Friction factors and Nusselt numbers for fully developed laminar flow in annuli

2002 ◽  
Author(s):  
Charl G. Jat Du Toit
Keyword(s):  
Laminar Flow ◽  
Nusselt Numbers ◽  
Friction Factors

scholarly journals Transition From the Turbulent to the Laminar Regime for Internal Convective Flow With Large Property Variations

1970 ◽  
Vol 92 (3) ◽  
pp. 506-512 ◽  
Author(s):  
C. W. Coon ◽  
H. C. Perkins
Keyword(s):  
Laminar Flow ◽  
Turbulent Flow ◽  
Circular Tube ◽  
Reynolds Numbers ◽  
Bulk Temperature ◽  
Heating Rates ◽  
Nusselt Numbers ◽  
Friction Factors ◽  
High Heating ◽  
Flow Situation

The results of a primarily experimental study of the transition from turbulent flow to laminar flow as a consequence of high heating rates are presented. Results are reported for hydrodynamically fully developed, low Mach number flows of air and helium through a vertical, circular tube. The electrically heated section was 100 diameters in length; entering Reynolds numbers ranged from 1700–40,000, and maximum wall-to-bulk temperature ratios reached 4.4. As a means of predicting the occurrence of a transition from turbulent flow to laminar flow, the experimental results are compared to the acceleration parameter suggested by Moretti and Kays and to a modified form of the parameter that is appropriate to a circular tube. It is suggested that the variable property turbulent flow correlations do not provide acceptable predictions of the Nusselt number and the friction factor if the value 4μq′′G2DTcp≃1.5×10−6 based on bulk properties, is exceeded for an initially turbulent flow situation. It is further suggested that Nusselt numbers and friction factors at locations down-stream from the point xDlaminar≃(2×10−8)(Tinlet)(Reb,inlet)2TwTbmax−1 for bulk temperatures in degrees Rankine may be obtained from the laminar correlation equations even though the flow is initially turbulent.

Effects of Nonuniform Passages on Compact Heat Exchanger Performance

1980 ◽  
Vol 102 (3) ◽  
pp. 653-659 ◽  
Author(s):  
R. K. Shah ◽  
A. L. London
Keyword(s):  
Heat Exchanger ◽  
Laminar Flow ◽  
Heat Transfer Performance ◽  
Compact Heat Exchanger ◽  
Reduced Pressure ◽  
Nusselt Numbers ◽  
Friction Factors ◽  
Special Cases ◽  
Longitudinal Wall ◽  
Manufacturing Tolerances

Neighboring passages in a compact heat exchanger such as a rotary regenerator are never geometrically identical due to manufacturing tolerances. This passage-to-passage nonuniformity can result in a significant penalty on heat transfer performance with only a small compensating effect of reduced pressure drop. Continuous cylindrical passage geometries, operating with laminar flow, are particularly sensitive to these effects. In this paper, a procedure is outlined to establish the effective friction factors and Nusselt numbers for one fluid side of an exchanger having n different cylindrical passage geometries. Two special cases of longitudinal wall temperature variation are considered corresponding to conditions of Cmin/Cmax of zero and unity. The analysis is presented for both fully developed and developing laminar flow.

Heat Transfer in a Surfactant Drag-Reducing Solution—A Comparison With Predictions for Laminar Flow

2005 ◽  
Vol 128 (6) ◽  
pp. 557-563 ◽  
Author(s):  
Paul L. Sears ◽  
Libing Yang
Keyword(s):  
Heat Transfer ◽  
Laminar Flow ◽  
Reynolds Numbers ◽  
High Heat ◽  
High Heat Flux ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Nusselt Numbers ◽  
Drag Reducing Additive ◽  
Good Agreement

Heat transfer coefficients were measured for a solution of surfactant drag-reducing additive in the entrance region of a uniformly heated horizontal cylindrical pipe with Reynolds numbers from 25,000 to 140,000 and temperatures from 30to70°C. In the absence of circumferential buoyancy effects, the measured Nusselt numbers were found to be in good agreement with theoretical results for laminar flow. Buoyancy effects, manifested as substantially higher Nusselt numbers, were seen in experiments carried out at high heat flux.

Hydoroil-Based Micro Pin Fin Heat Sink

2006 ◽  
Author(s):  
Ali Kosar ◽  
Chih-Jung Kuo ◽  
Yoav Peles
Keyword(s):  
Heat Sink ◽  
Hydraulic Performance ◽  
Heat Fluxes ◽  
Heat Sinks ◽  
Transfer Coefficients ◽  
Pin Fin ◽  
Nusselt Numbers ◽  
Friction Factors ◽  
Pin Fins ◽  
Micro Pin Fins

An experimental study on thermal-hydraulic performance of de-ionized water over a bank of shrouded NACA 66-021 hydrofoil micro pin fins with wetted perimeter of 1030-μm and chord thickness of 100 μm has been performed. Average heat transfer coefficients have been obtained over effective heat fluxes ranging from 4.0 to 308 W/cm2 and mass velocities from 134 to 6600 kg/m2s. The experimental data is reduced to the Nusselt numbers, Reynolds numbers, total thermal resistances, and friction factors in order to determine the thermal-hydraulic performance of the heat sink. It has been found that prodigious hydrodynamic improvement can be obtained with the hydrofoil-based micro pin fin heat sink compared to the circular pin fin device. Fluid flow over pin fin heat sinks comprised from hydrofoils yielded radically lower thermal resistances than circular pin fins for a similar pressure drop.

