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Technical Briefs

On the Generalized Brinkman Number Definition and Its Importance for Bingham Fluids

[+] Author and Article Information
P. M. Coelho1

Departamento de Engenharia Mecânica, CEFT, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugalpmc@fe.up.pt

J. C. Faria

Departamento de Engenharia Mecânica, CEFT, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugalem07027@fe.up.pt

1

Corresponding author.

J. Heat Transfer 133(5), 054505 (Feb 03, 2011) (4 pages) doi:10.1115/1.4003169 History: Received September 06, 2010; Revised December 02, 2010; Published February 03, 2011; Online February 03, 2011

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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Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

Grahic Jump Location
Figure 3

Relation between Nu and 8/Bn for several positive generalized Brinkman numbers, Br∗, Eq. 11

Grahic Jump Location
Figure 4

Relation between Nu and 8/Bn for several negative Br∗, Eq. 11

Grahic Jump Location
Figure 1

Schematic diagram of the problem under study and the nondimensional coordinate system

Grahic Jump Location
Figure 2

Relation between Nu and 8/Bn for several Brinkman numbers according to literature, Eq. 12

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