Integral transform solution of internal flow problems based on Navier-Stokes equations and primitive variables formulation

International Journal for Numerical Methods in Engineering

Volumn 69, Issue 3, 2007, Pages 544-561

  de Lima, G G C ^a   Santos, C A C ^a   Haag, A ^b   Cotta, R M ^b  

^a FEDERAL UNIVERSITY OF PARAÍBA   (Brazil)

^b FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

Hybrid methods; Integral transforms; Internal flow; Navier Stokes equations; Primitive variables

Indexed keywords

BOUNDARY CONDITIONS; CHANNEL FLOW; CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; INCOMPRESSIBLE FLOW; LAMINAR FLOW; NAVIER STOKES EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS;

HYBRID METHODS; INTEGRAL TRANSFORMS; INTERNAL FLOW; PRIMITIVE VARIABLES;

MATHEMATICAL TRANSFORMATIONS;

BOUNDARY CONDITIONS; CHANNEL FLOW; CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; INCOMPRESSIBLE FLOW; LAMINAR FLOW; MATHEMATICAL TRANSFORMATIONS; NAVIER STOKES EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS;

EID: 33846276148     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1780     Document Type: Article

References (31)

1. Minkowycz WJ, Sparrow EM, Murthy JY. Handbook of Numerical Heat Transfer (2nd edn). Wiley: New York, 2006.
2. Cotta RM. Integral Transforms in Computational Heat and Fluid Flow. CRC Press: Boca Raton, FL, U.S.A., 1993.
3. Cotta RM. Benchmark results in computational heat and fluid flow - the integral transform method. International Journal of Heat and Mass Transfer 1994; 37(Suppl. 1):381-394 (Invited Paper).
4. Cotta RM, Mikhailov MD. Heat Conduction - Lumped Analysis, Integral Transforms, Symbolic Computation. Wiley: New York, 1997.
5. Cotta RM (ed.). The Integral Transform Method in Thermal and Fluids Science and Engineering. Begell House: New York, 1998.
6. Santos CAC, Quaresma JNN, Lima JA (eds). Benchmark Results for Convective Heat Transfer in Ducts - The Integral Transform Approach. ABCM Mechanical Sciences Series. Editora E-Papers, Part 1, Chapter II, Rio de Janeiro, 2001; 17-38.
7. Cotta RM, Orlande HRB. Hybrid approaches in heat and mass transfer - a Brazilian experience with applications in national strategic projects. Heat Transfer Engineering 2003; 24(4):1-5 (Invited Editorial).
8. Cotta RM, Mikhailov MD. Hybrid methods and symbolic computations. In Handbook of Numerical Heat Transfer (Chapter 16, 2nd edn), Minkowycz WJ, Sparrow EM, Murthy JY (eds). Wiley: New York, 2006.
9. Cotta RM, Carvalho TMB. Hybrid analysis of boundary layer equations for internal flow problems. Proceedings of the 7th International Conference on Numerical Methods in Laminar and Turbulent Flow, Part 1, Stanford, CA, July 1991; 106-115.
10. Carvalho TMB, Cotta RM, Mikhailov MD. Flow development in the entrance region of ducts. Communications in Numerical Methods in Engineering 1993; 9:503-509.
11. Machado HA, Cotta RM. Integral transform method for boundary layer equations in simultaneous heat and fluid flow problems. International Journal of Numerical Methods for Heat and Fluid Flow 1995; 5:225-237.
12. Pimentel LCG, Cotta RM. Developing turbulent duct flow - hybrid solution via integral transforms and algebraic models. International Journal of Numerical Methods for Heat and Fluid Flow 1998; 8(1):10-26.
13. Figueira da Silva E, Cotta RM. Benchmark results for internal forced convection through integral transformation. International Communications in Heat and Mass Transfer 1996; 23(7):1019-1029.
14. Figueira da Silva E, Cotta RM. Mixed convection within vertical parallel-plates - hybrid solution by integral transforms. Numerical Heat Transfer Part A - Applications 1998; 33:85-106.
15. Machado HA, Cotta RM. Integral transform computation of compressible boundary layers. Hybrid Methods in Engineering 1999; 1(2):139-160.
16. Machado HA, Cotta RM. Analysis of internal convection with variable physical properties via integral transformation. Numerical Heat Transfer Part A - Applications 1999; 36(7):699-724.
17. Perez Guerrero JS, Cotta RM. Integral transform method for Navier-Stokes equations in stream function-only formulation. International Journal for Numerical Methods in Fluids 1992; 15:399-409.
18. Pérez Guerrero JS, Cotta RM. Integral transform solution of developing laminar duct flow in Navier-Stokes formulation. International Journal for Numerical Methods in Fluids 1995; 20:1203-1213.
19. Perez Guerrero JS, Cotta RM. Benchmark integral transform results for flow over a backward-facing step. Computers and Fluids 1996; 25(5):527-540.
20. Pereira LM, Perez Guerrero JS, Cotta RM. Integral transformation of the Navier-Stokes equations in cylindrical geometry. Computational Mechanics 1998; 21(1):60-70.
21. Lima JA, Perez Guerrero JS, Cotta RM. Hybrid solution of the averaged Navier-Stokes equations for turbulent flow. Computational Mechanics 1997; 19(4):297-307.
22. Leal MA, Perez Guerrero JS, Cotta RM. Natural convection inside two-dimensional cavities - the integral transform method. Communications in Numerical Methods in Engineering 1999; 15:113-125.
23. Quaresma JNN, Cotta RM. Integral transform method for the Navier-Stokes equations in steady three-dimensional flow. Proceedings of the 10th ISTP - International Symposium on Transport Phenomena, Kyoto, Japan, November 1997; 281-287.
24. Perez Guerrero JS, Quaresma JNN, Cotta RM. Simulation of laminar flow inside ducts of irregular geometry using integral transforms. Computational Mechanics 2000; 25(4):413-420.
25. Ramos R, Perez Guerrero JS, Cotta RM. Stratified flow over a backward facing step - hybrid solution by integral transforms. International Journal for Numerical Methods in Fluids 2001; 35(2):173-197.
26. Leal MA, Machado HA, Cotta RM. Integral transform solutions of transient natural convection in enclosures with variable fluid properties. International Journal of Heat and Mass Transfer 2000; 43(21):3977-3990.
27. Figueira da Silva E, Perez Guerrero JS, Cotta RM. A comparison of integral transform strategies for solving the boundary layer equations. Proceedings of the 6th National Thermal Sciences Meeting, ENCIT-96, Florianópolis, SC, Brasil, November 1996.
28. Wang YL, Longwell PA. Laminar flow in the inlet section of parallel plates. AIChE Journal 1964; 10:323-329.
29. Anderson DA, Tannehill JC, Pletcher RH. Computational Fluid Mechanics and Heat Transfer. Hemisphere Publishing Corporation: U.S.A., 1984.
30. Wolfram S. Mathematica: A System for Doing Mathematics by Computer. Addison-Wesley: Reading, MA, 1991.
31. IMSL Library. Microsoft FORTRAN PowerStation. Houston, TX, 1997.