Friction Factors for Fully Developed Turbulent Flow in Ducts With and Without Heat Transfer

1964 ◽  
Vol 86 (3) ◽  
pp. 627-636 ◽  
Author(s):  
G. W. Maurer ◽  
B. W. LeTourneau
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Circular Tube ◽  
Rectangular Channel ◽  
Reynolds Numbers ◽  
Inlet Temperature ◽  
Equivalent Diameter ◽  
Friction Factors ◽  
Rectangular Channels ◽  
Fully Developed Turbulent Flow

Tests were performed with water flowing vertically upward through a 0.087-in. × 1-in. × 27-in. long rectangular channel to determine friction factors with and without heat transfer. The following range of variables was covered: Mass velocities: 0.60 × 106 to 4.0 × 106 lbm/hr-ft2; Heat flux: 0 to 1.6 × 106 Btu/hr-ft2; Inlet temperature: 59 to 510 deg F; Pressures: 300 to 2000 psia. The isothermal data confirmed the use of the hydraulic equivalent diameter with the conventional circular tube friction factors for narrow rectangular channels at Reynolds numbers from 4 × 103 to 5 × 105. Using the results of the heated tests and the data existing in the literature, a general correlation was formulated which correlated the data for both water and air.

Local Single-Phase Heat Transfer Research of Natural Circulation in Narrow Rectangular Channel

2017 ◽  
Author(s):  
Zhiqiang Zhu ◽  
Xiaxin Cao ◽  
Changqi Yan ◽  
Chunping Tian
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Inclination Angle ◽  
Local Nusselt Number ◽  
Single Phase ◽  
Natural Circulation ◽  
Rectangular Channel ◽  
Inlet Temperature

In order to explore and analyze the heat transfer characteristics in narrow rectangular channel, experiments on local single-phase heat transfer of natural circulation in a one-side heating narrow rectangular channel have been conducted under vertical and inclined condition. The thermotechnical parameters such as inlet temperature, heat flux and inclination angle varies during the experiments. The width of the flow channel is 40 mm and the narrow gap is 2 mm. It is heated from one side with a homogeneous and constant heat flux and the working medium is deionized water. Based on the experimental results, under vertical condition, the driving force in the loop goes up and the Reynolds number also increases when the inlet temperature is elevated, which causes an increase in local Nusselt number. When the heat flux rises, the local Nusselt number increases and the heat transfer temperature difference increases. The local Nusselts number is influenced by entrance effect and the entrance region length is computed for laminar and turbulent flow. Under inclined condition, with the inclination angle from −30° to 30°, it is found that when the inclination angle is positive, the local Nusselt number in fully developed region is larger than that under vertical condition and increases with the angle value, even though the Reynolds number decreases by the effect of incline. This phenomenon is explained by giving an analysis of the natural convection, which is characterized by the normal Grashof number, in the direction perpendicular to the heating plat. Moreover, the variation of heat transfer is also interpreted on the basis of field coordination principle. However, when the inclination angle is negative, the heat transfer shows no obvious difference between vertical condition and inclined condition.

CFD Analysis on Wall Boiling Model During Subcooled Boiling in Vertical Narrow Rectangular Channel

2018 ◽  
Author(s):  
Tingting Ren ◽  
Changqi Yan ◽  
Meiyue Yan ◽  
Shengzhi Yu
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Fluid Model ◽  
Rectangular Channel ◽  
Subcooled Boiling ◽  
Site Density ◽  
Rectangular Channels ◽  
Two Fluid Model ◽  
Nucleate Site ◽  
Two Fluid

Two-fluid model is a common method to simulate the subcooled flow boiling heat transfer, in which the wall boiling model is mainly used for the partition of wall heat flux and the mass transfer between two phases on the wall. The model determines the amount of vapor phase and predicts the cross-sectional void fraction in the channel, nucleate site density and bubble departure diameter play an important role in the accurate prediction of wall boiling model. Eulerian two-fluid model coupled with Rensselaer Polytechnic Institute (RPI) wall boiling model is employed to simulate the heat transfer characteristics and boiling phenomena in vertical narrow rectangular channels by using FLUENT code. Based on the experimental data of subcooled boiling in vertical narrow rectangular channel, different combinations of nucleate site density and bubble departure diameter correlations are used to calculate under different conditions of heat flux and inlet subcooling. Comparing the calculated heat transfer coefficients along the vertical height with experimental results, it can be found that these two parameters have a significant effect on the subcooled boiling heat transfer in narrow rectangular channels. Different parameter combinations lead to differences in wall heat flux distribution, different heat flux and inlet subcooling also have different effects on these models, which eventually lead to different evaporative heat flux, thus affecting the prediction of void fraction.

