Begell House Inc.
Hybrid Methods in Engineering
HME
1099-2391
2
2
2000
DISPERSION OF BUOYANT AIRBORNE CONTAMINANTS
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10.1615/HybMethEng.v2.i2.10
S. D.
Wright
The School of the Environment, University of Leeds, Leeds, LS2 9JT, England
Lionel
Elliott
Department of Applied Mathematical Studies, The University of Leeds, Leeds LS2 9JT, West Yorkshire, England.
Derek B.
Ingham
Centre for CFD, Department of Applied Mathematical Studies, The University of Leeds, Leeds, LS2 9JT, UK; Energy-2050, Faculty of Engineering, University of Sheffield, Sheffield, S10 2TN, UK
The ability to predict in advance the dispersion patterns of contaminants released into our local working environment, atmosphere, or oceans can aid in minimizing contamination of the local and global environment. A practical method used to achieve this aim is the Fokker-Planck solution—the concentration equation used to determine the dispersion pattern of a contaminant—and much research into this solution, both theoretical and numerical, has been undertaken. Obtaining physical realistic results requires an accurate numerical solution of the concentration equation in conjunction with the Navier-Stokes equations and a suitable turbulence model. This article considers the equations governing the release of a buoyant contaminant and presents a practical method for decoupling the Navier-Stokes and concentration equations. This permits the concentration equation to be solved even when the flow field is already known—for instance, from experiment. Furthermore, a simple yet effective numerical procedure is developed that increases the accuracy of the numerical solution of the governing equations of motion. These methods will be applied to model the release of a contaminant in the neighborhood of large-scale topography within the atmosphere; however, the techniques could be applied to a wide variety of engineering problems.
ANALYTICAL SOLUTION OF THE EXTENDED GRAETZ PROBLEM WITH AXIAL CONDUCTION AND CONVECTIVE BOUNDARY CONDITIONS
12
10.1615/HybMethEng.v2.i2.20
Affonso Silva
Telles
Curso de Pos-Graduagao em Tecnologia de Processos Quimicos e Bioquimicos (TPQB), Departamento de Engenharia Quimica, Escola de Quimica, Centre de Tecnologia, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil
E. M.
Queiroz
Curso de Pas-Graduacao em Tecnologia de Processes Quimicos e Bioquimicos (TPQB), Departamento de Engenharia Quimica, Escola de Quimica, Bloco E, Centro de Tecnologia, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil
G. Elmor
Filho
Departamento de Engenharia Quimica (DE-5), Institute Militar de Engenharia (IME); Curso de Pos-Graduacao em Tecnologia de Processos Quimicos e Bioquimicos (TPQB), Departamento de Engenharia Quimica, Escola de Quimica, Centre de Tecnologia, FURJ, Brazil
This article presents an analytical solution to the extended Graetz problem, in a circular pipe, with axial heat conduction, subjected to boundary conditions of the third kind. A mathematical scheme for solving this type of heat transfer problem was proposed by the present authors [1]. The solution employs a complete basis for the set of square integrable functions, orthogonal to the Hermite polynomials. The temperature profile is obtained as an infinite series of products of functions, resulting in decomposition of the energy equation into a set of ordinary differential equations, each of which depends on the two previous equations only. This allows a straightforward solution of the set of equations. The effects of the external Biot number and the axial conduction in fluid on the surface temperature, bulk temperature, heat flux, and Nusselt number are shown.
AN INTEGRAL APPROACH TO UNCONFINED AQUIFER RESPONSE TO DIFFERENT SCENARIOS OF RECHARGE
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10.1615/HybMethEng.v2.i2.30
Okey Oseloka
Onyejekwe
Department of Civil Engineering, University of Durban, Westvill, Durban, South Africa
A modified boundary integral procedure, hereinafter referred to as the Green-element method (GEM), is applied to simulate flows in an unconfined aquifer. Numerical considerations permit the solution of the integral replication of die governing nonlinear partial differential equation by domain discretization. This is implemented in such a way that the application of the boundary integral theory is further enhanced. GEM facilitates the incorporation of nonlinearity into the boundary integral theory by exploiting the advantages of the finite element method. Numerical results obtained from GEM for various scenarios of water level fluctuations in both one-dimensional and two-dimensional unconfined aquifer are compared with those of similar studies. In all the cases tested, encouraging results are obtained, thus confirming that GEM is accurate and yields accurate results.
DECOMPOSITION METHOD WITH MATHEMATICA
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10.1615/HybMethEng.v2.i2.40
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
In contrast to Adomian's approach, the decomposition technique presented herein for solving nonlinear functional equations is made before the solution, which permitted all existing solution techniques to be used. It is demonstrated by examples that the decomposition method gives the same results as the perturbation method. Some examples solved by Adomian are also considered. Notwithstanding that the solutions coincide with a power series expansion of the exact solutions, they converge in the limited region, which is extended by using the Shanks transformation.
