**Chairs:**

**Antônio Fábio Carvalho
da Silva**
**Departamento de Engenharia Mecânica
Universidade Federal de Santa Catarina**

**Antonio Jose da Silva Neto**
**Instituto Politecnico - UERJ**

**Sérgio Colle**
**Departamento de Engenharia Mecânica
Universidade Federal de Santa Catarina**

s13p02

**ANALYTICAL
STUDY ON THE SHAPE EVOLUTION OF ELLIPSOIDAL PARTICLES UNDER DIFFUSION PROCESSES**

José F. Branco - [email protected]

Instituto Politécnico
de Viseu, Departamento de Engenharia Mecânica e Gestão Industrial

ESTV - Campus Politécnico,
3500 VISEU, Portugal

Carlos T. Pinho - [email protected]

Universidade do Porto, CEFT....
DEMEGI

Faculdade de Engenharia
- Rua dos Bragas, 4099 PORTO, Portugal

Rui A. Figueiredo - [email protected]

Universidade de Coimbra,
Departamento de Engenharia Mecânica

FCTUC - Pinhal de Marrocos,
3030 COIMBRA, Portugal

In the treatment of the combustion of solids, or of any physical-chemical processes where solid particles interact with a fluid - such as the evaporation or dissolution of solid particles - it is a common practice to assume, for the sake of simplicity, that particles are spherical. The shape of real particles can be quit different from this simplified approach and, generally, it is not possible to develop simple mathematical models to represent the real particle-fluid interactions. A shape closely related with the sphere is a prolate ellipsoid. Diffusion around ellipsoids has already been studied. Pinho and Guedes de Carvalho (1986), for instance, used the ellipsoidal shape to assess the error involved in approximating real particles by spheres. These authors developed an analytical model to represent the shape evolution of a prolate ellipsoid under pure diffusion and used a numerical model in the case of pure kinetic control. In this work, the shape evolution of a prolate ellipsoid, under pure diffusion or under pure kinetic control, was studied again, but now by means of an entirely analytic solution. As a result, a set of equations and graphs, describing the evolution of the particle being consumed, were obtained in a simpler way.

Keywords: Ellipsoidal particles,
Mass transfer, Diffusion, Kinetic control, Shape evolution

s13p03

Nathan Mendes - [email protected]

Gerson H. Santos - [email protected]

Pontifícia Universidade
Católica do Paraná (PUCPR/CCET),

Laboratório de Sistemas
Térmicos (LST)

Rua Imaculada Conceição,
1155 Curitiba-PR, 80.215-901, Brasil

We describe a mathematical model applied to analysis of hygrothermal behavior of buildings. We use a lumped approach to model the room air temperature and humidity and a multi-layer model in finite differences for the building envelope. The capacitance model allows to study the room transient air humidity and temperature when it is submitted to the weather of the city of Curitiba-PR, Brazil. To evaluate the building performance with thermal parameters, we have written a program in C which includes air infiltration, conduction loads, internal gains of people, lights and equipment and solar radiation. In the results section, we show the influences of simulation time step on internal temperature and humidity and temperature profiles within the building envelope.

Keywords: Heat and mass transfer
in Buildings, Building simulation, Sensitivity analysis

s13p09

**CONVERGENCE
OF THE GITT APPROXIMATIONS IN HEAT TRANSFER AND FLUID MECHANICS PROBLEMS**

Rubén Panta Pazos
- e-mail : [email protected]

Faculdade de Matemática,
Pontifícia Universidade Católica do Rio Grande do Sul (PUCRS),
Av Ipiranga 6681, CEP 90619-900, Porto Alegre - RS - Brazil.

Marco Túllio de Vilhena
- e-mail : [email protected]

Instituto de Matemática,
Universidade Federal do Rio Grande do Sul (UFRGS), Av Bento Gonçalves
9500, CEP 91509-900, Porto Alegre - RS - Brazil.

Renato Machado Cotta - e-mail
: [email protected]

Departamento de Engenharia
Mecânica, EE/COPPE, Universidade Federal do Rio de Janeiro (UFRJ),
Cidade Universitária - Centro de Tecnologia - Bloco G, Ilha do Fundão,
CEP 21945-970, Rio de Janeiro - RJ - Brazil.