Heat Transfer and Friction Factor Measurements in Ducts With Staggered and In-Line Ribs

1993 ◽  
Vol 115 (1) ◽  
pp. 58-65 ◽  
Author(s):  
Ying-Jong Hong ◽  
Shou-Shing Hsieh
Keyword(s):  
Heat Transfer ◽  
Local Heat Transfer ◽  
Reynolds Numbers ◽  
Local Heat ◽  
Aspect Ratios ◽  
Friction Factors ◽  
Rectangular Channels ◽  
Channel Aspect Ratio ◽  
Semi Empirical ◽  
Rib Roughened

The combined effects of rib alignment and channel aspect ratio on the distributions of the local heat transfer coefficient and on the friction factors for developing and fully developed flow in short square and rectangular channels (L/DH = 13.5–18) with a pair of opposite rib-roughened walls were determined for Reynolds numbers ranging from 13,000 to 130,000. The channel aspect ratios are 1/2 and 1 and the rib alignment configurations are arranged as staggered and in-line types, respectively. The pitch to rib height ratio is 5.31 for all test channels. The local heat transfer distributions on the bottom rib-roughened wall from the channel entrance to the downstream region are presented and discussed. Semi-empirical heat transfer and friction correlations are developed, and the results are compared with those of previous investigations for similarly configured channels, which were roughened by regularly spaced transverse ribs.

scholarly journals Numerical study of heat transfer in rectangular channels with single pin fin and pin fin-dimple

2019 ◽  
Vol 124 ◽  
pp. 01010
Author(s):  
A. N. Rogalev ◽  
N. D. Rogalev ◽  
V. O. Kindra ◽  
S. K. Osipov ◽  
A. S. Zonov
Keyword(s):  
Heat Transfer ◽  
Cooling System ◽  
Numerical Study ◽  
Rectangular Channel ◽  
Reynolds Numbers ◽  
Heat Transfer Analysis ◽  
Navier Stokes ◽  
Pin Fin ◽  
Rectangular Channels ◽  
Calculation Results

Evaluation of the heat transfer and hydraulic performance of a new pin fin-dimple cooling system in a rectangular channel shows its advantage. The performance are compared with the pin fin system ones with 3-D Reynolds averaged Navier-Stokes (RANS) equations. The fluid flow and heat transfer analysis for the Reynolds numbers from 8000 to 70000 involved the shear stress transport turbulence model. The new system forms a high-intensity vortex around the pin fin-dimple that increases the near-wall turbulent mixing level that intensifies the heat transfer. The calculation results indicate increases of the averaged Nusselt number and the averaged friction factor of 7–13% and 7–12% respectively against the pin fin.

Effects of a High Porous Material on Heat Transfer and Flow in a Circular Tube

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
Koichi Ichimiya ◽  
Tetsuaki Takeda ◽  
Takuya Uemura ◽  
Tetsuya Norikuni
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Porous Material ◽  
Entropy Generation ◽  
Circular Tube ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Working Fluid ◽  
Equivalent Diameter

This paper describes the heat transfer and flow characteristics of a heat exchanger tube filled with a high porous material. Fine copper wires (diameter: 0.5 mm) were inserted in a circular tube dominated by thermal conduction and forced convection. The porosity was from 0.98 to 1.0. The working fluid was air. The hydraulic equivalent diameter was cited as the characteristic length in the Nusselt number and the Reynolds number. The Nusselt number and the friction factor were expressed as functions of the Reynolds number and porosity. The thermal performance was evaluated by the ratio of the Nusselt number with and without a high porous material and the entropy generation. It was recognized that the high porous material was effective in low Reynolds numbers and the Reynolds number, which minimized the entropy generation existed.

