christov [email protected]
Dept. of Mathematics, University of Louisiana at Lafayette,
Lafayette, LA 70504-1010

J. Pontes [email protected]
Metallurgy and Materials Engineering Department EE/COPPE/UFRJ
PO Box 68505 21945-970 Rio de Janeiro RJ, Brazil

Using the operator-splitting method a computationally e_cient second-order in time implicit di_erence scheme is developed for the Swift-Hohenberg equation (S-H). For each time step the scheme involves internal iterations which improve the stability and increase the accuracy with which the Lyapunov functional for S-H is approximated. Di_erent cases of pattern formation are treated and shown that the new scheme reaches the stationary pattern several times faster than the previously used _rst-order in time schemes. The results for the stationary pattern are compared with our previous results and shown to be in good qualitative and quantitative agreement.

Keywords: Nonlinear Systems, B_enard Convection, Implicit Methods, Finite Diference Methods
 
 



s06p02

EXPERIMENTAL INVESTIGATION OF HEAT TRANSFER ENHANCEMENT IN A CIRCULAR DUCT WITH CIRCUMFERENTIAL FINS AND CIRCULAR DISKS

Taebeom Seo [email protected]
Department of Mechanical Engineering, Inha University,
253, Yonghyundong, Namgu, Inchon, 402-751, korea
Sang Won Byun

Myoung Ryol Jung [email protected]
Department of Mechanical Engineering, Graduate School, Inha University,
253, Yonghyundong, Namgu, Inchon, 402-751, Korea

The characteristics of heat transfer and pressure drop for fully developed turbulent flow in a tube with circumferential fins and circular disks were experimentally studied. The various spacing and sizes of circumferential fins and circular disks were selected as the design parameters, while the effects of these parameters on heat transfer enhancement and pressure drop were investigated. In order to quantify the effect of heat transfer enhancement and the increase of pressure drop due to the fins and disks in a tube, the Nusselt numbers and the friction factors for the various configurations and the operating conditions were compared to those for a corresponding smooth tube. The results showed that the heat transfer rate was significantly enhanced by increasing the height of circumferential fins and decreasing the pitch of circumferential fins. On the other hand, the influence of the disk radius and the fin-disk spacing were not significant. Based on the experimental results, a correlation for estimating the Nusselt number was suggested.

Keywords: Heat transfer enhancement, Circumferential fin, Circular disk, Heat Exchanger
 
 



s06p03

NUMERICAL ANALYSIS OF THE TURBULENT NATURAL CONVECTION IN A SOLAR CHIMNEY

Cristiana S. Brasil - [email protected]
Ramón M. Valle - [email protected]
Márcio F. B. Cortez - [email protected]
André G. Ferreira - [email protected]
Universidade Federal de Minas Gerais, Departamento de Engenharia Mecânica
Avenida Antônio Carlos, 6627 - 31270-901 - Belo Horizonte, MG, Brasil

This paper presents a theoretical analysis of the turbulent natural convection in a solar chimney operating in steady flow, with prescribed conditions of temperature in the ground. The solar radiation heats the air under the cover, which flows to the tower without artificial pumping. The hot air produced may be used to dry several agricultural products. The numerical analysis of the natural convection in this kind of dryer has fundamental importance on the design and building of this device. The mathematical model includes the conservation laws for mass, momentum and thermal energy and the transport equations for the turbulence model variables (k and e ). The k- e model of turbulence with wall functions was used. A computational code using the Finite Volume Method in Generalized Coordinates was developed to solve the system of equations that describes thermal and hydrodynamically the flow. The velocity and temperature fields are shown to the flow in the solar chimney. With geometrical alterations on the device, one can obtain a detailed description of the flow, which allow the guideline for a suitable configuration to build an experimental prototype.

Keywords: Solar chimney, Turbulence, Natural convection
 



s06p04

NUMERICAL ANALYSIS OF THE CONVECTIVE TRANSFERENCE OF HEAT IN ELECTRONIC BOARDS

Marcelo C. Silva - [email protected]
Universidade Estadual de Campinas - UNICAMP/Faculdade de Engenharia Mecânica - FEM
Departamento de Energia - DE
Campinas - SP - Brasil
Caixa Postal 6122 CEP 13088-970
Carlos A. A. Vilela - [email protected]

In this work a numerical study of the convective transference of heat in boards of electronic circuits is presented printed matters, where the electronic components are a heat source. The study for a range of number of Reynols 50 ( Re ( 1000 and Grashof number 103 ( Gr ( 106 is made. The profiles of velocity, temperature, streamlines and nusselt number are obtained. The equations that describe the behavior of the fluid are decided using the methods of finite volumes with Power-Law scheme, and the method of the finite elements with method SUPG. The results obtained for the method of the finite elements had been obtained using software ANSYS.