The Generalized Integral Transform Technique (GITT) has used in Heat Transfer and Fluid Mechanics problems for two or more dimensions and has many extensions. The basic idea consist in choosing an appropriate integral transform pair through an associated auxiliary problem, an Sturm-Liouville problem, to be applied in the original partial differential equation governing the involved phenomenon, which results in a denumerable system of coupled ordinary differential equations. The approximation is the truncation of the infinite system in a sufficiently large order and solve it through standard numerical procedures obtaining the so-called complete solution. Then we invoke the inversion formula to construct the potential. In this work we attempt to give an appropriate formulation employing the functional analysis tools. We outline the proof of the convergence of the GITT approximations to the exact solution, defining the error of the approximated potential with respect to the exact solution.

Keywords: GITT approximations
, C0-semigroups.

s13p10

**HEAT
AND MASS TRANSFER CORRELATIONS FOR EVAPORATIVE CONDENSERS - COMPARATIVE
STUDY**

Luben Cabezas Gómez
- e-mail: [email protected]

João Roberto Bastos
Zoghbi Filho - e-mail: [email protected]

José M. Saiz Jabardo
- e-mail: [email protected]

Departamento de Engenharia
Mecânica, Escola de Engenharia de São Carlos, USP. Av. Trabalhador
São-carlense, N° 400-Centro, São Carlos, SP. CEP 13566-590.

Evaporative coolers are extensively used by the process industry for water cooling operations. Physical mechanisms of heat and mass transfer involved are complex and so is the geometry of the air/water interface. As a result, heat and mass transfer correlations representative of these mechanisms are scarce. This paper has considered some of the most representative correlations of the literature. In order to evaluate their performance, a simulation model developed elsewhere has been applied to four commercial evaporative coolers. Heat and mass transfer correlations have been successively introduced into the simulation model and results compared with manufacturer catalogue data. The maximum obtained deviation was 6%, the correlation by Tezuka et al. (1971) being the one that best fitted the catalogue data.

Keywords: Evaporative Coolers,
Heat-and-Mass Transfer, Correlations.

s13p14

**EFFICIENCY
OF RARE-EARTH MAGNETS DIRECT CURRENT ELECTROMAGNETIC PUMP**

Eduardo M. Borges - e-mail:
[email protected]

Francisco A. Braz Filho
- e-mail: [email protected]

Lamartine N. F. Guimarães
- e-mail: [email protected]

Francisco Sircilli Neto
- e-mail: [email protected]

Angelo Passaro - e-mail:
[email protected]

Instituto de Estudos Avançados
(IEAv - CTA), 12231-970, São José dos Campos, SP, Brasil.

The electricity conductor fluid flow can be controlled by direct current electromagnetic pumps by the magnetic induction field intensity and by the electric current inputs. In this work are presented the rare-earth magnets direct current electromagnetic pumps project, theoretical and experimental evaluations used to define pump geometry, your operational characteristics and efficiency data.

Keywords: Electromagnetic
pumps, Computational simulation, Liquid metal.

s13p16

**THERMAL
PROPERTIES ESTIMATION OF POLYMERIC MATERIALS WITH THE SIMULATED ANNEALING
METHOD**

Francisco J. C. P. Soeiro
- [email protected]

Departamento de Engenharia
Mecânica, Faculdade de Engenharia, Universidade do Estado do Rio
de Janeiro, CEP 20550-013, Rio de Janeiro, RJ, Brasil.

Gil de Carvalho - [email protected]

Antônio José
da Silva Neto * - [email protected]

Instituto Politécnico,
Universidade do Estado do Rio de Janeiro, CP 97282, CEP 28601-970, Nova
Friburgo, RJ, Brasil.

An ever-growing demand has been observed for the development and thermal characterization of new materials. In this work we present the solution on an inverse problem with the Levenberg-Marquardt (LM) method and the Simulated Annealing (SA) method for the simultaneous estimation of the thermal conductivity and specific heat o new polymeric materials. Real experimental data obtained with a sample of a polymeric material with lignin, a by-product of the sugar cane bagasse, are used.

Keywords: Inverse Problems,
Thermal characterization, Levenberg-Marquardt, Simulated Annealing.

s13p21

**HEAT,
MOMENTUM AND MASS TRANSFER IN RAREFIED GASES BETWEEN TWO ROTATING CYLINDERS**

Felix Sharipov - [email protected]_sica.ufpr.br

Departamento de Física,
Universidade Federal do Paraná, Caixa Postal 19081, 81531-990 Curitiba,
Brazil

Liliana M. Gramani Cumin
- [email protected]_sica.ufpr.br

Gilberto M. Kremer - [email protected]_sica.ufpr.br

The mass, heat and momentum transfer through a rare_ed gas con_ned between two coaxial rotating cylinders is investigated. The evaporation and condensation of the gas on the cylinder surfaces is assumed. The state of equilibrium is perturbed by small deviations of pressure, temperature and angular velocity on the inner cylinder. The _elds of the pressure, temperature, velocity, heat ux vector, and stress tensor are calculated in the wide range of the Knudsen number. In the free molecular and transition regimes the kinetic model of the Boltzmann equation has been solved numerically by the discrete velocity method. Further, the Onsager reciprocity relations between the cross-e_ects are tested.