DEVELOPMENT OF THERMAL MODELS FOR A SPACE PASSIVE HEAT SWITCH
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10.1615/HybMethEng.v2.i2.50
Fernando
Milanez
Department of Energy Engineering, Federal University of Santa Catarina, Ararangua
88900-000, Brazil
Marcia Barbosa Henriques
Mantelli
Heat Pipe Laboratory (LABTUCAL), Federal University of Santa Catarina, Mechanical Engineering Department, 88040-900, Trindade, Florianopolis, SC, Brazil
The objectives of this work are to present and compare theoretical models for predicting the overall thermal resistance of a passive bimetallic heat switch. The heat switch was developed to reduce the thermal load coming from the satellite structure to cryogenic sensors. The overall thermal resistance of the heat switch is a function of its mean temperature level. A brief description of the heat switch and of its working principle is presented. Two analytical two-dimensional models, one analytical one-dimensional model, and one numerical two-dimensional model are presented. The analytical two-dimensional models were developed using a novel technique to solve a two-dimensional boundary-value problem with coupled domains. This new technique proved to be quite accurate when compared with the numerical two-dimensional simulation of the heat switch temperature field. The one-dimensional model demonstrated that the heat flow in the heat switch is one-dimensional over almost the full range of operation of the heat switch.
THREE GREEN ELEMENT FORMULATIONS FOR BURGERS' EQUATION
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10.1615/HybMethEng.v2.i2.60
Akpofure E.
Taigbenu
Department of Civil & Water Engineering, National University of Science & Technology, Bulawayo, Zimbabwe
Burgers' equation, which provides a useful model for many diverse and seemingly unrelated phenomena such as shock flows, turbulence, wave propagation in combustion chambers, vehicular traffic movement, and acoustic transmission, is simulated with three formulations of the Green element method (GEM), and their results are compared. The Green element method is a novel way of implementing the singular boundary integral theory so that the theory is of more general application, and a banded global coefficient is achieved, thereby enhancing ease of its inversion and computational efficiency. These formulations are obtained essentially by using three Green's functions along a unified approach that achieves an integral representation of the differential operator via Green's identity, and numerically implements that integral representation element by element. The resultant discretized element equations are recursive, allowing for the transient history of the solution to be obtained at discrete time intervals. Because the Green's function of the first formulation does not have the time variable, the treatment of the temporal derivative is done by a generalized two-level difference approximation. The discretized element equations are nonlinear, requiring further simplification of linearization either by the Newton-Raphson or Picard algorithm. With three numerical examples, it is shown that the first formulation gives optimal results at about twice the computing time of the second formulation, which is fastest in computing speed.
ANALYSIS OF LAMINAR FORCED CONVECTION IN ANNULAR DUCTS USING INTEGRAL TRANSFORMS
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10.1615/HybMethEng.v2.i2.70
Luiz M.
Pereira
Laboratory of Transmission and Technology of Heat, LTTC, Engenharia Mecanika, EE/COPPE, Universidade Federal do Rio de Janeiro, Cx. Postal 68503, Ilha do Fundao, Rio de Janeiro, Brasil
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
Jesus Salvador
Perez Guerrero
Brazilian Nuclear Energy Commission - CNEN
Laminar forced convection in annular ducts is analyzed using the Generalized Integral Transform Technique (GITT) to solve the Navier-Stokes and energy equations in the cylindrical coordinates system. Some cases involving different aspect ratios, given by the relation between internal and external duct diameters, and for Prandtl number Pr = 0.72, are more closely considered. Numerical results are obtained for local temperature profiles, bulk mean temperature, and local Nusselt number. Comparisons with previous results in the literature are performed to validate the present simulation.
SOLUTION FOR THERMAL ENTRY REGION IN LAMINAR FLOW OF BINGHAM PLASTICS WITHIN ANNULAR DUCTS VIA INTEGRAL TRANSFORMATION
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10.1615/HybMethEng.v2.i2.80
U. C. S.
Nascimento
Chemical Engineering Department, Universidade Federaldo Para-UFPA, Campus Univenitario do Guama, Rua Augusta Correa, 01, 66075-900—Belem, PA, Brazil
Joao N. N.
Quaresma
School of Chemical Engineering, Universidade Federal do Para, FEQ/UFPA, Campus Universitario do Guama, 66075-110, Belem, PA, Brazil
Emanuel N.
Macedo
Mechanical Engineering Department, Chemical Engineering Department, Universidade Federal do Para-UFPA, Campus Universitario do Guama, RuaAugusto Correa, 01, 66075-900 -Belem, PA, Brazil
The thermal entry region in laminar flow of Bingham plastics within concentric annular ducts is solved analytically through the classical integral transform technique. Boundary conditions of the first kind are prescribed either at the inner or outer wall duct in order to verity the effects on the temperature field in the fluid. Nusselt numbers axe calculated along both the thermal entry and fully developed regions with high accuracy for different yield numbers and aspect ratios, which are systematically tabulated and graphically presented.