Publication Cover
Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 52, 2007 - Issue 12
212
Views
13
CrossRef citations to date
0
Altmetric
Original Articles

Eigenfunction Expansion Solution for Boundary-Layer Equations in Cylindrical Coordinates: Simultaneously Developing Flow in Circular Tubes

, , &
Pages 1123-1149 | Received 08 Oct 2006, Accepted 21 Sep 2007, Published online: 19 Sep 2007

REFERENCES

  • W. J. Minkowycz , E. M. Sparrow , and J. Y. Murthy , Handbook of Numerical Heat Transfer, , 2d ed. , Wiley , New York , 2006 .
  • R. M. Cotta and M. D. Mikhailov , Hybrid Methods and Symbolic Computations , in W. J. Minkowycz , E. M. Sparrow , and J. Y. Murthy (eds.), Handbook of Numerical Heat Transfer, , 2d ed. , pp. 493 – 522 , Wiley , New York , 2006 .
  • R. M. Cotta , Integral Transforms in Computational Heat and Fluid Flow , CRC Press , Boca Raton , FL , 1993 .
  • R. M. Cotta , Benchmark Results in Computational Heat and Fluid Flow: The Integral Transform Method , Int. J. Heat Mass Transfer , vol. 37 ( suppl. 1 ), pp. 381 – 393 , 1994 .
  • R. M. Cotta , The Integral Transform Method in Thermal and Fluid Sciences and Engineering , Begell House , New York , 1998 .
  • C. A. C. Santos , J. N. N. Quaresma , and J. A. Lima , Benchmark Results for Convective Heat Transfer in Ducts: The Integral Transform Approach , ABCM Mechanical Sciences Series, Editora E-Papers , Rio de Janeiro , Brazil , 2001 .
  • R. M. Cotta , C. A. C. Santos , J. N. N. Quaresma , and J. S. Pérez-Guerrero , Hybrid Integral Transforms in Convection-Diffusion: Recent Applications in Internal Flow Simulation, Invited Lecture , Proc. 4th Int. Conf. on Computational Heat and Mass Transfer, 4th ICCHMT , Paris-Cachan , France , 2005 , vol. 1 , pp. 153 – 164 .
  • R. M. Cotta , Hybrid Numerical-Analytical Approach to Nonlinear Diffusion Problems, Numer. Heat Transfer B , vol. 17, pp. 217–226, 1990.
  • J. B. Campos Silva , R. M. Cotta , and J. B. Aparecido , Analytical Solutions to Simultaneously Developing Laminar Flow inside Parallel-Plates Channel , Int. J. Heat Mass Transfer , vol. 35 , pp. 887 – 895 , 1992 .
  • J. S. Perez Guerrero and R. M. Cotta , Integral Transform Method for Navier-Stokes Equations in Stream Function-Only Formulation , Int. J. Numer. Meth. Fluids , vol. 15 , pp. 399 – 409 , 1992 .
  • T. M. B. Carvalho , R. M. Cotta , and M. D. Mikhailov , Flow Development in Entrance Region of Ducts , Commun. in Numer. Meth. Eng. , vol. 9 , pp. 503 – 509 , 1993 .
  • A. J. K. Leiroz and R. M. Cotta , On the Solution of Nonlinear Elliptic Convection-Diffusion Problems through the Integral Transform Method , Numer. Heat Transfer B , vol. 23 , pp. 401 – 411 , 1993 .
  • R. M. Cotta and J. E. V. Gerk , Mixed Finite Difference/Integral Transform Approach for Parabolic-Hyperbolic Problems in Transient Forced Convection , Numer. Heat Transfer B , vol. 25 , pp. 433 – 448 , 1994 .
  • H. A. Machado and R. M. Cotta , Integral Transform Method for Boundary Layer Equations in Simultaneous Heat and Fluid Flow Problems , Int. J. Numer. Meth. Heat Fluid Flow , vol. 5 , pp. 225 – 237 , 1995 .
  • J. S. Pérez Guerrero and R. M. Cotta , Integral Transform Solution of Developing Laminar Duct Flow in Navier-Stokes Formulation , Int. J. Numer. Meth. Fluids , vol. 20 , pp. 1203 – 1213 , 1995 .
  • E. Figueira da Silva and R. M. Cotta , Benchmark Results for Internal Forced Convection through Integral Transformation , Int. Commun. Heat Mass Transfer , vol. 23 , pp. 1019 – 1029 , 1996 .
  • J. S. Pérez Guerrero and R. M. Cotta , Benchmark Integral Transform Results for Flow Over a Backward-Facing Step , Comput. Fluids , vol. 25 , pp. 527 – 540 , 1996 .
  • J. A. Lima , J. S. Pérez Guerrero , and R. M. Cotta , Hybrid Solution of the Averaged Navier-Stokes Equations for Turbulent Flow , Comput. Mech. , vol. 19 , pp. 297 – 307 , 1997 .
  • J. N. N. Quaresma and R. M. Cotta , Integral Transform Method for the Navier-Stokes Equations in Steady Three-Dimensional Flow , Proc. 10th ISTP—Int. Symp. on Transport Phenomena , Kyoto , Japan , 1997 , pp. 281 – 287 .
