Begell House Inc.
Hybrid Methods in Engineering
HME
1099-2391
1
2
1999
COMBINED FREE-CONVECTION HEAT AND MASS TRANSFER ABOVE A NEAR-HORIZONTAL SURFACE IN A POROUS MEDIUM
15
10.1615/HybMethEng.v1.i2.10
Md. Anwar
Hossain
Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh
Ioan
Pop
Department of Applied Mathematics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania
Kambiz
Vafai
Department of Mechanical Engineering, University of California, Riverside, CA 92521-0425 USA
An analytical study is done on the combined heat and mass transfer in natural convection above a slightly inclined plate embedded in a porous medium. The Darcy-Boussinesq approximations are incorporated in the governing boundary-layer equations. A series solution which is valid near the leading edge of the surface is initially obtained, followed by an asymptotic expansion, which is valid for the trailing edge. A numerical solution of the complete boundary-layer equations, which uses the method of continuous transformation, joins the two solutions obtained above. A thorough examination of all possible physical limiting conditions revealed the existence of two distinct regime maps.
ON THE INTEGRAL TRANSFORM SOLUTION OF LAMINAR BOUNDARY LAYERS WITH DISTRIBUTED SUCTION
16
10.1615/HybMethEng.v1.i2.20
Jian
Su
Interdisciplinary Nucleus of Fluid Dynamics, NIDF, Mechanical Eng. Dept., POLI & COPPE, Universidade Federal do Rio de Janeiro, Brazil; Nuclear Eng. Dept., POLI & COPPE, Universidade Federal do Rio de Janeiro, Brazil
The velocity field associated with perturbations to the Blasius solution through a distributed wall suction is considered. The generalized integral transform technique is employed in a hybrid numerical-analytical solution of the two-dimensional boundary-layer equations, written in terms of the perturbation velocities. The linearized boundary-layer equations are integral-transformed by eliminating the transversal coordinate and reducing the partial differential equations (PDEs) to an infinite system of coupled linear ordinary differential equations for the transformed potentials. A leading-order approximate solution, in analytic form, is obtained by neglecting all nondiagonal elements of the coefficient matrices. The approximate-analytic solution shows an algebraic decay of the disturbance, which is confirmed by a complete hybrid numerical-analytical solution of the full truncated system. This is handled through well-known initial-value problem solvers with automatic precision control. The original nonlinear boundary-layer equations are then recovered by adding the neglected quadratic terms to the linearized system and solved by the same integral transform technique. Better convergence behavior of the integral transform solutions is shown by comparison with the finite-difference solutions.
MULTIREGION CONJUGATE HEAT TRANSFER
19
10.1615/HybMethEng.v1.i2.30
Shmuel
Olek
Planning Development and Technology Division, Israel Electric Corporation Ltd., Haifa, Israel
An analytical method based on eigenfunction expansions is developed for solving the steady-state two-dimensional conjugate heat transfer in rectangular or cylindrical multilayered flow of non-Newtonian fluids. The flow is hydrodynamically fully developed, but thermally developing. The solid and fluid domains are treated as a single region with discontinuities. The present solution method can be applied to the general case that involves an arbitrary number of fluids and solids in a generally layered configuration, where the fluids may have a general form of the velocity distribution. Results of the present approach for various cases are validated against other solutions. A detailed parametric study is carried out for a flow of a Newtonian fluid inside a thick-wall pipe.
INTEGRAL TRANSFORM COMPUTATION OF COMPRESSIBLE BOUNDARY LAYERS
22
10.1615/HybMethEng.v1.i2.40
Humberto Araujo
Machado
Institute de Aeronautica e Espaco − IAE Pg. Mal. Eduardo Gomes, 50, Vila das Acacias 12228-904, Sao Jose dos Campos, SP, Brazil; Universidade do Estado do Rio de Janeiro − UERJ, Faculdade de Tecnologia − FAT, Rodovia Presidente Dutra km 298 - Polo Industrial, 27537-000, Resende, RJ, Brazil
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
The generalized integral transform technique (GITT) is employed in the hybrid numerical-analytical solution of the compressible boundary-layer equations in the streamfunction-only formulation, as written for the laminar flow of a Newtonian fluid within a parallel-plates channel. The solution methodology is applied to a mixed-convection problem and the convergence behavior of the present error-controlled solution is studied. Numerical results from this more general model are compared to the Boussinesq formulation, in an attempt to investigate the limits of this common approximation, together with critical comparisons to some literature results.
UNSTEADY ONE-DIMENSIONAL ADVECTION MODELING USING THE CCMC SCHEME
10
10.1615/HybMethEng.v1.i2.50
Huan-Lin
Luo
Department of Civil Engineering, I-Shou University, Taiwan, Republic of China
A new approach, characteristic convective with monotonic conservation (CCMC), is proposed for modeling the advective transport equation. The procedures of the method in solving the pure one-dimensional convective equation are presented. With the construction of the convective characteristic curves for slope and curvature of the convective interpolation in the control volume, these two curves provide a tool to construct a more accurate convective interpolation without phase angle shift. A set of benchmark problems, including three critical test profiles, is used to examine the new scheme.
INTEGRAL TRANSFORM SOLUTION FOR THE INTERNAL BOUNDARY LAYER OF NON-NEWTONIAN FLUIDS
12
10.1615/HybMethEng.v1.i2.60
R. N. O.
Magno
Chemical Engineering Department, Universidade Federal do Para — UFPA, Belem, Para, 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 hydrodynamic boundary layer for a non-Newtonian fluid, following the power-law model for the shear stress, is studied in the entrance region of a parallel-plates channel. The hybrid numerical-analytical solutions for the developing flow velocity profiles are obtained by using the generalized integral transform technique (GITT). Benchmark results are established for velocity profiles with different power-law indices, which are compared with results previously reported in the literature and demonstrating excellent agreement. In this problem, a streamfunction formulation is employed which offers better computational performance in terms of convergence rates than the primitive-variables version.