Experimental and Numerical Investigation of Convection Heat Transfer of CO2 at Super-Critical Pressures in a Vertical Mini Tube

2006 ◽  
Author(s):  
Peixue Jiang ◽  
Yu Zhang ◽  
Runfu Shi
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Wall Temperature ◽  
Flow Direction ◽  
Convection Heat Transfer ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Heat Fluxes ◽  
Inlet Temperature ◽  
Convection Heat

Convection heat transfer of CO2 at supercritical pressures in a 0.27mm diameter vertical mini tube was investigated experimentally and numerically. The tests investigated the effects of inlet temperature, pressure, mass flow rate, heat flux, buoyancy and flow direction on the convection heat transfer. The experimental results indicate that for inlet Reynolds numbers exceeding 4000, the flow direction and buoyancy force have little influence on the local wall temperature, with no deterioration of the convection heat transfer observed in either flow direction. The convection heat transfer coefficient initially increases with increasing heat flux and then decreases with further increases in the heat flux for both upward and downward flows. These effects are due to the variation of the thermophysical properties, especially cp. For inlet Reynolds numbers less than 2900, the local wall temperature varies nonlinearly for both flow directions. The numerical results correspond well with the experimental data for inlet Reynolds numbers exceeding 4000 using several turbulence models, especially the Realizable k-ε turbulence model. However, for inlet Reynolds numbers less than 2900, none of the turbulence models could properly simulate the convection heat transfer at super-critical pressures with high heat fluxes.

Numerical Prediction of Flow and Heat Transfer in a Rectangular Channel With a Built-In Circular Tube

2003 ◽  
Vol 125 (3) ◽  
pp. 413-421 ◽  
Author(s):  
S. Tiwari ◽  
G. Biswas ◽  
P. L. N. Prasad ◽  
Sudipta Basu
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Circular Tube ◽  
Transverse Velocity ◽  
Rectangular Channel ◽  
Saddle Points ◽  
Reynolds Numbers ◽  
Transition To Turbulence ◽  
Bottom Plate ◽  
Flow And Heat Transfer

A numerical investigation of flow and heat transfer in a rectangular duct with a built-in circular tube was carried out for moderate Reynolds numbers and varying blockage ratios. Since the heat transfer in the duct is dictated by the flow structure, the study was directed towards characterization of the flow. To this end, the topological theory shows promise of becoming a powerful tool for the study of flow structures. The limiting streamlines on the tube and the bottom plate reveal a complex flow field. The separation lines and points of singularity (saddle points and nodal points) were investigated. The iso-Nusselt number contours and span-averaged Nusselt number distribution in the flow passage shed light on the heat transfer performance in the duct. The investigation was necessitated by the need to enhance heat transfer in fin-tube heat exchangers through identification of the zones of poor heat transfer. The predicted results compare well with the well documented experimental results available in the literature. In the range of Reynolds numbers considered for the present case, no need is felt to employ any turbulence model in order to describe the heat transfer behavior. Time series signals of the transverse velocity component in the wake zone are presented with their FFT and time-delay plots. The onset of turbulence is not observed up to the highest value of the Reynolds number considered in the present case. This confirms that the transition to turbulence is delayed in the present case compared with that observed for flow past a circular tube placed in an infinite medium. The reason may be attributed to the narrow gap between the no-slip channel walls.

An Experimental and Numerical Study of Heat Transfer and Pressure Loss in a Rectangular Channel With V-Shaped Ribs

2006 ◽  
Author(s):  
Michael Maurer ◽  
Jens von Wolfersdorf ◽  
Michael Gritsch
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Enhancement ◽  
Thermal Performance ◽  
Pressure Loss ◽  
Numerical Study ◽  
Rectangular Channel ◽  
Reynolds Numbers ◽  
Transfer Enhancement ◽  
High Reynolds Numbers ◽  
High Reynolds