Keywords: Finite Volumes, mixed convection, electronic circuits.
 



s06p05

NUMERICAL ANALYSIS OF THE ACTUAL AIRFLOW IN A SOLAR CHIMNEY

André G. Ferreira - [email protected]
Márcio F.B. Cortez - [email protected]
Ramón M. Valle - [email protected]
Cristiana S. Brasil - [email protected]
Universidade Federal de Minas Gerais, Departamento de Engenharia Mecânica
Av. Antônio Carlos, n° 6627- cep: 31270-901 - Belo Horizonte, MG, Brasil.

This paper presents a numerical analysis of the turbulent natural convection of the airflow in a solar chimney, under actual solar radiation conditions. The solar chimneys are devices that consist of a transparent radial cover and of a tubular tower positioned in its center. The ground absorbs part of the incident solar radiation on the cover, heating the air in the greenhouse and inducing an upward airflow on the tower. It was developed a model that allows the evaluation of the ground temperature as a function of an energetic balance involving the incident solar radiation. The flow is described by the conservation laws for mass, momentum and thermal energy and the transport equations for the turbulence model (k and e ). A computational code using the Finite Volume Method in Generalized Coordinates was developed to solve these equations. Outlet dimensionless parameters are presented as functions of the radiation time and conditions, besides the unsteady behavior of the ground surface temperature.

Keywords: Solar chimney, Turbulence, Solar energy
 



s06p07

EXPERIMENTAL EVALUATION OF THE THERMAL PERFORMANCE OF AIR CONDENSERS WITH DIFFERENT GEOMETRICAL CONFIGURATIONS

João Roberto Bastos Zoghbi Filho
José Maria Saiz Jabardo
Universidade de São Paulo, Laboratório de Refrigeração, Departamento de Engenharia Mecânica,
CEP13560-970, São Carlos-SP, Brasil. E-mail: [email protected], [email protected]

Present study deals with the effect of different fin configurations over the thermo-hydraulic behavior of small refrigerating air condensers. Tests have been performed in a wind tunnel specially adapted to adequately control the air temperature and flow rate. Five commercial condensers have been tested, involving units with wavy and two configurations of louver fins. Obtained results confirmed those reported in the literature. according to which louver fins present better thermal performance whereas imposing higher pressure drop in the air flow.

Keywords: air condensers; wavy fin; louver fin; heat transfer enhancement.
 



s06p08

ACCURATE INTEGRAL TRANSFORM RESULTS FOR NATURAL CONVECTION IN A SQUARE CAVITY AT HIGH RAYLEIGH NUMBER

Marco Aurélio Leal - [email protected]
Jesús Salvador Pérez Guerrero - [email protected]
Comissão Nacional de Energia Nuclear, Coordenação de Rejeitos Radioativos - COREJ
Rua General Severiano, 90 - Botafogo
Rio de Janeiro - RJ - 22294.900- Brazil

The classical thermally driven square cavity problem, with adiabatic top and bottom walls, offers challenging test cases for the co-validation of numerical methods. In this work, the laminar steady-state streamfunction-only formulation of the flow equations and the associated energy equation, under Boussinesq approximation, is employed to obtain accurate results through Generalized Integral Transform Techinique (GITT) for high Rayleigh numbers, where the very desirable hybrid characteristics of the GITT are explored in a situation of strong non-linear effects. Results will be presented for two different values of the Rayleigh number, 10 6 and 10 7 , always for Prandtl number equal 0.71, and critical comparisons against previously reported benchmark solutions will be then performed.

Keywords: Natural convection, Integral transform, Hybrid method
 
 



s06p09

MIXED CONVECTION INSIDE A HORIZONTAL TUBE WITH AN INNER RECTANGULAR PLATE

João B. Dias
Genésio J. Menon - [email protected]
Dênio L. Panissi
EFEI - Escola Federal de Engenharia de Itajubá, Departamento de Engenharia Mecânica
Av. BPS, 1303, Bairro Pinheirinho -37500-000 - Itajubá, MG, Brasil.