Keywords: Boltzmann equation,
Knudsen number, Transport Phenomena

s13p23

**HIGH
ORDER FINITE DIFFERENCE AND ANALYTICAL APPROACH IN DRYING**

Duarte, J.B.F. - [email protected],

OMNI/LIA/MCC and DF/UFC,

Universidade Federal do
Cear_a, Rua Carolina Sucupira 62/603, CEP 60140-120 Fortaleza - Ce, Brasil

Ribeiro, J.W. - [email protected]

Symbolic computation, rule
based and functional programming are applied with the generalised integral
transform method, GITT, to analytical and numerically solve

a Luikov non-linear problem,
using automatic manipulation over analytical formulae. A _ltering technique
split up the general problem to accelerate the convergence and the

homogeneous problem is transformed
in a initial value problem and solved by Mathematica packages. A Table
exhibits excellent numerical results for the dimensionless temperature
and moisture distributions that are compared with values obtained by the
higher order _nite di_erence method, HOFDM.

Keywords: Symbolic computation,
Integral transform, Luikov problem

s13p26

João E. F. Carmo

Universidade Federal da
Paraiba (UFPB), CCT, Departamento de Física, CEP 58109-970, Campina
Grande-PB, Brasil

Antonio G. B. Lima - E-mail:
[email protected]

Universidade Federal da
Paraiba (UFPB), CCT, Departamento de Engenharia Mecânica, CEP 58109-970,
Campina Grande-PB, Brasil

A numerical solution of the diffusion equation to describe mass transfer inside oblate spheroids, considering diffusion coefficient and convective boundary condition, is presented. The diffusion equation in oblate spheroidal coordinate system was used, for a bidimensional case, and the finite-volume method was employed to discretize the basic equation. The equation was solved iteratively using the Gauss-Seidel method. As application plots are presented for several aspect ratios. The effects of the Fourier number, Biot number and the aspect ratio of the body on the drying rate and moisture content during the process are presented. To investigate the effect of the aspect ratio only, different results of the average moisture content, are showed. The results shown that the model is consistent and it may be used to solve other cases as those that include disk and sphere and/or those with variable properties under small modifications.

Keywords: Mass transfer,
Ellipsoid, Numerical, Oblate spheroid

s13p27

Gilmar O. Veloso - [email protected]

Depart. de Engenharia Mecânica
- UFRGS

Rua Sarmento Leite, 425
- cep 90050-170 Porto Alegre, RS

Horácio A . Vielmo
- [email protected]

Depart. de Engenharia Mecânica
- UFRGS

Rua Sarmento Leite, 425
- cep 90050-170 Porto Alegre, RS

Viktor Krioukov - [email protected]

Depart. de Tecnologia -
UNIJUÍ

The objective of this work is to continue the mathematical model of the processes in an extractor " De Smet " developed previously, in which were considered: the countercurrent flows of the miscela and of the solid; the mass transfer between the solid particles and bulk phase; diffusion for every field extraction; existence of the drainage sessions and of shipment; influence of the trays in the evolution of the characteristics; the transient regime of the operation. In the present work it was considered: the oil losses because of the imperfect extraction; the displacement of the miscela among washing sessions, etc. The results are compared with the experimental data obtained in the industrial installation. The numerical studies were accomplished to evaluate the influence of the solvent consumption.

Keyword: Extraction, Modeling,
Oil, Industrial installation.

s13p28

**MODELING
AND SIMULATION OF LIMESTONE CALCINATION IN ROTARY KILNS**

Marcio A. Martins, [email protected]

Leandro S. Oliveira, [email protected]

Adriana S. Franca, [email protected]

Chemical Engineering Department/Universidade
Federal de Minas Gerais

R. Espirito Santo, 35 -
6 o andar 30160-030 Belo Horizonte, MG, Brazil

A one-dimensional mathematical model was developed for the simulation of limestone calcination in rotary kilns. The model is comprised of ordinary differential equations derived from mass and energy conservation principles. The system of equations is solved by a fourth-order Runge-Kutta method. The model predicts, in the axial direction, temperature profiles for the bed of particles, the gas phase and the kiln internal wall. It also predicts the composition profile for the bed. The results from the simulation of the calcination systems presented good agreement with experimental data measured in a pilot kiln.