An experimental and numerical study was conducted to determine the thermal performance of V-shaped ribs in a rectangular channel with an aspect ratio of 2:1. Local heat transfer coefficients were measured using the steady state thermochromic liquid crystal technique. Periodic pressure losses were obtained with pressure taps along the smooth channel sidewall. Reynolds numbers from 95,000 to 500,000 were investigated with V-shaped ribs located on one side or on both sides of the test channel. The rib height-to-hydraulic diameter ratios (e/Dh) were 0.0625 and 0.02, and the rib pitch-to-height ratio (P/e) was 10. In addition, all test cases were investigated numerically. The commercial software FLUENT™ was used with a two-layer k-ε turbulence model. Numerically and experimentally obtained data were compared. It was determined that the heat transfer enhancement based on the heat transfer of a smooth wall levels off for Reynolds numbers over 200,000. The introduction of a second ribbed sidewall slightly increased the heat transfer enhancement whereas the pressure penalty was approximately doubled. Diminishing the rib height at high Reynolds numbers had the disadvantage of a slightly decreased heat transfer enhancement, but benefits in a significantly reduced pressure loss. At high Reynolds numbers small-scale ribs in a one-sided ribbed channel were shown to have the best thermal performance.

Heat Transfer to Supercritical Water in Vertical Annular Channel and 3-Rod Bundle

2009 ◽  
Author(s):  
V. G. Razumovskiy ◽  
Eu. N. Pis’mennyy ◽  
A. Eu. Koloskov ◽  
I. L. Pioro
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Supercritical Water ◽  
Annular Channel ◽  
Heat Fluxes ◽  
Inlet Temperature ◽  
Outlet Temperature ◽  
Rod Bundle ◽  
Temperature Regimes ◽  
Outside Diameter

The results of heat transfer to supercritical water flowing upward in a vertical annular channel (1-rod channel) and tight 3-rod bundle consisting of the tubes of 5.2-mm outside diameter and 485-mm heated length are presented. The heat-transfer data were obtained at pressures of 22.5, 24.5, and 27.5 MPa, mass flux within the range from 800 to 3000 kg/m2·s, inlet temperature from 125 to 352°C, outlet temperature up to 372°C and heat flux up to 4.6 MW/m2 (heat flux rate up to 2.5 kJ/kg). Temperature regimes of the annular channel and 3-rod bundle were stable and easily reproducible within the whole range of the mass and heat fluxes, even when a deteriorated heat transfer took place. The data resulted from the study could be applicable for a reference estimation of heat transfer in future designs of fuel bundles.

Numerical Simulation of Flow and Heat Transfer in Rectangular Channel With Different Aspect Ratios

2016 ◽  
Author(s):  
Liu Wenhua ◽  
Mo Yang ◽  
Li Ling ◽  
Qiao Liang ◽  
Yuwen Zhang
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
Characteristic Length ◽  
Rectangular Channel ◽  
Equivalent Diameter ◽  
Correction Coefficient ◽  
Corner Region ◽  
Flow And Heat Transfer ◽  
Aspect Ratios

Turbulent flow and heat transfer in rectangular channel has an important significance in engineering. Conventional approach to caculate Nusselt number of rectangular channel approximately is to take the equivalent diameter as the characteristic length and use the classic circular channel turbulent heat transfer coefficient correlations. However, under these conditions, the caculation error of Nusselt number can reach to 14% and thus this approach can not substantially describe the variation of Nusselt number of rectangular cross-sections with different aspect ratios. Therefore, caculation by using equivalent diameter as the characteristic length in classic experiment formula needs to be corrected. Seven groups of rectangular channel models with different aspect ratios have been studied numerically in this paper. By using standard turbulence model, the flow and heat transfer law of air with varing properties has been studied in 4 different sets of conditions in Reynolds number. The simulation and experimental results are in good agreement. The simulation results show that with the increase of aspect ratio, the cross-sectional average Nusselt number increased, Nusselt number of circumferential wall distributed more evenly and the difference between the infinite plate channel and square channel went up to 25%. The effects of corner region and long\short sides on heat transfer have also been investigated in this paper. Results show that in rectangular channel, heat transfer in corner region is significantly weaker than it in other region. With the increase of aspect ratio, effect on the long side of heat transfer of the short side is gradually reduced, and then eventually eliminates completely in the infinite flat place. Based on the studies above, correction coefficient for rectangular channels with different aspect ratios has been proposed in this paper and the accuracy of the correction coefficient has been varified by numerical simulations. This can reflect the variation of Nusselt number under different aspect ratios more effectively and thus has current significance for project to calculate Nusselt number of heat transfer in rectangular channel.

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