Laminar Heat Transfer Between a Series of Parallel Plates With Surface-Mounted Discrete Heat Sources

1995 ◽  
Vol 117 (1) ◽  
pp. 52-62 ◽  
Author(s):  
S. H. Kim ◽  
N. K. Anand
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Thermal Resistance ◽  
Friction Factor ◽  
Thermal Performance ◽  
Average Nusselt Number ◽  
Computational Domain ◽  
Heat Sources ◽  
Parallel Plates ◽  
Independent Parameters

Two-dimensional laminar heat transfer between a series of parallel plates with surface mounted block heat sources was numerically studied. These channels resemble cooling passages of electronic equipment. Consideration was given only to periodically fully developed flow (PDF) and heat transfer. The computational domain was subjected to periodic condition in the streamwise direction and repeated condition in the cross-stream direction (double cyclic). The governing equations were solved by a finite volume technique. Calculations were made for a wide range of independent parameters (Re, ks/kf, s/w, d/w, H/w, and t/H). Consideration was given only to airflow (Pr=0.7). The friction factor was found to be a strong function of channel height and a weak function of block spacing. The thermal performance was studied in terms of the average Nusselt number and overall thermal resistance. For the most part, the thermal performance was independent of the Reynolds number, however, it deteriorated drastically for Re ≤ 500. The thermal resistance was found to decrease with an increase in substrate conductivity up to a particular value of ks/kf, and beyond this value thermal resistance did not decrease further. This value of ks/kf is a function of geometric parameters and occurs between 1 and 10. Correlations in terms of independent parameters were developed for friction factor, average Nusselt number, and thermal resistance.

Turbulent Heat Transfer Between a Series of Parallel Plates With Surface-Mounted Discrete Heat Sources

1994 ◽  
Vol 116 (3) ◽  
pp. 577-587 ◽  
Author(s):  
S. H. Kim ◽  
N. K. Anand
Keyword(s):  
Heat Transfer ◽  
Thermal Resistance ◽  
Electronic Equipment ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Computational Domain ◽  
Heat Sources ◽  
Parallel Plates ◽  
Wide Range ◽  
Independent Parameters

Two-dimensional turbulent heat transfer between a series of parallel plates with surface mounted discrete block heat sources was studied numerically. The computational domain was subjected to periodic conditions in the streamwise direction and repeated conditions in the cross-stream direction (Double Cyclic). The second source term was included in the energy equation to facilitate the correct prediction of a periodically fully developed temperature field. These channels resemble cooling passages in electronic equipment. The k–ε model was used for turbulent closure and calculations were made for a wide range of independent parameters (Re, Ks/Kf, s/w, d/w, and h/w). The governing equations were solved by using a finite volume technique. The numerical procedure and implementation of the k–ε model was validated by comparing numerical predictions with published experimental data (Wirtz and Chen, 1991; Sparrow et al., 1982) for a single channel with several surface mounted blocks. Computations were performed for a wide range of Reynolds numbers (5 × 104–4 × 105) and geometric parameters and for Pr = 0.7. Substrate conduction was found to reduce the block temperature by redistributing the heat flux and to reduce the overall thermal resistance of the module. It was also found that the increase in the Reynolds number decreased the thermal resistance. The study showed that the substrate conduction can be an important parameter in the design and analysis of cooling channels of electronic equipment. Finally, correlations for the friction factor (f) and average thermal resistance (R) in terms of independent parameters were developed.

Heat Transfer and Flow Friction Characteristics for Compact Cold Plates

2003 ◽  
Vol 125 (1) ◽  
pp. 104-113 ◽  
Author(s):  
Chang-Yuan Liu ◽  
Ying-Huei Hung
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Thermal Resistance ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Average Nusselt Number ◽  
Cold Plate ◽  
Air Mass

Both experimental and theoretical investigations on the heat transfer and flow friction characteristics of compact cold plates have been performed. From the results, the local and average temperature rises on the cold plate surface increase with increasing chip heat flux or decreasing air mass flow rate. Besides, the effect of chip heat flux on the thermal resistance of cold plate is insignificant; while the thermal resistance of cold plate decreases with increasing air mass flow rate. Three empirical correlations of thermal resistance in terms of air mass flow rate with a power of −0.228 are presented. As for average Nusselt number, the effect of chip heat flux on the average Nusselt number is insignificant; while the average Nusselt number of the cold plate increases with increasing Reynolds number. An empirical relationship between Nu¯cp and Re can be correlated. In the flow frictional aspect, the overall pressure drop of the cold plate increases with increasing air mass flow rate; while it is insignificantly affected by chip heat flux. An empirical correlation of the overall pressure drop in terms of air mass flow rate with a power of 1.265 is presented. Finally, both heat transfer performance factor “j” and pumping power factor “f” decrease with increasing Reynolds number in a power of 0.805; while they are independent of chip heat flux. The Colburn analogy can be adequately employed in the study.