In this work the laminar mixed convection inside a horizontal tube, with an axial rectangular inner plate, is analyzed. The following conditions are assumed: the inner plate is insulated and the tube has axially uniform heat flux and circumferentially uniform temperature. The finite element method, with the linear triangular element, is utilized to solve the conservation equations for the stream function ( . ), vorticity ( . ), temperature ( . ) and axial velocity (W). The Nusselt number (Nu) and the friction factor-Reynolds number product (fRe) are determined in terms of the radius ratio (RR), aspect ratio of the plate (AR), Rayleigh number (Ra) and a constant Prandtl number (Pr = 0,7). Temperature distribution and stream function distribution are presented for: Pr = 0.7, RR = 2.0, AR = 0.5 and 1.0 and Ra = 1 ×10 4 , 1 ×10 5 and 1 ×10 6 .

Keywords: Mixed convection, Finite element method, Heat transfer, Numerical methods.
 
 



s06p12

NATURAL CONVECTION IN SURFACES WITH PROTRUDING HEAT SOURCES SUBJECTED TO DIFFERENT BOUNDARY CONDITIONS

Ricardo A. V. Ramos - [email protected]
Departamento de Engenharia Mecânica, Faculdade de Engenharia de Ilha Solteira, UNESP
Caixa Postal 31 - 15385-000 - Ilha Solteira, SP
Luiz F. Milanez - [email protected]
Departamento de Energia, Faculdade de Engenharia Mecânica, UNICAMP
Caixa Postal 6122 - 13081-970 - Campinas, SP

In this work the effect of the natural convection on the flow and on the heat transfer in adiabatic surfaces with protruding heat sources simulating electronic components is studied numerically, for different boundary conditions. The flow is assumed in steady state, laminar and two-dimensional. The physical properties are considered constants and the Boussinesq approximation is used. The method of the finite control volumes to discretize the equations is used and the numerical solution is obtained by the SIMPLE algorithm. The results obtained are the velocity and temperature fields and the temperature distribution along the surface where the sources are mounted, as a function of the power dissipated, the power distribution in the sources, the spacing between them and the aspect ratio of the domain. The temperature levels in each of the situations are compared, thus permitting the choice of the configuration with the lower temperature level to reduce the possibility of failure of the components.

Keywords: Natural convection, Heat sources, Finite volumes method.
 
 



s06p19

ESTIMATION OF UNKNOWN WALL HEAT FLUX IN TURBULENT CIRCULAR PIPE FLOW

Jian Su - [email protected]
Nuclear Engineering Department, COPPE/UFRJ, CP 68509, Rio de Janeiro, 21945-970, Brazil
Antônio J. Silva Neto - [email protected]
Adriane B. Lopes
Instituto Politécnico, Universidade do Estado do Rio de Janeiro, CP 97282, Nova Friburgo, Rio de Janeiro, 28601-970, Brazil

Abstract. An inverse heat convection problem is solved for the estimation of a nonuniform wall heat flux in a thermally developing, hydrodynamically developed turbulent flow in a circular pipe based on temperature measurements obtained at several different locations in the stream.  The direct problem of turbulent forced convection is solved with a finite difference method with appropriate algebraic turbulence modelling.  The unknown wall heat flux is represented by a one-dimensional finite element interpolation.  Nodal values at several chosen points are determined as unknown parameters by the Levenberf-Marquardt algorithm.  The effects of sensor number and position are examined.

Keywords: Turbulent forced convection, Inverse convection problem, Levenberg-Marquardt algorithm, Algebraic turbulence modelling, Finite difference method.
 
