In this technical note we discuss the importance of using a generalized Brinkman number definition for laminar pipe flow of a Bingham fluid, when viscous dissipation effects are relevant. We show that adapting the Brinkman number definition commonly used for Newtonian fluids directly to the more general class of non-Newtonian fluids does not calculate correctly the ratio between heat generated by viscous dissipation and heat transfer at the wall and leads to a distortion of the graphical representation of the Nusselt number, Nu, rendering difficult, if not impossible, the comparisons of the Nu behavior between different Brinkman numbers. The use of the proposed generalized Brinkman number removes these problems and simultaneously it has the merit of being independent of any reference apparent viscosities.
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On the Generalized Brinkman Number Definition and Its Importance for Bingham Fluids
P. M. Coelho,
P. M. Coelho
Departamento de Engenharia Mecânica, CEFT, Faculdade de Engenharia,
e-mail: pmc@fe.up.pt
Universidade do Porto
, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
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J. C. Faria
J. C. Faria
Departamento de Engenharia Mecânica, CEFT, Faculdade de Engenharia,
e-mail: em07027@fe.up.pt
Universidade do Porto
, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
Search for other works by this author on:
P. M. Coelho
Departamento de Engenharia Mecânica, CEFT, Faculdade de Engenharia,
Universidade do Porto
, Rua Dr. Roberto Frias, 4200-465 Porto, Portugale-mail: pmc@fe.up.pt
J. C. Faria
Departamento de Engenharia Mecânica, CEFT, Faculdade de Engenharia,
Universidade do Porto
, Rua Dr. Roberto Frias, 4200-465 Porto, Portugale-mail: em07027@fe.up.pt
J. Heat Transfer. May 2011, 133(5): 054505 (4 pages)
Published Online: February 3, 2011
Article history
Received:
September 6, 2010
Revised:
December 2, 2010
Online:
February 3, 2011
Published:
February 3, 2011
Citation
Coelho, P. M., and Faria, J. C. (February 3, 2011). "On the Generalized Brinkman Number Definition and Its Importance for Bingham Fluids." ASME. J. Heat Transfer. May 2011; 133(5): 054505. https://doi.org/10.1115/1.4003169
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