Begell House Inc.
Hybrid Methods in Engineering
HME
1099-2391
3
4
2001
NUSSELT NUMBER VARIATION IN MICROCHANNELS
18
Gokturk
Tunc
Mechanical Engineering and Materials Science Department, Rice University, 6100 Main Street, MS 321, Houston, TX 77005, USA
Yildiz
Bayazitoglu
Mechanical Engineering and Materials Science Department, Rice University
Laminar, gaseous flow convective heat transfer in rectangular, parallel plates and circular microchannels is analyzed using the integral transform technique. The slip flow regime is considered. The Nusselt number variation with the Knudsen number is given to show the effects of rarefaction on heat transfer. As the Knudsen number increases, the Nusselt number decreases for all geometries. Between the limits of the slip flow regime, 0 < Kn ≤ 0.12, a reduction of 30−40% in the Nusselt number is observed. Viscous heating is found to be important. A positive Brinkman number will increase the Nusselt number for a uniform temperature and decrease it for a uniform heat flux boundary condition.
NUMERICAL SIMULATION OF SOLID-LIQUID PHASE CHANGE PROCESSES: THE NEED FOR BENCHMARK SOLUTIONS
14
Dominique
Gobin
Laboratoire FAST-URA CNRS 871 (Universites Paris VI et Paris XI) Campus Universitaire − Batiment 502 91405 Orsay Cedex, France
Benoit
Goyeau
CentraleSupélec
Sophie
Mergui
Fluides, Automatique et Systemes Thermiques (FAST), Universites Paris VI et Paris XI-UMR CNRS 7608, Campus Universitaire, Bat. 502. 91405 Orsay Cedex, France
This article deals with a general discussion on the definition of comparison exercises in the field of solid-liquid phase change processes. There is a continuous effort in this area to develop new mathematical models and to provide accurate numerical simulation results. The main difficulty in benchmarking is to provide reference solutions, except in very simple cases. It is also shown that reference experiments, with well controlled boundary conditions and well documented measurements, are extremely scarce in the heat transfer literature. This article presents state-of-the-art of the validation attempts in the different subproblems raised by the simulation of a complete phase change process.
SLOSHING IN A CIRCULAR CONICAL TANK
56
I. P.
Gavrilyuk
Berufakademie Thuringen-Staatliche Studienakademie, 99817, Eisenach, Am Wartenberg 2, Germany
I. A.
Lukovsky
National Academy of Sciences of Ukraine, Institute of Mathematics, Tereschenkivska 3, 01601 Kiev, Ukraine
A. N.
Timokha
National Academy of Sciences of Ukraine, Institute of Mathematics, Tereschenkivska 3, 01601 Kiev, Ukraine
We develop a nonconformal transformation technique and combine it with the variational modal approach for modeling the nonlinear sloshing of an incompressible fluid with irrotational flow. No overturning, breaking, or shallow fluid waves are assumed; the fluid partly occupies an arbitrary smooth tank with rigid walls having a noncylindrical shape. In its theoretical part, the article assumes that the tank's cavity can be smoothly transformed into an artificial cylindrical domain, where the equation of free surface allows for both normal form and modal (Fourier) decomposition of the instantaneous surface shape. This transformation has singularities in the lower (upper) vertexes of the tank. It leads to degenerating boundary problems, but spectral, variational theorems and modal systems save invariant formulations. The main body of the article derives modal theory for sloshing in a circular conical tank. Linearized and nonlinear problems are examined in curvilinear coordinates. The spectral problem on natural modes is solved by the variational method. Solutions are expanded in a series by solid spheric harmonics satisfying the zero-Neumann condition everywhere on the walls. The algorithm is robust and numerically efficient for calculating both the lower and higher natural modes. Calculations are validated by experimental data by Bauer [4] and Mikishev & Dorozhkin [29]. Derivation of the approximate weakly nonlinear modal theory is based on the variational approach by Lukovsky [24] within modal functions ordered in accordance with the Moiseyev detuning. The theory is valid when the semi-apex angle α of the conical tank is between 25° and 55°. This is due to internal resonance at 6° and 12°, and because surface waves become shallow for α > 60°. The theory distinguishes planar and rotating resonant steady-state waves forced by sway. Hard-soft spring for amplitude response of the rotating wave is observed when α is close to 41°. Three-dimensional animation of wave motions accounts for second-order flows and facilitates the physical treatment.
ONE-DIMENSIONAL APPROXIMATE ANALYTICAL SOLUTIONS OF HEAT CONDUCTION IN SEMI-INFINITE SOLIDS WITH TEMPERATURE-DEPENDENT PROPERTIES
36
Gaetano
Barbaro
DETEC, Università di Napoli Federico II, P.le Tecchio 80, 80125 Napoli, Italy
Nicola
Bianco
Dipartimento di Ingegneria Industriale, Università degli Studi di Napoli Federico II, Napoli, Italy
Oronzio
Manca
Dipartimento di Ingegneria Industriale e dell'Informazione, Università degli
Studi della Campania "Luigi Vanvitelli," Aversa (CE), Italy
A new method to obtain approximate one-dimensional transient analytical solution of the nonlinear heat conduction equation with temperature-dependent thermal properties is proposed. In this method the Kirchhoff transform and the enthalpy formulation of the heat conduction equation are used, and approximate solutions are obtained by minimizing the estimated error in the temperature range of interest. The method is compared with other techniques, and it shows an improved agreement with numerical solutions of one-dimensional transient nonlinear conductive problems. The method is applied to one-dimensional problems, and two solutions for continuous and on-off heat laser sources are calculated. The estimated error formulas give a criterion of the reliability of the method. The accuracy of the calculated approximate solutions is determined by comparison with the corresponding numerical ones and is found to be satisfactory.