 



s06p20

ASPECT RATION EFFECT IN A THERMALLY-DRIVEN RECTANGULAR OPEN CAVITY WITH AN ISOTHERMAL SHROUDING WALL

Admilson Teixeira Franco - [email protected]
Federal Center for Education in Technology - CEFET-PR
Department of Mechanical Engineering - DAMEC
Thermal Sciences Laboratory - LACIT
Concurrent Engineering R&D Laboraotyr - NuPES
Av. Sete de Setembro, 3165
80230-901 - Curitiba - PR - Brazil

Marcelo Moreira Ganzarolli - [email protected]
State University of Campinas - UNICAMP
Mechanical Engineering Faculty - FEM, Energy Department - DE
Cidade Universitária Zeferino Vaz
13081970 - Campinas - SP - Brazil

Abstract. Natural convection in a rectangular open cavity with the presence of an isothermal shrouding wall is investigated.  The horizontal walls of the cavity are adiabatic.  One vertical wall is heated uniformly and another is open to a fluid reservoir.  The shrouding wall is placed in front of this opening forming a vertical channel.  Laminar and two-dimensional flow is assumed for a Rayleigh number ranging from 10^3 - 10^7.  The numerical solution is carried out with the Finite Volume-SOLA method.  The aspect ratios considered are B = L/H = 0.5, 3.0 and 6.0, where L and H are the cavity width and height, respectively.  The Rayleigh number and the aspect ratios effect on the isotherms, streamlines and average Nusselt number are reported.

Keywords: Natural convection, Aspect ratio effect, Shrouding wall, Open cavity, SOLA method.
 
 



s06p21

EXPERIMENTAL STUDY OF THERMOSYPHONS APPLIED IN BAKERY OVENS

Alexandre Kupka - [email protected]
Universidade Federal de Santa Catarina - Departamento de Engenharia Mecânica
C.P. - 476 - Campus Universitário - Trindade - 88040-900 - Florianópolis - SC - Brasil

Marcia B. H. Mantelli - [email protected]
Universidade Federal de Santa Catarina - Departamento de Matemática
Campus Universitário - Trindade - Florianópolis - SC - Brasil

Ricardo Assis Penteado - [email protected]
Universidade Federal de Santa Catarina - Departamento de Engenharia Mecânica
C.P. - 476 - Campus Universitário - Trindade - 88040-900 - Florianópolis - SC - Brasil

The present paper study thermosyphons applied to bakery ovens with special attention in the energy conservation and the quality of final baked product. A prototype simulating one internal section of a commercial oven was built for the experimental study. Stainless steel/water thermosyphons are installed vertically, close to the two lateral walls of this section The thermosyphons are very efficient heat exchangers and improves the temperature distribution inside the oven, saving energy and avoiding the product waste by under or overcooking. This research also intends to replace electric power and GLP by natural gas as the energy source, that is available in the South of Brazil, after the recent implantation of the Brazil/Bolivia gas line. The gas combustion happens in a separated chamber, so that, just the heated air are in contact with be bread in the cooking chamber. The final product has better quality and is free from the combustion residues.

Keywords: Thermosyphon, bakery oven, natural convection in enclosures.
 
 



s06p22

NUMERICAL STUDY OF BUOYANCY AND THERMOCAPILLARY FORCES IN A CAVITY COMPOSED OF TWO IMMISCIBLE SUPERPOSED FLUIDS

Dênio L. Panissi - [email protected]
Genésio J. Menon - [email protected]
João B. Dias - [email protected]
Escola Federal Engenharia de Itajubá, Departamento de Engenharia Mecânica
Av. Pinheirinho 1303, Bairro BPS, CEP 37500-000 - Itajubá, MG, Brasil

Natural convection induced by thermocapillary and buoyancy forces, in a rectan-gular cavity, heated from the sides by a uniform heat flux, containing two immiscible super-posed fluids, was numerically studied. In this cavity, laminar regime and constant physical properties were considered. Thermocapillary stress at interface of layers and density in buoyancy terms were assumed as dependents of temperature. The governing equations were written using non-dimensional variables and streamfunction-vorticity formulation. The problem was resolved using the Finite Element Method. The results present stream function, tem-perature distribution, velocity profile, and Nusselt number, for a set of non-dimensional numbers (Prandtl, Rayleigh, and Marangoni). Some numerical results were compared with an experimental research, reported in the literature, and found in good agreement.

Keywords: Natural convection, Buoyancy, Thermocapillary, Finite element method.
 