Experimental Investigation of Coil Curvature Effect on Heat Transfer and Pressure Drop Characteristics of Shell and Coil Heat Exchanger

2014 ◽  
Vol 7 (1) ◽  
Author(s):  
M. R. Salem ◽  
K. M. Elshazly ◽  
R. Y. Sakr ◽  
R. K. Ali
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Exchanger ◽  
Friction Factor ◽  
Heat Exchangers ◽  
Average Nusselt Number ◽  
Transfer Coefficients ◽  
Nusselt Numbers ◽  
Fanning Friction Factor ◽  
Coil Heat

The present work experimentally investigates the characteristics of convective heat transfer in horizontal shell and coil heat exchangers in addition to friction factor for fully developed flow through the helically coiled tube (HCT). The majority of previous studies were performed on HCTs with isothermal and isoflux boundary conditions or shell and coil heat exchangers with small ranges of HCT configurations and fluid operating conditions. Here, five heat exchangers of counter-flow configuration were constructed with different HCT-curvature ratios (δ) and tested at different mass flow rates and inlet temperatures of the two sides of the heat exchangers. Totally, 295 test runs were performed from which the HCT-side and shell-side heat transfer coefficients were calculated. Results showed that the average Nusselt numbers of the two sides of the heat exchangers and the overall heat transfer coefficients increased by increasing coil curvature ratio. The average increase in the average Nusselt number is of 160.3–80.6% for the HCT side and of 224.3–92.6% for the shell side when δ increases from 0.0392 to 0.1194 within the investigated ranges of different parameters. Also, for the same flow rate in both heat exchanger sides, the effect of coil pitch and number of turns with the same coil torsion and tube length is remarkable on shell average Nusselt number while it is insignificant on HCT-average Nusselt number. In addition, a significant increase of 33.2–7.7% is obtained in the HCT-Fanning friction factor (fc) when δ increases from 0.0392 to 0.1194. Correlations for the average Nusselt numbers for both heat exchanger sides and the HCT Fanning friction factor as a function of the investigated parameters are obtained.

Effect of Groove Dimension on Thermal Performance of Turbulent Fluid Flow in Internally Grooved Tube

2016 ◽  
Author(s):  
Sogol Pirbastami ◽  
Samir Moujaes
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Pressure Drop ◽  
Kinetic Energy ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Turbulent Kinetic Energy ◽  
Thermal Performance ◽  
Tube Length ◽  
Pitch Length

A Computational Fluid Dynamics (CFD) study of heat enhancement in helically grooved tubes was carried out by using a 3-dimensional simulation with the STARCCM+ simulation package software. The k-ε model selected for turbulent flow simulation and the governing equations were solved by using the finite volume method. Geometric models of the current study include 3 rectangular grooved tubes with different groove width (w) and depth (e) which varies from 0.2 mm to 0.6 mm for the same tube length of 2.0m and diameter of 7.1 mm. The simulations were performed in the Reynolds number (Re) range of 4000–10000 with a uniform wall heat flux of 3150 w/m2 applied as a boundary condition on the surface of each tube. The purpose of this research is to investigate the effect of different groove dimensions on the thermal performance and pressure drop of water inside the grooved tubes and clarify the structural nature of the flow in regards to flow swirl and turbulent kinetic energy distributions. It was found that the highest performance belongs to the groove with these dimensions (w = 0.2 mm and e = 0.2 mm) which was considered for further study. Then, for these same groove dimensions four pitch size to tube diameter (p/D) ratios ranging from 1 to 18 were simulated for the same 2.0 m length tube. The results for Nusselt number (Nu) and friction factor (f) showed that by increasing the (p/D) ratio both the Nu numbers and the friction factors (f) values decrease. With a smaller pitch length (p) the turbulence intensity generated by the internal groove was also found to increase. The physical behavior of the turbulent flow and heat transfer characteristics were observed by contour plots which showed an increasing swirl flow and turbulent kinetic energy as p/D decreases. With an increase of the Nu number for smaller p/D ratio, a penalty of a higher pressure drop was obtained. The results were validated with a previous experimental work and the average error between the experimental and CFD Nu numbers and f were 13% and 8% respectively. A higher level of turbulent kinetic energy is observed near the grooves, as compared to the smooth areas of the pipe surface away from the grooves, which are expected to lead to higher levels of heat transfer. The effect of pitch length (p) on the flow pattern were plotted by streamlines along the tubes, by decreasing the pitch size (p/D ratio) an increase in the swirl is noticed as evidenced by the plots of the path lines. Finally, empirical correlations for Nusselt number and friction factor were provided as a function of p/D and Re number. This study indicates that the incorporation of the internal groove, of particular dimensions, can lead to an improvement of performance in heat exchanger devices. A limited variation of the groove dimensions was conducted and it was found that the values of Nu and f do not improve with an increase of (w) nor with that of (e) from 0.2–0.6 mm.

