Correlating laminar convection in slots with developing flow

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.

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Laminar Convection in Circular Tubes With Developing Flow

Journal of Heat Transfer ◽

10.1115/1.4047834 ◽

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%.

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

Journal of Heat Transfer ◽

10.1115/1.3250591 ◽

1988 ◽

Vol 110 (4a) ◽

pp. 901-909 ◽

Cited By ~ 42

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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