  • R. M. Cotta and L. C. G. Pimentel , Developing Turbulent Duct Flow: Hybrid Solution via Integral Transforms and Algebraic Models , Int. J. Numer. Meth. Heat Fluid Flow , vol. 8 , pp. 10 – 26 , 1998 .
  • E. Figueira da Silva and R. M. Cotta , Mixed Convection within Vertical Parallel-Plates: Hybrid Solution by Integral Transforms , Numer. Heat Transfer A , vol. 33 , pp. 85 – 106 , 1998 .
  • L. M. Pereira , J. S. Pérez Guerrero , and R. M. Cotta , Integral Transformation of the Navier-Stokes Equations in Cylindrical Geometry , Comput. Mech. , vol. 21 , pp. 60 – 70 , 1998 .
  • M. A. H. Bolivar , P. L. C. Lage , and R. M. Cotta , Integral Transform Solution of the Laminar Thermal Boundary Layer Problem for Flow past Two-Dimensional and Axisymmetric Bodies , Numer. Heat Transfer A , vol. 33 , pp. 779 – 797 , 1998 .
  • E. Figueira da Silva , J. S. Pérez Guerrero , and R. M. Cotta , Integral Transform Solution of Boundary Layer Equations in Streamfunction-Only Formulation , Int. J. Non-Linear Mech. , vol. 34 , pp. 51 – 61 , 1999 .
  • H. A. Machado and R. M. Cotta , Analysis of Internal Convection with Variable Physical Properties via Integral Transformation , Numer. Heat Transfer A , vol. 36 , pp. 699 – 724 , 1999 .
  • L. S. B. Alves and R. M. Cotta , Transient Natural Convection inside Porous Cavities: Hybrid Numerical-Analytical Solution and Mixed Symbolic-Numerical Computation , Numer. Heat Transfer A , vol. 38 , pp. 89 – 110 , 2000 .
  • J. S. Pérez Guerrero , J. N. N. Quaresma , and R. M. Cotta , Simulation of Laminar Flow inside Ducts of Irregular Geometry Using Integral Transforms, Comput. Mech. , vol. 25, pp. 413–420, 2000.
  • L. M. Pereira , J. S. Pérez Guerrero , and R. M. Cotta , Analysis of Laminar Forced Convection in Annular Ducts Using Integral Transforms , Hybrid Meth. Eng. , vol. 2 , pp. 221 – 232 , 2000 .
  • S. Cheroto , J. S. Pérez Guerrero , C. A. C. Santos , and S. Kakaç , Integral Transform for Periodic Laminar Forced Convection in Simultaneously Developing Flow , Numer. Heat Transfer A , vol. 38 , pp. 653 – 679 , 2000 .
  • L. A. Sphaier and R. M. Cotta , Integral Transform Analysis of Multidimensional Eigenvalue Problems within Irregular Domains , Numer. Heat Transfer B , vol. 38 , pp. 157 – 175 , 2000 .
  • S. C. Hirata , B. Goyeau , D. Gobin , and R. M. Cotta , Stability of Natural Convection in Composite Enclosures Using Integral Transforms , Numer. Heat Transfer B , vol. 50 , pp. 409 – 424 , 2006 .
  • R. K. Shah and A. L. London , Laminar Flow Forced Convection in Ducts , Advances in Heat Transfer , Supplement 1 , Academic Press , New York , 1978 .
  • S. Kakaç , Handbook of Single-Phase Convective Heat Transfer , Wiley , New York , 1987 .
  • E. M. Sparrow , S. H. Lin , and T. S. Lundgren , Flow Development in the Hydrodynamic Entrance Region of Tubes and Ducts , Phys. Fluids , vol. 7 , pp. 338 – 347 , 1964 .
  • R. W. Hornbeck , Laminar Flow in the Entrance Region of a Pipe , Appl. Sci. Res. A , vol. 13 , pp. 224 – 232 , 1964 .
  • J. Liu , Flow of a Bingham Fluid in the Entrance Region of an Annular Tube , M.S. thesis , University of Wisconsin—Milwaukee , 1974 .
  • R. W. Hornbeck , An All-Numerical Method for Heat Transfer in the Inlet of a Tube , Proc. ASME, Winter Annual Meeting , Chicago , 1965 , Paper 65-WA/HT-36 .
  • M. K. Jensen , Simultaneously Developing Laminar Flow in an Isothermal Circular Tube , Int. Commun. Heat Mass Transfer , vol. 16 , pp. 811 – 820 , 1989 .
  • F. Fedele , D. L. Hitt , and R. D. Prabhu , Revisiting the Stability of Pulsatile Pipe Flow , Eur. J. Mech. B/Fluids , vol. 24 , pp. 237 – 254 , 2005 .
  • IMSL Library, MATH/LIB , Houston , TX , 1991 .
  • R. M. Cotta and M. N. Özisik , Laminar Forced Convection of Power-Law Non-Newtonian Fluids Inside Ducts , Wärme- und Stoffübertragung , vol. 20 , pp. 211 – 218 , 1986 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.