A solution to the turbulent Graetz problem by matched asymptotic expansions—II the case of uniform wall heat flux

1971 ◽  
Vol 26 (4) ◽  
pp. 559-565 ◽  
Author(s):  
Robert H. Notter ◽  
C.A. Sleicher
Keyword(s):  
Heat Flux ◽  
Asymptotic Expansions ◽  
Wall Heat Flux ◽  
Matched Asymptotic Expansions ◽  
Graetz Problem ◽  
Uniform Wall ◽  
Uniform Wall Heat Flux

Laminar Convective Heat Transfer of a Bingham Plastic in a Circular Pipe With Uniform Wall Heat Flux: The Graetz Problem Extended

1999 ◽  
Vol 121 (3) ◽  
pp. 556-563 ◽  
Author(s):  
T. Min ◽  
J. Y. Yoo
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Yield Stress ◽  
Wall Heat Flux ◽  
Circular Pipe ◽  
Bingham Plastic ◽  
Graetz Problem ◽  
Uniform Wall ◽  
Uniform Wall Heat Flux

Thermally developing laminar flow of a Bingham plastic in a circular pipe with uniform wall heat flux has been studied analytically. Expressions for the fully developed temperature and Nusselt number are presented in terms of the yield stress, Peclet number, and Brinkman number. The solution to the Graetz problem has been obtained by using the method of separation of variables, where the resulting eigenvalue problem is solved approximately by using the method of weighted residuals. The effects of the yield stress, Peclet, and Brinkman numbers on the Nusselt number are discussed. In particular, it is shown that the heat transfer characteristics in the entrance region are significantly affected by the yield stress with the inclusion of viscous dissipation.

Graetz problem in curved pipes with uniform wall heat flux

1974 ◽  
Vol 29 (1) ◽  
pp. 401-418 ◽  
Author(s):  
Mitsunobu Akiyama ◽  
K. C. Cheng
Keyword(s):  
Heat Flux ◽  
Wall Heat Flux ◽  
Curved Pipes ◽  
Graetz Problem ◽  
Uniform Wall ◽  
Uniform Wall Heat Flux

An experimental investigation of a solar chimney model with uniform wall heat flux

2003 ◽  
Vol 38 (7) ◽  
pp. 893-906 ◽  
Author(s):  
Z.D. Chen ◽  
P. Bandopadhayay ◽  
J. Halldorsson ◽  
C. Byrjalsen ◽  
P. Heiselberg ◽  
...  
Keyword(s):  
Heat Flux ◽  
Experimental Investigation ◽  
Wall Heat Flux ◽  
Solar Chimney ◽  
Uniform Wall ◽  
Uniform Wall Heat Flux
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