FREE CONVECTION EFFECTS ON GRAETZ PROBLEM FOR LARGE PRANDTL NUMBER FLUIDS IN HORIZONTAL TUBES WITH UNIFORM WALL HEAT FLUX

1974 ◽  
Author(s):  
K. C. Cheng ◽  
Jenn-Wuu Ou
Keyword(s):  
Heat Flux ◽  
Free Convection ◽  
Prandtl Number ◽  
Wall Heat Flux ◽  
Horizontal Tubes ◽  
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.

Vorticity-Velocity Method for the Graetz Problem and the Effect of Natural Convection in a Horizontal Rectangular Channel With Uniform Wall Heat Flux

1987 ◽  
Vol 109 (3) ◽  
pp. 704-710 ◽  
Author(s):  
F. C. Chou ◽  
G. J. Hwang
Keyword(s):  
Heat Flux ◽  
Prandtl Number ◽  
Numerical Solutions ◽  
Rectangular Channel ◽  
Wall Heat Flux ◽  
Entrance Region ◽  
Grashof Number ◽  
Uniform Wall ◽  
Laminar Convection ◽  
Uniform Wall Heat Flux

Numerical solutions given by a vorticity-velocity method are presented for combined free and forced laminar convection in the thermal entrance region of a horizontal rectangular channel without the assumptions of large Prandtl number and small Grashof number. The channel wall is heated with a uniform wall heat flux. Typical developments of temperature profile, secondary flow, and axial velocity at various axial positions in the entrance region are presented. Local friction factor and Nusselt number variations are shown for Rayleigh numbers Ra = 104, 3×104, 6×104, and 105 with the Prandtl number as a parameter. The solution for the limiting case of large Prandtl number and small Grashof number obtained from the present study confirms the data of existing literature. It is observed that the large Prandtl number assumption is valid for Pr = 10 when Ra ≤ 3×104 but for a larger Prandtl number when the Rayleigh number is higher.

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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