On the Numerical Investigation of Natural-Convection Heat Sinks Across a Wide Range of Flow and Operating Conditions
Many designs for natural-convection heat sinks and semi-empirical correlations have been proposed in the recent years, but they are only valid in a limited range of Elenbaas numbers <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-10-01
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| Series: | Fluids |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2311-5521/9/11/252 |
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| Summary: | Many designs for natural-convection heat sinks and semi-empirical correlations have been proposed in the recent years, but they are only valid in a limited range of Elenbaas numbers <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mi>l</mi></mrow></semantics></math></inline-formula> and were mostly tested for laminar flows. To alleviate those limits, parametric studies with 2D and quasi-3D models were carried out, in ranges of Grashof numbers up to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.55</mn><mo>×</mo><msup><mn>10</mn><mn>11</mn></msup></mrow></semantics></math></inline-formula> and Elenbaas numbers up to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3.42</mn><mo>×</mo><msup><mn>10</mn><mn>7</mn></msup></mrow></semantics></math></inline-formula>. Ansys Fluent’s laminar, transition-SST, SST k-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula> and k-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula> models were applied. In addition, when used in this valid range, i.e., mean Elenbaas numbers, with the simplified quasi-3D model, the transition-SST model could predict better results, overestimating the heat flux by 10 to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>15</mn><mo>%</mo></mrow></semantics></math></inline-formula> compared to semi-empirical correlations. The 2D model was not deemed satisfying, regarding turbulence models. Consequently, a quasi-3D model was developed: it appeared to be an efficient trade-off between computational time and prediction accuracy, in particular for turbulence models. New grouping factors were also found, to ensure proper dimensioning of natural-convection heat sinks. They corresponded to non-dimensional parameters that dictated the physical behaviour of the heat sink with respect to the semi-empirical correlations. Typically, the ratio of the spacing to the optimal spacing predicted by Bar-Cohen’s correlation turned out to be an appropriate grouping factor with a threshold of 1, above which the fins could safely be considered as isolated, thus greatly simplifying all further calculations. |
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| ISSN: | 2311-5521 |