Keywords: lime, heat transfer,
numerical analysis.

s13p30

Gilberto Carlos Thomas -
[email protected]

UFRGS, Departamento de Engenharia
Mecânica

Rua Sarmento Leite, 425,
90050-170 - Porto Alegre, RS

Viktor Krioukov - [email protected]

UNIJUÍ, Departamento
de Tecnologia

Rua São Francisco,
501-Cx. P. 560-98700-000 - Ijuí, RS

Luis Moreira

UNICRUZ, Departamento de
Matemática

Cruz Alta - RS.

This work is destined to the problems of mathematical modelagem of extraction of vegetable oil of soy grains in installation of the type " Rotocell ". The mathematical model comes through system of the equations in having derived partial and differentiate ordinary. In the first version of the model they were considered among another: counter-corrent crusaders flows of the raw material and miscela inside of the extractor; diffusion of the oil for the extraction field; transfer of the oil of the phase pore to the phase bulk; influence of the reservoirs in elapsing of the processes; existence of the drainage zones and shipment; regime operation transient. In this work the model is developed considering: the dependences of the viscosity and of the density in function of the concentration of the oil in the miscela, the transfer of the oil between the phases solid and pore in the extraction field and in the section of the shipment, the oil losses in the drainage phase. These alterations made the model and more practical application. The numeric simulations were accomplished for the industrial regime, when in the extraction field the great difference exists initially between the concentrations of the phases pore and bulk.

Keywords: Oil extraction,
mathematical Model, Drainage and shipment.

s13p33

**SIMULTANEOUS
HEAT AND MASS TRANSFER DURING THE DRYING OF PROLATE SPHEROIDAL SOLIDS**

Antonio G. B. de Lima - E-mail:
[email protected]

Departamento de Engenharia
Mecânica, CCT, Universidade Federal da Paraíba (UFPB), CEP
58109-970, Cx. Postal 10069, Campina Grande-PB, Brasil.

Silvia A. Nebra - E-mail:
[email protected]

Departamento de Energia,
FEM, Universidade Estadual de Campinas (UNICAMP), CEP13083-970, Cx. Postal
6122,Campinas-SP, Brasil.

Drying is a simultaneous heat and moisture transport problem. Heat and mass transfer in solids may be described by the energy and mass equations, in conjunction with the initial and boundary conditions. If solid properties, including the diffusion coefficient, are invariant, its possible to treat both heat and mass transfer in a similar manner. This work presents an investigation of the simultaneous heat and mass transfer during the drying of solids with prolate spheroidal shape. A two-dimensional diffusional model applied to a prolate spheroid is presented considering the liquid diffusion as the only mechanism of moisture transport and allowing convective and evaporative boundary conditions at the surface of the solid. The resulting equations are solved numerically using the finite-volume method. To validate the numerical model, results of the mean moisture content and center temperature obtained were compared with experimental data of wheat grain drying and good agreement was obtained. The convective and diffusion coefficients were obtained by fitting the model to experimental data, minimizing the sum of square residuals, in successive trials. The diffusion phenomenon inside a prolate spheroid represents to a higher degree of precision the problem under consideration in comparison to the current approach which uses spherical or cylindrical geometry.

Keywords: Drying, Mass transfer,
Ellipsoidal geometry, Wheat, Numerical

s13p34

Lucilia B. Dantas - [email protected]

Helcio R. B. Orlande - [email protected]

Renato M. Cotta - [email protected]frj.br

DEM/EE & PEM/COPPE/UFRJ

Cidade Universitária,
Cx. Postal 68503

Rio de Janeiro, RJ, 21945-970

This work deals with the solution of the heat and mass transfer problem during drying of capillary porous media. The physical problem considered here is described by the linear Luikov's equations in cylindrical coordinates. Such equations are integrated along the radial direction in order to reduce the number of independent spatial variables. Two different approaches used to represent the dependent variables at the cylinder surface include: (i) The Lumped Approach and (ii) The Coupled Integral Equations Approach (CIEA). The use of the CIEA results on a formulation as simple as that for the lumped approach but much more accurate, since the gradients along the radial direction are not neglected.

Keywords: Luikov's equations,
Heat and mass transfer, Drying, Coupled Integral Equations Approach