Entrance and Exit Losses for Developing Flow in Plain Fin Heat Sinks

2003 ◽  
Author(s):  
Ralph L. Webb ◽  
Jin Wook Paek
Keyword(s):  
Pressure Drop ◽  
Parallel Plate ◽  
Flow Region ◽  
Heat Sinks ◽  
Graphical Form ◽  
Parallel Plates ◽  
Fully Developed Flow ◽  
Developing Flow ◽  
Contraction Ratio ◽  
Electronic Heat

Prediction of pressure drop for duct flow through heat sinks involves calculation of inlet and exit losses. These predictions are typically done using Kc and Ke for “parallel plate channels” from the Kays and London book, Compact Heat Exchangers. However, these equations assume fully developed flow at the exit and thus include the effect of full velocity profile development. Electronic heat sinks operate in the “developing flow” region. So, use of the published Kc and Ke from the Kays and London book will result in over-estimate of the actual Kc and Ke values. The authors have performed analysis that allows accurate calculation of Kc and Ke values with parallel plate channels for operation in the “developing flow” region. The results are presented in graphical form as a function of contraction ratio and x+ (= x/DhRe). These results will allow accurate estimate of Kc and Ke values for developing flow. Entrance and exit losses can account for as much as 30% of the total pressure drop in electronic heat sinks having short flow lengths. However, the error associated with evaluation of Kc and Ke based on fully developed flow for parallel plates is small.

Wall-retardation effects on particles settling through non-Newtonian fluids in parallel plates

2016 ◽  
Vol 70 (10) ◽  
Author(s):  
Guo-Dong Zhang ◽  
Ming-Zhong Li ◽  
Jian-Quan Xue ◽  
Lei Wang ◽  
Jin-Lin Tian
Keyword(s):  
Parallel Plate ◽  
Linear Trend ◽  
Flow Region ◽  
Newtonian Fluids ◽  
Size Ratio ◽  
Retardation Effect ◽  
Parallel Plates ◽  
Sodium Carboxymethylcellulose ◽  
New Correlation ◽  
Fluid Media

AbstractWalls can exert a retardation effect on particles settling in bounded fluid media. In this work, the parallel plate retardation effect was studied for particles falling in non-Newtonian fluids along the centreline of parallel plate ducts. The eccentric effect was also investigated for those particles which approached the wall. For spheres settling in sodium carboxymethylcellulose (CMC) solutions, the variation in wall factors against the size ratio of the sphere’s diameter to the parallel plate wall spacing shows a non-linear trend; the particle settling velocity is independent at small size ratio, and then decreases quickly with increase in size ratio. A new correlation was presented covering a wider range of size ratios (0.02 < λ < 0.83) in the flow region of 0.0011 <

Estimation of transient boundary flux for a developing flow in a parallel plate channel

2014 ◽  
Vol 24 (3) ◽  
pp. 522-544 ◽  
Author(s):  
Ajit Kumar Parwani ◽  
Prabal Talukdar ◽  
P.M.V. Subbarao
Keyword(s):  
Heat Flux ◽  
Inverse Problem ◽  
Parallel Plate ◽  
Practical Importance ◽  
Unknown Boundary ◽  
Parallel Plates ◽  
Content Type ◽  
Developing Flow ◽  
Boundary Flux ◽  
Plate Channel

Purpose – The purpose of this paper is to develop a numerical model for estimating the unknown boundary heat flux in a parallel plate channel for the case of a hydrodynamically and thermally developing laminar flow. Design/methodology/approach – The conjugate gradient method (CGM) is used to solve the inverse problem. The momentum equations are solved using an in-house computational fluid dynamics (CFD) source code. The energy equations along with the adjoint and sensitivity equations are solved using the finite volume method. Findings – The effects of number of measurements, distribution of measurements and functional form of unknown flux on the accuracy of estimations are investigated in this work. The prediction of boundary flux by the present algorithm is found to be quite reasonable. Originality/value – It is noticed from the literature review that study of inverse problem with hydrodynamically developing flow has not received sufficient attention despite its practical importance. In the present work, a hydrodynamically and thermally developing flow between two parallel plates is considered and unknown transient boundary heat flux at the upper plate of a parallel plate channel is estimated using CGM.