 



s06p23

FORCED CONVECTION HEAT TRANSFER PROBLEM FOR LIQUID FLOW IN TUBES WITH TEMPERATURE DEPENDENT VISCOSITY VARIATIONS

Fábio da Silva e Oliveira Filho - [email protected]
Rodrigo O. Castro Guedes - [email protected]
Francesco Scofano Neto - [email protected]
Instituto Militar de Engenharia, Departamento de Engenharia Mecânica e de Materiais, Praça
Gen. Tibúrcio 80, 22290-270, Rio de Janeiro, RJ, Brasil

Forced convection heat transfer problem for liquid flow in circular tubes is studied. The solution methodology follows the hybrid analytical-numerical Generalized Integral Transform Technique (GITT). A fully developed velocity profile at tube inlet is considered in the presence of a thermally developing temperature profile. Moreover, thermophysical properties are held constant while dynamic viscosity is allowed to vary.

Keywords: Internal forced convection, Variable viscosity
 
 



s06p24

HEAT TRANSFER ENHANCEMENT OF A PLATE FINNED ELLIPTICAL TUBE USING VORTEX GENERATORS: AN EXPERIMENTAL STUDY

Rubén Borrajo Pérez - [email protected]
Jurandir Itizo Yanagihara - [email protected]
Juan José González Bayón - [email protected]
Department of Mechanical Engineering
Polytechnic School - University of São Paulo.
05508-900 - São Paulo, SP, Brazil.

Vortex generators have been extensively used in the recent years for different fin-tube compact heat exchanger geometries. The heat transfer enhancement effects and the relatively low increments in the flow losses were verified for the circular tube geometry. However, the use of vortex generators in elliptical tubes, which have better aerodynamic performance, was not carried out yet. In this work, the influence of the position and the angle of attack of the vortex generators and the Reynolds number on the heat transfer enhancement of a finned elliptical tube with eccentricity 0.5 was analyzed. The naphthalene sublimation technique was used to determine the average Nusselt number. The changes in the flow patterns on the fin surface were observed using a mass transfer technique based on color sensitive evaporation. An instrumented open circuit wind tunnel was used for the experimental tests.

Keywords: Vortex generators, elliptical tube, compact heat exchangers, naphthalene sublimation.
 
 



s06p25

HEAT TRANSFER IN DUCTS OF VARYING CROSS-SECTION USING A LINEAR k-e MODEL AND A PARABOLIC SOLVER

Edimilson J. Braga - e-mail: [email protected]
Marcelo J.S. de-Lemos - e-mail: [email protected]
Departamento de Energia - IEME, Instituto Tecnológico de Aeronáutica - ITA
12228-900 São José dos Campos - SP - Brasil

Heated turbulent confined jet flow is numerically investigated. The development of subsonic jets with higher and lower central velocity and temperature is considered. A marching-forward numerical integration technique is used to sweep the computational domain. Both cases of gradual enlargements or contractions of sinusoidal duct walls are calculated. Turbulence is handled with the standard linear isotropic k- e model. Previous comparisons reproduced experimental data showing that, within contractions, turbulence is damped whereas, in diffusers, the valued of k is increased. Solution of the energy equation further shows interesting dissimilarities between turbulent kinetic energy and heat transfer. In contracting ducts, while turbulence in damped, the turbulent Nusselt number increases. Along enlargements, overall turbulent heat transfer is damped.

Keywords: Turbulent heat transfer, Coaxial jets, Diffusers and contractions
 
 



s06p27

NUMERICAL ANALYSIS OF NATURAL CONVECTION IN OSCILLATING ENCLOSURES

Susie C. Keller - [email protected]
Federal University of Rio Grande do Sul, Dep. of Pure and Applied Mathematics, PPGMAp
Av. Bento Gonçalves, 9500 - 90501-900 - Porto Alegre, RS, Brazil

Álvaro L. De Bortoli - [email protected]
Federal University of Rio Grande do Sul, Dep. of Pure and Applied Mathematics,
Av. Bento Gonçalves, 9500 - 90501-900 - Porto Alegre, RS, Brazil

The present work develops a numerical method for the buoyancy-driven flow in rectangular enclosures. The configuration consists of two isolated horizontal walls and two vertical walls at temperatures Theat and Tcold. The analysis is based on the incompressible formulation with the Boussinesq approximation, which is appropriate for relatively small temperature differences between the vertical walls. The method is based on the finite difference explicit Runge-Kutta multistage scheme for solving the Navier-Stokes, continuity and energy equations. Numerical tests are carried out for fixed and oscillating cavities, where the Coriolis force must be taken into consideration. Obtained results showed to compare well with numerical/experimental data found in the literature for steady and unsteady flow situations for Rayleigh numbers between 10 2 and 10 5 and Prandtl numbers ranging from 0.005 to 1.0.