Analysis of Combined Forced and Free Flow in a Vertical Channel With Viscous Dissipation and Isothermal-Isoflux Boundary Conditions

1999 ◽  
Vol 121 (2) ◽  
pp. 349-356 ◽  
Author(s):  
A. Barletta
Keyword(s):  
Boundary Conditions ◽  
Parallel Plate ◽  
Vertical Channel ◽  
Uniform Heat Flux ◽  
Viscous Heating ◽  
Perturbation Expansions ◽  
Nusselt Numbers ◽  
Buoyancy Parameter ◽  
Laminar Mixed Convection ◽  
Friction Factors

Fully developed and laminar mixed convection in a parallel-plate vertical channel is investigated in the case of non-negligible viscous heating. The channel walls are subjected to asymmetric boundary conditions: One wall experiences a constant and uniform heat flux, while the other is kept at a uniform and constant temperature. The velocity field and the temperature field are evaluated analytically by means of perturbation expansions with respect to a buoyancy parameter, i.e., the ratio between the Grashof number and the Reynolds number. The Nusselt numbers and the friction factors are obtained as functions of the buoyancy parameter.

Spatially Resolved Heat Transfer and Friction Factors in a Rectangular Channel With 45-Deg Angled Crossed-Rib Turbulators

2003 ◽  
Vol 125 (3) ◽  
pp. 575-584 ◽  
Author(s):  
P. M. Ligrani ◽  
G. I. Mahmood
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Rectangular Channel ◽  
Test Surface ◽  
Spatially Resolved ◽  
Nusselt Numbers ◽  
Friction Factors ◽  
Smooth Channel ◽  
Rib Turbulators

Spatially resolved Nusselt numbers, spatially averaged Nusselt numbers, and friction factors are presented for a stationary channel with an aspect ratio of 4 and angled rib turbulators inclined at 45 deg with perpendicular orientations on two opposite surfaces. Results are given at different Reynolds numbers based on channel height from 10,000 to 83,700. The ratio of rib height to hydraulic diameter is .078, the rib pitch-to-height ratio is 10, and the blockage provided by the ribs is 25% of the channel cross-sectional area. Nusselt numbers are given both with and without three-dimensional conduction considered within the acrylic test surface. In both cases, spatially resolved local Nusselt numbers are highest on tops of the rib turbulators, with lower magnitudes on flat surfaces between the ribs, where regions of flow separation and shear layer reattachment have pronounced influences on local surface heat transfer behavior. The augmented local and spatially averaged Nusselt number ratios (rib turbulator Nusselt numbers normalized by values measured in a smooth channel) vary locally on the rib tops as Reynolds number increases. Nusselt number ratios decrease on the flat regions away from the ribs, especially at locations just downstream of the ribs, as Reynolds number increases. When adjusted to account for conduction along and within the test surface, Nusselt number ratios show different quantitative variations (with location along the test surface), compared to variations when no conduction is included. Changes include: (i) decreased local Nusselt number ratios along the central part of each rib top surface as heat transfer from the sides of each rib becomes larger, and (ii) Nusselt number ratio decreases near corners, where each rib joins the flat part of the test surface, especially on the downstream side of each rib. With no conduction along and within the test surface (and variable heat flux assumed into the air stream), globally-averaged Nusselt number ratios vary from 2.92 to 1.64 as Reynolds number increases from 10,000 to 83,700. Corresponding thermal performance parameters also decrease as Reynolds number increases over this range, with values in approximate agreement with data measured by other investigators in a square channel also with 45 deg oriented ribs.

Laminar flow of soursop juice through concentric annuli: Friction factors and rheology

2007 ◽  
Vol 78 (4) ◽  
pp. 1343-1354 ◽  
Author(s):  
A.C.A. Gratão ◽  
V. Silveira ◽  
J. Telis-Romero
Keyword(s):  
Laminar Flow ◽  
Friction Factors

Heat Transfer Enhancement Using a Convex-Patterned Surface

2003 ◽  
Vol 125 (2) ◽  
pp. 274-280 ◽  
Author(s):  
H. K. Moon ◽  
T. O’Connell ◽  
R. Sharma
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Enhancement ◽  
Reynolds Numbers ◽  
Smooth Wall ◽  
Transfer Enhancement ◽  
Transfer Coefficients ◽  
Patterned Surface ◽  
Nusselt Numbers ◽  
Friction Factors ◽  
Smooth Channel

The heat transfer rate from a smooth wall in an internal cooling passage can be significantly enhanced by using a convex patterned surface on the opposite wall of the passage. This design is particularly effective for a design that requires the heat transfer surface to be free of any augmenting features (smooth). Heat transfer coefficients on the smooth wall in a rectangular channel, which had convexities on the opposite wall were experimentally investigated. Friction factors were also measured to assess the thermal performance. Relative clearances δ/d between the convexities and the smooth wall of 0, 0.024, and 0.055 were investigated in a Reynolds number ReHD range from 15,000 to 35,000. The heat transfer coefficients were measured in the thermally developed region using a transient thermochromic liquid crystal technique. The clearance gap between the convexities and the smooth wall adversely affected the heat transfer enhancement NuHD. The friction factors (f ), measured in the aerodynamically developed region, were largest for the cases of no clearance δ/d=0). The average heat transfer enhancement Nu¯HD was also largest for the cases of no clearance δ/d=0, as high as 3.08 times at a Reynolds number of 11,456 in relative to that Nuo of an entirely smooth channel. The normalized Nusselt numbers Nu¯HD/Nuo, as well as the normalized friction factors f/fo, for all three cases, decreased with Reynolds numbers. However, the decay rate of the friction factor ratios f/fo with Reynolds numbers was lower than that of the normalized Nusselt numbers. For all three cases investigated, the thermal performance Nu¯HD/Nuo/f/fo1/3 values were within 5% to each other. The heat transfer enhancement using a convex patterned surface was thermally more effective at a relative low Reynolds numbers (less than 20,000 for δ/d=0) than that of a smooth channel.

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