Symmetric Sink Flow Between Parallel Plates

1978 ◽  
Vol 100 (4) ◽  
pp. 477-484 ◽  
Author(s):  
H. D. Murphy ◽  
M. Coxon ◽  
D. M. McEligot
Keyword(s):  
Boundary Layer ◽  
Volumetric Flow Rate ◽  
Internal Boundary Layer ◽  
Internal Boundary ◽  
External Boundary ◽  
Parallel Plates ◽  
Fully Developed Flow ◽  
Developing Flow ◽  
Steady Laminar ◽  
Disk Spacing

Steady, laminar, incompressible flow converging radially between two stationary disks is investigated numerically as a continuously developing flow problem under the internal boundary layer approximations. At dimensionless radii much greater than one the velocity profile becomes parabolic and invariant, but at radii less than one a typical external boundary layer evolves close to the wall with an approximately uniform core region; and the boundary layer thickness decreases from one-half the disk spacing to values proportional to the local radii as the flow accelerates. At large radii the friction factor approaches the classic value obtained for fully developed flow between infinite plates, 6ν/Vt, but at small radii it approaches the constant 2.17/R0, where R0 is an overall Reynolds number based on the volumetric flow rate and the disk spacing and is independent of radius. Tabular and graphical results are provided for the intermediate range of radii, where both viscous and inertial effects are important and exact analyses are not available.

Validation of Analytical Methods for Parallel Plate Fin Heat Sinks

2004 ◽  
Author(s):  
Guoping Xu ◽  
Henry Jung
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Pressure Drop ◽  
Test Data ◽  
Analytical Methods ◽  
Parallel Plate ◽  
Heat Sinks ◽  
Analytical Models ◽  
Experimental Investigations ◽  
Duct Flow

Several analytical models to predict heat transfer and pressure drop performance for parallel plate fin heat sinks are available in the literature. However, the experimental data to validate these models are very limited especially for high fin density heat sinks. In this paper, a new method is proposed to predict thermal performance in both laminar flow and turbulent flow. This method and other models selected from the literature have been compared to the test data. Experimental investigations were conducted with fully-duct flow for parallel plate fin heat sinks to measure overall thermal resistance and pressure drop. Three heat sinks with different fin materials and fin configurations are tested. We conclude by recommending some of the analytical methods for engineering applications by comparing the test data with predictions.

scholarly journals Applicability of the Cox-Merz Rule to High-Density Polyethylene Materials with Various Molecular Masses

Polymers ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1218
Author(s):  
Raffael Rathner ◽  
Wolfgang Roland ◽  
Hanny Albrecht ◽  
Franz Ruemer ◽  
Jürgen Miethlinger
Keyword(s):  
Molecular Weight ◽  
Pressure Drop ◽  
High Molecular Weight ◽  
High Density Polyethylene ◽  
Parallel Plate ◽  
Empirical Relationship ◽  
Polymer Processing ◽  
High Density ◽  
Viscosity Data ◽  
Molecular Masses

The Cox-Merz rule is an empirical relationship that is commonly used in science and industry to determine shear viscosity on the basis of an oscillatory rheometry test. However, it does not apply to all polymer melts. Rheological data are of major importance in the design and dimensioning of polymer-processing equipment. In this work, we investigated whether the Cox-Merz rule is suitable for determining the shear-rate-dependent viscosity of several commercially available high-density polyethylene (HDPE) pipe grades with various molecular masses. We compared the results of parallel-plate oscillatory shear rheometry using the Cox-Merz empirical relation with those of high-pressure capillary and extrusion rheometry. To assess the validity of these techniques, we used the shear viscosities obtained by these methods to numerically simulate the pressure drop of a pipe head and compared the results to experimental measurements. We found that, for the HDPE grades tested, the viscosity data based on capillary pressure flow of the high molecular weight HDPE describes the pressure drop inside the pipe head significantly better than do data based on parallel-plate rheometry applying the Cox-Merz rule. For the lower molecular weight HDPE, both measurement techniques are in good accordance. Hence, we conclude that, while the Cox-Merz relationship is applicable to lower-molecular HDPE grades, it does not apply to certain HDPE grades with high molecular weight.

scholarly journals Evaluation of Active Heat Sinks Design under Forced Convection—Effect of Geometric and Boundary Parameters

Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2041
Author(s):  
Eva C. Silva ◽  
Álvaro M. Sampaio ◽  
António J. Pontes
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Additive Manufacturing ◽  
Pressure Drop ◽  
Forced Convection ◽  
Thermal Performance ◽  
Heat Sinks ◽  
Trapezoidal Shape ◽  
Computational Fluid Dynamics Simulations ◽  
Dynamics Simulations

This study shows the performance of heat sinks (HS) with different designs under forced convection, varying geometric and boundary parameters, via computational fluid dynamics simulations. Initially, a complete and detailed analysis of the thermal performance of various conventional HS designs was taken. Afterwards, HS designs were modified following some additive manufacturing approaches. The HS performance was compared by measuring their temperatures and pressure drop after 15 s. Smaller diameters/thicknesses and larger fins/pins spacing provided better results. For fins HS, the use of radial fins, with an inverted trapezoidal shape and with larger holes was advantageous. Regarding pins HS, the best option contemplated circular pins in combination with frontal holes in their structure. Additionally, lattice HS, only possible to be produced by additive manufacturing, was also studied. Lower temperatures were obtained with a hexagon unit cell. Lastly, a comparison between the best HS in each category showed a lower thermal resistance for lattice HS. Despite the increase of at least 38% in pressure drop, a consequence of its frontal area, the temperature was 26% and 56% lower when compared to conventional pins and fins HS, respectively, and 9% and 28% lower when compared to the best pins and best fins of this study.

Thermally developing forced convection flow through porous concentric pipes annular duct

2021 ◽  
pp. 095440622110022
Author(s):  
Farhan Ahmed
Keyword(s):  
Flow Region ◽  
Axial Direction ◽  
Darcy Number ◽  
Convection Flow ◽  
Axial Distance ◽  
Cross Sectional ◽  
Developing Flow ◽  
Annular Sector ◽  
Flow Through ◽  
The Cross

This article shows the thermally developing flow through concentric pipes annular sector duct by describing the Darcy Brinkman flow field. The cross sectional convection-diffusion terms are transformed in power law discretized form by integrating over the differential volume, whereas backward difference scheme is used in the axial direction of heat flow. With the help of semi implicit method for pressure linked equations-revised ( SIMPLE-R), we get the solution of the governing problem. The graphs of velocity profiles against R and average Nusselt number against axial distance are plotted for different values of Darcy number and geometrical configuration parameters. It has been pointed out that velocity and thermal entrance length decrease, when we decrease the value of Darcy number. By decreasing the cross section of the concentric pipes annular sector duct in the transverse direction, thermally fully developed flow region develops earlier.

Two-Phase Flow and Heat Transfer in Rectangular Micro-Channels

2003 ◽  
Author(s):  
Weilin Qu ◽  
Seok-Mann Yoon ◽  
Issam Mudawar
Keyword(s):  
Heat Transfer ◽  
Pressure Drop ◽  
Flow Pattern ◽  
Two Phase Flow ◽  
Flow Patterns ◽  
Heat Sinks ◽  
Phase Flow ◽  
Micro Channel ◽  
Two Phase ◽  
Micro Channels

Knowledge of flow pattern and flow pattern transitions is essential to the development of reliable predictive tools for pressure drop and heat transfer in two-phase micro-channel heat sinks. In the present study, experiments were conducted with adiabatic nitrogen-water two-phase flow in a rectangular micro-channel having a 0.406 × 2.032 mm cross-section. Superficial velocities of nitrogen and water ranged from 0.08 to 81.92 m/s and 0.04 to 10.24 m/s, respectively. Flow patterns were first identified using high-speed video imaging, and still photos were then taken for representative patterns. Results reveal that the dominant flow patterns are slug and annular, with bubbly flow occurring only occasionally; stratified and churn flow were never observed. A flow pattern map was constructed and compared with previous maps and predictions of flow pattern transition models. Annual flow is identified as the dominant flow pattern for conditions relevant to two-phase micro-channel heat sinks, and forms the basis for development of a theoretical model for both pressure drop and heat transfer in micro-channels. Features unique to two-phase micro-channel flow, such as laminar liquid and gas flows, smooth liquid-gas interface, and strong entrainment and deposition effects are incorporated into the model. The model shows good agreement with experimental data for water-cooled heat sinks.

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