Keywords: Natural convection, (Un)steady flows, Finite difference, Runge-Kutta.
 
 



s06p28

ON THE PHYSICAL SIGNIFICANCE OF SOME DIMENSIONLESS NUMBERS USED IN HEAT TRANSFER AND FLUID FLOW

Clovis R. Maliska
Computational Fluid Dynamics Laboratory-SINMEC
Mechanical Engineering Department
Federal University of Santa Catarina
88040-900-Florianópolis-SC-Brazil
[email protected]

Dimensionless numbers are of key importance in parametric analysis of engineering problems. They are also extremely useful in understanding the similarity among problems belonging to the same broad class. However, in spite of its importance in phenomenological analysis, their physical interpretation is usually not given or is contradictory in the literature. Well-known dimensionless numbers, like Re and Ra, are frequently misinterpreted in textbooks widely used by engineering students. The main goal of this paper is to present a physical interpretation of the Reynolds, Peclet, Rayleigh and Boussinesq numbers based on the ratio of advective and diffusive fluxes of heat and momentum. With the help of scale analysis it is shown that when the dimensionless numbers are related to the ratio of advective and diffusive fluxes,  the physical meaning is straightforward.
 
 



s06p29

NUMERICAL OPTIMIZATION AND PERFORMANCE COMPARISON OF STAGGERED CIRCULAR AND ELLIPTIC TUBES IN FORCED CONVECTION

R. S. Matos - [email protected]
J. V. C. Vargas - [email protected]
Universidade Federal do Paraná, Departamento de Engenharia Mecânica
Cx. P. 19011 - 81531-990 - Curitiba, PR, Brasil

In this study, a two-dimensional (2-D) heat transfer analysis was performed in circular and elliptic tubes heat exchangers. The numerical results for the equilateral triangle staggering configuration, obtained with the finite element method were then validated qualitatively by means of direct comparison to previously published experimental results for circular tubes heat exchangers (Stanescu et al., 1996). Next, a numerical geometric optimization was conducted to maximize the total heat transfer rate between the given volume and the given external flow both for circular and elliptic arrangements, for general staggering configurations. The results are reported for air in the laminar regime, in the range 800 Re 300 L ==, where L is the swept length of the fixed volume. Circular and elliptical arrangements with the same flow obstruction cross sectional area were compared on the basis of maximum total heat transfer. The effect of ellipses eccentricity was also investigated. A relative heat transfer gain of up to 13 % is observed in the optimal elliptical arrangement, as compared to the optimal circular one. The heat transfer gain, combined with the relative pressure drop reduction of up to 25 % observed in previous studies (Brauer, 1964; Bordalo and Saboya, 1995) show the elliptical arrangement has the potential for a considerably better overall performance than the traditional circular one.

Keywords: Finite element method, Heat exchangers, Geometric optimization
 
 



s06p30

SIMULTANEOUS ESTIMATION OF TWO BOUNDARY HEAT FLUXES IN PARALLEL PLATE CHANNELS

Marcelo J. Colaço - [email protected]
Helcio R. B. Orlande - [email protected]
Department of Mechanical Engineering, EE/COPPE
Federal University of Rio de Janeiro, UFRJ
Cid. Universitária, Cx. Postal: 68503
Rio de Janeiro, RJ, 21945-970, Brazil

This paper deals with the use of the conjugate gradient method of function estimation for the identification of two unknown boundary heat fluxes in a parallel plate channel. The fluid flow is assumed to be laminar and hydrodynamically developed. The boundary heat fluxes are supposed to vary in time and along the channel. Temperature measurements taken inside the channel are used in the inverse analysis. The accuracy of the present solution approach is examined by using simulated measurements containing random errors, for strict cases involving functional forms with discontinuities or sharp-corners for the boundary heat fluxes.