ANALYSIS OF FORCED CONVECTION IN A MICROTUBE WITH WAVY WALLS
14
Steady laminar flow of an incompressible fluid through a tube of almost circular cross-section is examined analytically, first for the case of a tube whose wall is wavy in the azimuthal direction, and then for one wavy in the axial direction. For the first case, a complete solution of the flow and forced convection heat transfer (for constant flux at the boundary) is possible for a wall of arbitrary cross-section. It is shown that, for a fixed axial pressure gradient, any departure from circularity leads to a reduction in volume flux and a reduction in heat transfer. For the second case, no simple analytic solution is possible, but estimates of the increase in resistance due to a departure from circularity have been made.
INTEGRAL TRANSFORMS FOR HEAT AND FLUID FLOW IN TWO- AND THREE-DIMENSIONAL POROUS MEDIA
14
Renato M.
Cotta
Laboratory of Nano- and Microfluidics and Microsystems, LabMEMS,
Mechanical Engineering Department and Nanotechnology Engineering Dept.,
POLI & COPPE, Universidade Federal do Rio de Janeiro, Cidade Universitária,
Cx. Postal 68503, Rio de Janeiro, RJ, CEP 21945-970, Brazil; Interdisciplinary Nucleus for Social Development—NIDES/CT, UFRJ, Brazil;
Mechanical Engineering Department, University College London, UCL, United
Kingdom
H. Luz
Neto
Instituto Nacional de Tecnologia — INT, Rio de Janeiro, Brazil
Leonardo
Alves
Departamento de Engenharia Mecânica - TEM
Universidade Federal Fluminense - UFF
Joao N. N.
Quaresma
School of Chemical Engineering, Universidade Federal do Para, FEQ/UFPA, Campus Universitario do Guama, 66075-110, Belem, PA, Brazil
Hybrid numerical—analytical algorithms, based on the generalized integral transform technique, are developed and reviewed to handle transient two-and three-dimensional heat and fluid flow in cavities filled with a porous material. A general formulation and solution methodology for horizontal and vertical cavities is developed. To illustrate the algorithm computational behavior, specific situations are more closely considered, under the Darcy model for natural convection in porous medium filled cavities. The problem is analyzed with and without the time derivative term in the flow equations, using a vorticity-vector potential formulation, which automatically reduces to the stream-function-only formulation for two-dimensional situations. Results for rectangular (2-D) and parallelepiped (3-D) vertical cavities are presented to demonstrate the convergence behavior of the proposed eigenfunction expansion solutions, and comparisons with previously reported numerical solutions are critically performed.
AN EIGENVALUE PROBLEM WITH NONLINEAR DEPENDENCE OF THE EIGENVALUE
6
B. R.
Makaveev
Ronan Engineering, Woodland Hills, CA, USA
Mikhail D.
Mikhailov
Applied Mathematics Center, PO Box 384, Sofia, Technical University, Sofia, Bulgaria; and Mechanical Engineering Department—EE/COPPE/UFRJ, Universidade Federal do Rio de Janeiro, Cidade Universitaria, CP 68.503, Rio de Janeiro, RJ, 21945-970, Brasil
Mathematica software has been used to solve the eigenvalue problem y''[x] + (λ + λ2x2)y[x] = 0, y[−1] = 0, y[1] = 0. A table of the first 50 eigenvalues with 25 accurate digits is presented. A Mathematica function is given that computes a desired eigenvalue with specified accuracy.
NUMERICAL SIMULATION OF THREE-DIMENSIONAL FLOW OVER CYLINDERS USING A HYBRID METHOD
28
Sergio Hamilton
Sphaier
Ocean Engineering Department - EP/COPPE/UFRJ, CP50508, 21945-970, Rio de Janeiro, RJ, Brazil
Mauro Costa
de Oliveira
Petrobras Research Center, CENPES Cidade Universitaria, Q. 7 Ilha do Fundao Rio de Janeiro, RJ, Brazil 21949-900
Knowledge of fluid loading is essential to the design of deep water structures for oil production, particularly because of the fluid-structure interaction. This interaction gives rise to the phenomenon of vortex-induced vibrations, which can significantly reduce the fatigue life of cylindrical structures. This article proposes a hybrid numerical-analytical method to assess three-dimensional flows acting over cylinders. The incompressible Navier-Stokes equations in primitive variables are considered, and, in addition, the projection method is applied in order to attain a sequential procedure. Because the problem to be studied is the flow over cylinders, the dimension corresponding to the cylinder length is in a special situation, enabling the equations to be transformed following the generalized integral transform technique (GITT). This approach results in the change of a partial differential equation in three-dimensional coordinates by a system of two-dimensional equations in the transformed variables. The computational time reduction that this replacement allows is substantial. This new problem is discretized in space and time, using, respectively, the finite element and the finite difference methods. After that, the original variables are retrieved, and it is possible to calculate forces over the cylinder. In this article, the method is applied to a parallel-plate, two-dimensional channel and to a fixed three-dimensional cylinder.
Volume 3 Indices
4