Performance of Shrouded Pin-Fin Heat Sinks for Electronic Cooling
Bibliographic record
Abstract
The objective of this study is to analyze the performance of a cylindrical pin-fin heat sink in laminar forced convection. The mathematical models are presented for predicting thermal and hydraulic resistances for both in-line and staggered arrangements. Analytical/empirical correlations of friction and heat transfer coefficients are used in the analysis. The analyses are performed by using parametric variation of resistances. The effects of thermal joint, spreading, and contact resistances as well as the thermal conductivity on the overall thermal performance are examined. For a given size and heat load, it is observed that the overall performance of a pin-fin heat sink depends on a number of parameters including the dimensions of the pin-fins, pin density, longitudinal and transverse spacings, interface material, location and size of heat sources, method of manufacturing, type of heat-sink material, approach velocity, and arrangement of pins. It is also observed that the thermal resistance decreases whereas pressure drop increases with an increase in approach velocity, pin diameter, and pin density. Nomenclature Ab = area of the base plate ≡ L × W ,m 2 Ac = cross-section or contact area of a single pin, m 2 Afin = surface area of a single pin, m 2 Ahs = surface area of heat sink, m 2 CV = control volume D = pin diameter, m f = friction factor H = pin height, m h = average heat transfer coefficient, W/m 2 · K he = uniform effective film coefficient, W/m 2 · K k = thermal conductivity, W/m · K ks = harmonic mean thermal conductivity for the two solids, W/m · K L = length of heat sink in flow direction, m m = fin performance parameter, m −1 N = total number of pins in heat sink ≡ NT NL NL = number of pins in the longitudinal direction NT = number of pins in the transverse direction Nu D = Nusselt number based on pin diameter ≡ Dh/k f P = contact pressure, N/m 2 Pr = Prandtl number ≡ ν/α Q = total heat transfer rate, W Rc = contact resistance between fins and the baseplate, K/W R f = total resistance of fluid side of heat sink, K/W Rfilm = thermal resistance of exposed (unfinned) surface of the baseplate, K/W Rfin = resistance of a fin, K/W R j = thermal joint resistance between the source and the baseplate, K/W Rm = material resistance of the baseplate, K/W Rs = thermal spreading resistance in the baseplate, K/W
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".