Keywords: Conjugate gradient method, function estimation, forced convection, laminar flow, parallel plate channel
 
 



s06p32

COOLING OF AN ISOTHERMAL PLATE BY A CONFINED TWO-DIMENSIONAL AIR JET

Márcio Antonio Bazani - [email protected]
Carlos A.C. Altemani - [email protected]
Universidade Estadual de Campinas - FEM - Departamento de Energia
Caixa Postal 6122 - CEP 13.083-970 - Campinas - SP - Brazil

Atmospheric air is the most convenient fluid for the cooling of electronic equipment but, due to its thermal properties, enhanced convective heat transfer techniques are usually required for the proper thermal design. One possibility consists of impinging turbulent air jets on the components' surfaces, usually within confined spaces. The purpose of this paper is to present numerical results associated to the convective cooling of a heated plate by a two-dimensional turbulent air jet. The air jet issues from a slot on the confinement plate, directed normal to the parallel impingement plate. It spreads symmetrically, confined in the space between the two parallel plates. The high-Reynolds k- e turbulence model with wall functions was used for the numerical simulations of the flow and heat transfer. The effects of the plates' distance, the slot width and the jet Reynolds number on the convective heat transfer were considered in the analysis. Comparisons were made with numerical and experimental results from the literature. A sensitivity analysis was carried out for distinct parameters of the adopted turbulence model.

Keywords: confined 2D jet, k-e turbulence model, numerical results, heat transfer comparisons.
 
 



s06p33

SIMILARITY SOLUTION FOR HYPERSONIC FLOWS

Marcos Eidi Hatori - [email protected]
Divisão de Engenharia Aeronáutica - ITA
José B. Pessoa Filho - [email protected]
Divisão de Sistemas Espaciais - IAE
Centro Técnico Aerospacial
12228-904 - São José dos Campos - SP - Brasil

Aerodynamic heating at the stagnation point of a microsatellite moving at hypersonic speed through the earth's atmosphere is calculated by solving the laminar, compressible, axisymmetric boundary layer equations. Air is assumed to be in local thermochemical equilibrium. The boundary layer equations are solved by using the similarity concept. Since some initial conditions of the similar equations are unknown, the solution procedure is iterative. To improve the convergence of the numerical procedure, two auxiliary systems of ordinary differential equations are defined leading to a computationally efficient algorithm. Based upon the calculated velocity, temperature and species concentration profiles along the boundary layer, it is possible to evaluate aerodynamic heating at the stagnation point. An excellent agreement was observed between the results obtained in this work and others available in the literature.

Key-words: Similarity Solution, Hypersonic Flow, Boundary Layer Equations, Equilibrium, Aerodynamic Heating.
 
 



s06p34

LARGE-EDDY SIMULATION, WITH DYNAMICAL SUB-GRID SCALE, APPLIED TO COMBINED CONVECTION

Elie L. Martínez Padilla - [email protected]
Universidade Federal de Uberlândia, Faculdade de Engenharia Mecânica
Campus Santa Mônica, CEP: 38400-902
Uberlândia, MG, Brasil
Aristeu da Silveira Neto - [email protected]
Universidade Federal de Uberlândia, Faculdade de Engenharia Mecânica
Campus Santa Mônica, CEP: 38400-902
Uberlândia, MG, Brasil

Large-Eddy Simulation with Smagorinsky and Dynamical sub-grid scale models was used to analyse numerically the combined convection over a heated and rotating cylinder. Several situations governed by the Grashof and Froude numbers were simulated. Results were compared with experimental data. The dynamical sub-grid scale model gives better results, as compared with Smagorinsky model. The eddy viscosity vanishes automatically near the cylinder wall. Finally the dynamical model is very expensive as compared with Smagorinsky model.

Keywords: Large-Eddy Simulation; Dynamical Sub-Grid Scale Model; Combined Convection.
 
 



s06p35

NUMERICAL SIMULATION OF MIXED CONVECTION IN A SEMI OPENED RECTANGULAR REGION

Rogério Fernandes Brito - [email protected]
Genésio José Menon - [email protected]
Escola Federal de Engenharia de Itajubá, Departamento de Engenharia Mecânica
Av. BPS, 1303 - 37500-903 - Itajubá, MG, Brasil

In this work the laminar mixed convection inside a semi opened rectangular cavity is studied. The bottom and top horizontal surfaces are thermally insulated and the right and left vertical surfaces are assumed to be respectively the hot and cold isothermal surfaces. The fluid is introduced at a low temperature through an opening in the left vertical surface and leaves the cavity through another opening in the right vertical surface. The finite element method is used to solve the conservation equations in a dimensionless way, for temperature ( . ), stream function ( . ) and vorticity ( . ). The results for the average Nusselt number at the hot isothermal surface ( h Nu ), for the distribution of the dimensionless stream function ( . ) and for the dimensionless temperature ( . ) are presented as function of the thermal and geometrical parameters.