scholarly journals A study of turbulent heat transfer in convergent-divergent shaped microchannel with ribs and cavities using CFD

2020 ◽  
Vol 14 (1) ◽  
pp. 6344-6361
Author(s):  
Pankaj Srivastava ◽  
Anupam Dewan
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Thermal Resistance ◽  
Average Nusselt Number ◽  
Three Dimensional ◽  
Fluid Mixing ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Rectangular Microchannel ◽  
Better Than

This paper presents the effects of microchannel shape with ribs and cavities on turbulent heat transfer. Three-dimensional conjugate heat transfer using the SST k-ω turbulence model has been investigated for four different microchannels, namely, rectangular, rectangular with ribs and cavities, convergent-divergent (CD) and convergent-divergent with Ribs and Cavities (CD-RC). The flow field, pressure and temperature distributions and friction factor are analyzed, and thermal resistance and average Nusselt number are compared. The thermal performance of the CD-RC microchannel is found to be better than that of other microchannels considered in terms of an average Nusselt number increased from 16% to 40%. Heat transfer increases due to a strong fluid mixing and periodic interruption of boundary-layer. It is observed that with an increase in Reynolds number (Re), the thermal resitance drops rapidly. The thermal resistance of the CD-RC microchannel is decreased by 30% than that of the rectangular microchannel for Re ranging from 2500 to 7000. However, such design of microchannel loses its heat transfer effectiveness due to a high pumping power at high values of Re.

scholarly journals Evaluation of Multiple Semi-Twisted Tape Inserts in a Heat Exchanger Pipe Using Al2O3 Nanofluid

Nanomaterials ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 1570
Author(s):  
Yongfeng Ju ◽  
Tiezhu Zhu ◽  
Ramin Mashayekhi ◽  
Hayder I. Mohammed ◽  
Afrasyab Khan ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Heat Exchanger ◽  
Friction Factor ◽  
Base Fluid ◽  
Average Nusselt Number ◽  
Three Dimensions ◽  
Twisted Tape ◽  
Twisted Tapes

The hydrothermal performance of multiple semi-twisted tape inserts inside a heat exchanger pipe is numerically examined in three-dimensions. This study aims to find the optimum case for having the highest heat transfer enhancement with the lowest friction factor using nanofluid (Al2O3/water). A performance evaluation criterion (PEC) is defined to characterize the performance based on both friction factor and heat transfer. It was found that increasing the number of semi-twisted tapes increases the number of swirl flow streams and leads to an enhancement in the local Nusselt number as well as the friction factor. The average Nusselt number increases from 15.13 to 28.42 and the average friction factor enhances from 0.022 to 0.052 by increasing the number of the semi-twisted tapes from 0 to 4 for the Reynolds number of 1000 for the base fluid. By using four semi-twisted tapes, the average Nusselt number increases from 12.5 to 28.5, while the friction factor reduces from 0.155 to 0.052 when the Reynolds number increases from 250 to 1000 for the base fluid. For the Reynolds number of 1000, the increase in nanofluid concentration from 0 to 3% improves the average Nusselt number and friction factor by 6.41% and 2.29%, respectively. The highest PEC is equal to 1.66 and belongs to the Reynolds number of 750 using four semi-twisted tape inserts with 3% nanoparticles. This work offers instructions to model an advanced design of twisted tape integrated with tubes using multiple semi-twisted tapes, which helps to provide a higher amount of energy demand for solar applications.

