A THEORETICAL STUDY OF COMBINED NATURAL AND FORCED LAMINAR CONVECTION FOR DEVELOPING FLOW DOWN VERTICAL ANNULI

1970 ◽  
Author(s):  
K. Sherwin ◽  
J. D. Wallis
Keyword(s):  
Theoretical Study ◽  
Developing Flow ◽  
Vertical Annuli ◽  
Laminar Convection

Paper 34: A Study of Laminar Convection for Flow down Vertical Annuli

1967 ◽  
Vol 182 (8) ◽  
pp. 330-335
Author(s):  
K. Sherwin ◽  
J. D. Wallis
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Performance ◽  
Main Flow ◽  
Stable Form ◽  
Outer Diameter ◽  
Nusselt Numbers ◽  
Buoyancy Forces ◽  
Vertical Annulus ◽  
Vertical Annuli ◽  
Laminar Convection

Laminar convection in vertical systems is affected by buoyancy so that it becomes a combination of natural and forced convection. In downflow the buoyancy forces oppose the main flow. The problem has previously been studied for flows in vertical circular tubes and is here extended to flows in vertical annuli with uniformly heated inner surfaces. This configuration retains the simplicity desirable for both analysis and experiment, but also represents quite closely certain practical systems such as flow in nuclear reactors in which cylindrical components are placed axially in vertical coolant channels. Buoyancy forces opposing the main flow cause the fluid to be slowed down near the heat transfer surface until it is eventually reversed. In simple theory this flow reversal is associated with a decrease in heat transfer performance. An experimental study has been performed in a vertical annulus of ¾ in inner and 2¼ in outer diameter using water. Flow visualization by dye injection indicates that while small reversed flows may occur in a stable form, higher buoyancy forces give rise to radial components of the flow. These radial components cause the reversed flow regime to become unsteady and the Nusselt numbers to be higher than those predicted by laminar convection analysis.

Combined Forced and Free Convection in the Entrance Region of an Isothermally Heated Horizontal Pipe

1982 ◽  
Vol 104 (1) ◽  
pp. 153-159 ◽  
Author(s):  
Mikio Hishida ◽  
Yasutaka Nagano ◽  
M. S. Montesclaros
Keyword(s):  
Numerical Solutions ◽  
Entrance Region ◽  
Temperature Fields ◽  
Horizontal Pipe ◽  
Uniform Wall Temperature ◽  
Nusselt Numbers ◽  
Developing Flow ◽  
Uniform Wall ◽  
Secondary Velocity ◽  
Laminar Convection

Numerical solutions are given without the aid of a large Prandtl number assumption for combined forced and free laminar convection in the entrance region of a horizontal pipe with uniform wall temperature. The steady-state solutions have been obtained from the asymptotic time solutions of the time-dependent equations of momentum and energy with the Poisson equation for pressure. Results are presented for the developing primary and secondary velocity profiles, developing temperature fields, local wall shear stress, and local and average Nusselt numbers, which reveal how the developing flow and heat transfer in the entrance region are affected by the secondary flow due to buoyancy forces.

Laminar Convection in Circular Tubes With Developing Flow

2020 ◽  
Vol 142 (11) ◽  
Author(s):  
T. D. Bennett
Keyword(s):  
Circular Tube ◽  
Constant Heat Flux ◽  
Nusselt Numbers ◽  
Developing Flow ◽  
Wide Range ◽  
Extended Range ◽  
Prandtl Numbers ◽  
Laminar Convection ◽  
Heat And Momentum Transfer ◽  
Historical Range

Abstract The combined entry problem for the simultaneous development of heat and momentum transfer in a circular tube has been resolved over an extended range of inverse Graetz number ZH≥10−6 and for a wide range of Prandtl numbers 0.1≤Pr≤500. For the historical range of ZH≥5×10−4 and 0.7≤Pr≤50, earlier studies are within 5% of the current benchmark calculations, but for the new extended range of conditions, the best authoritative sources were in error by as much as 33%. Four new correlations are proposed for the local and average Nusselt numbers, and for the constant temperature and constant heat flux wall condition, which are accurate to 2.2% for all values of inverse Graetz number and Pr≥0.5. In contrast, legacy correlations typically had a 10–20% error range when compared to the results of this work, with many exhibiting larger errors and only few achieving errors as low as 5–10%.

Combined Forced and Free Laminar Convection in the Entrance Region of an Inclined Isothermal Tube

1988 ◽  
Vol 110 (4a) ◽  
pp. 901-909 ◽  
Author(s):  
D. Choudhury ◽  
S. V. Patankar
Keyword(s):  
Numerical Results ◽  
Entrance Region ◽  
Heat Transfer Characteristics ◽  
Local Pressure ◽  
Flow And Heat Transfer ◽  
Developing Flow ◽  
Free And Forced Convection ◽  
Laminar Convection ◽  
Independent Parameters ◽  
Axial Development

An analysis is made of the combined forced and free convection for laminar flow in the entrance region of isothermal, inclined tubes. This involves the numerical calculation of the developing flow with significant buoyancy effects. Three independent parameters are introduced: the Prandtl number Pr, a modified Rayleigh number Ra*, and Ω, a parameter that measures the relative importance of free and forced convection. The inclination angle does not appear explicitly in the formulation. Numerical results are obtained for Pr = 0.7, 5, and 10, and representative values of Ra* and Ω. The axial development of the velocity profiles, temperature field, local pressure gradient, and the Nusselt number are presented. These results reveal that the buoyancy effects have a considerable influence on the fluid flow and heat transfer characteristics of the development flow. A comparison of the numerical results with the available experimental data is also presented.

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