Keywords: Mixed convection, Heat transfer, Finite element
 
 



s06p37

FORCED AND NATURAL CONVECTION IN ANNULAR CONCENTRIC CHANNELS AND CAVITIES BY INTEGRAL TRANSFORMS

Luiz M. Pereira - [email protected]
Renato M. Cotta - [email protected]
Departamento de Engenharia Mecânica, EE/COPPE/UFRJ
Cx. Postal 68503 - 21945-970 - Ilha do Fundão, Rio de Janeiro, RJ, Brazil.

Jesús S. Pérez Guerrero - [email protected]
Coordenação de Rejeitos Radioativos, COREJ/CNEN
Rua General Severiano, 90 - 22294-900 - Botafogo, Rio de Janeiro, RJ, Brazil

A unified formulation for the study of forced and natural convection in annular concentric channels and cavities is presented. The Navier-Stokes and energy equations are solved using the Generalized Integral Transform Technique (GITT), which transforms the partial differential equations into a coupled ordinary differential system. The resulting system is solved numerically using well-known subroutines of scientific mathematical libraries. Numerical results for the three different physical situations are analyzed, related to forced convection in annular channels, natural convection in horizontal and vertical cavities, for various values of the governing parameters in each situation. Sets of benchmark results are generated in each case, to illustrate the proposed methodology, as well as to allow for critical comparisons with the available literature results.

Keywords: Forced and Natural Convection, Navier-Stokes Equations, Annular Ducts, Integral Transforms
 
 



s06p38

THERMAL AND FRICTION CHARACTERIZATION OF COMPACT HEAT EXCHANGER WITH ONE AND TWO ROWS OF ELLIPTICAL TUBES

Rubén Borrajo Perez - [email protected]
Jurandir Itizo Yanagihara - [email protected]
Department of Mechanical Engineering
Polytechnic School of the University of São Paulo.
05508-900 - São Paulo - SP - Brazil.

Compact heat exchangers are used in many technical applications. This work presents an experimental characterization of plate fin compact heat exchangers with one and two rows of elliptical tubes in the staggered arrangement. The average Nusselt number and friction factor for several transversal and longitudinal pitches were obtained. The naphthalene sublimation technique and the mass transfer analogy were applied to determine the Nusselt number. The friction factor was calculated by flow losses measurements using a weighted method by means of a balance. Experiments were carried out in an open circuit wind tunnel in the laminar flow regime. The Reynolds number based on the hydraulic diameter were varied between 200 and 1500. Correlations for the Colburn and Friction factors were obtained.

Keywords. Elliptical tubes, compact heat exchangers, naphthalene sublimation.
 
 



s06p39

THERMALLY DEVELOPING LAMINAR FLOW OF POWER-LAW NON-NEWTONIAN FLUIDS INSIDE RECTANGULAR DUCTS

Cléber Lisboa Chaves
Chemical Engineering Department-CT/Universidade Federal do Pará-UFPA

João Alves de Lima
Solar Energy Laboratory-LES/Universidade Federal da Paraíba-UFPB

Luiz Mariano Pereira
Laboratory of Transmission and Technology of Heat-LTTC/EE/COPPE/UFRJ

Emanuel Negrão Macêdo
Mechanical Engineering Department-CT/Universidade Federal do Pará-UFPA

João Nazareno Nonato Quaresma
Chemical Engineering Department-CT/Universidade Federal do Pará-UFPA
Campus Universitário do Guamá, Rua Augusto Corrêa, 01
66075-900 - Belém, PA, Brasil - E-mail:[email protected]

The so-called generalized integral transform technique is employed in the hybrid analytical-numerical solution of laminar forced convection to power-law fluids inside rectangular ducts, allowing for the solution of this problem involving a non-separable eigenvalue problem. Reference results are established for quantities of practical interest within the thermal entry region, for a wide range of the axial variable, power law indices and for the typical situation of a square duct. The accuracy of previously reported results from older codes using the earlier mentioned method (for Newtonian fluids), as well as from direct numerical approaches are then critically examined, for both the developing and fully developed regions.

Keywords: Laminar rectangular duct flow, Power-law non-Newtonian fluids, Laminar forced convection, Integral transform solution