An Approximate Method for Predicting Laminar Heat Transfer Between Parallel Plates Having Embedded Heat Sources

1995 ◽  
Vol 117 (1) ◽  
pp. 63-68 ◽  
Author(s):  
R. S. Figliola ◽  
P. G. Thomas
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Approximate Method ◽  
Numerical Solutions ◽  
Convection Heat Transfer ◽  
Flow Regimes ◽  
Experimental Result ◽  
Heat Sources ◽  
Parallel Plates ◽  
Two Dimensional Flow

An approximate method for predicting the forced convection heat transfer for flow between parallel plates having embedded, discrete heat sources on one or both sides is presented. The spacing between sources is considered as adiabatic and the two-dimensional flow is laminar. The characteristics of such a flow can be described as flow in the isolated plate, developing flow, and fully developed flow regimes. The analysis uses appropriate forms for the surface temperature and Nusselt number solutions for the flow regimes encountered. Superposition is then applied to develop the discrete array solution for temperature and Nusselt number regardless of the arbitrary and step nature of the boundary conditions. Comparisons to existing numerical solutions show good agreement to within five percent of the predicted temperatures. A direct simulation of an existing experimental result shows reasonable agreement in the Nusselt number solution. These results validate the methodology for practical use including electronic cooling applications.

Laminar Mixed Convection in Horizontal Concentric Annuli With Four Porous Blocks Attached on the Outside of the Inner Cylinder

2010 ◽  
Author(s):  
Yacine Ould-Amer
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Friction Factor ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Darcy Number ◽  
Conductivity Ratio ◽  
Laminar Mixed Convection ◽  
Porous Blocks

A numerical study is performed to investigate the performance of an innovative thermal system to improve the heat transfer in horizontal annulus. With attached four porous blocks on the inner cylinder, steady laminar mixed convection is presented for the fully developed region of horizontal concentric annuli. Results are presented for a range of the values of the Grashoff number, the Darcy number and the conductivity ratio between the porous medium and the fluid. Results are presented in the form of contours plots of the streamlines and for the temperature isotherms, and in terms of the overall heat transfer coefficients and friction factor. The average Nusselt number increases significantly with an increase of the conductivity ratio and the Grashoff number. With the use of the four porous blocks, the friction factor is consequently increased compared with the situation without porous blocks. The decrease of the Darcy number leads to an increase of the friction factor. If the fully fluid case is taken as a reference, the use of porous blocks is justified only when the ratio of the average Nusselt number to the friction factor is enhanced. The enhancement occurs for the Darcy number higher than 10−3 and for the higher conductivity ratio.

Enhanced heat transfer in a labyrinth channels with ribs of different shape

2019 ◽  
Vol 30 (2) ◽  
pp. 724-741
Author(s):  
Wei Du ◽  
Lei Luo ◽  
Songtao Wang ◽  
Jian Liu ◽  
Bengt Ake Sunden
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Factor ◽  
Gas Turbine ◽  
Flow Structure ◽  
Thermal Performance ◽  
Geometric Model ◽  
Minor Effect ◽  
Content Type ◽  
Labyrinth Channel

Purpose The purpose of this study is to enhance the thermal performance in the labyrinth channel by different ribs shape. The labyrinth channel is a relatively new cooling structure to decrease the temperature near the trailing region of gas turbine. Design/methodology/approach Based on the geometric similarity, a simplified geometric model is used. The k − ω turbulence model is used to close the Navier–Stokes equations. Five rib shapes (one rectangular rib, two arched ribs and two trapezoid ribs) and five Reynolds numbers (10,000 to 50,000) are considered. The Nusselt number, flow structure and friction factor are analyzed. Findings Nusselt number is tightly related to the rib shape in the labyrinth channel. The different shapes of the ribs result in different horseshoe vortex and wake region. In general, the arched rib brings the highest Nusselt number and friction factor. The Nusselt number is increased by 15.8 per cent compared to that of trapezoidal ribs. High Nusselt number is accompanied by the high friction factor in a labyrinth channels. The friction factor is increased by 64.6 per cent compared to rectangular ribs. However, the rib shape has a minor effect on the overall thermal performance. Practical implications This study is useful to protect the trailing region of advanced gas turbine. Originality/value This paper presents the flow structure and heat transfer characteristics in a labyrinth channel with different rib shapes.

The Nonlinear Increase of Nusselt Number With Friction Factor in Fully Developed Laminar Duct Flow

2004 ◽  
Vol 126 (5) ◽  
pp. 840-842 ◽  
Author(s):  
E. Van den Bulck
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Factor ◽  
Constant Heat Flux ◽  
Duct Flow ◽  
Parallel Plates ◽  
Physical Explanation ◽  
Constant Heat ◽  
Constant Wall Temperature ◽  
Nonlinear Increase

This paper deals with heat transfer in fully developed laminar flow in cylindrical ducts. For this type of flow, the product of friction factor with Reynolds number f Re and the Nusselt number are both constants. It is known that the Nusselt number increases with the shift of boundary condition from constant wall temperature to constant heat flux. Also, the ratio of the Nusselt number to f Re increases when the convexity of the duct is reduced, e.g., a cylinder visavis parallel plates. This paper gives a simple physical explanation for these two phenomenona.

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