Natural Convection Heat Transfer from an Isothermal Plate
Using boundary-layer theory, natural convection heat transfer formulas that are accurate over a wide range of Rayleigh numbers (<i>Ra</i>) were developed in the 1970s and 1980s for vertical and downward-facing plates. A comprehensive formula for upward-facing plates remained unsolved bec...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Thermo |
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| Online Access: | https://www.mdpi.com/2673-7264/3/1/10 |
| _version_ | 1797608851923533824 |
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| author | Aubrey Jaffer |
| author_facet | Aubrey Jaffer |
| author_sort | Aubrey Jaffer |
| collection | DOAJ |
| description | Using boundary-layer theory, natural convection heat transfer formulas that are accurate over a wide range of Rayleigh numbers (<i>Ra</i>) were developed in the 1970s and 1980s for vertical and downward-facing plates. A comprehensive formula for upward-facing plates remained unsolved because they do not form conventional boundary-layers. From the thermodynamic constraints on heat-engine efficiency, the novel approach presented here derives formulas for natural convection heat transfer from isothermal plates. The union of four peer-reviewed data-sets spanning <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi>R</mi><mi>a</mi><mo><</mo><msup><mn>10</mn><mn>12</mn></msup></mrow></semantics></math></inline-formula> has 5.4% root-mean-squared relative error (RMSRE) from the new upward-facing heat transfer formula. Applied to downward-facing plates, this novel approach outperforms the Schulenberg (1985) formula’s 4.6% RMSRE with 3.8% on four peer-reviewed data-sets spanning <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mn>10</mn><mn>6</mn></msup><mo><</mo><mi>R</mi><mi>a</mi><mo><</mo><msup><mn>10</mn><mn>12</mn></msup></mrow></semantics></math></inline-formula>. The introduction of the harmonic mean as the characteristic length metric for vertical and downward-facing plates extends those rectangular plate formulas to other convex shapes, achieving 3.8% RMSRE on vertical disk convection from Hassani and Hollands (1987) and 3.2% from Kobus and Wedekind (1995). |
| first_indexed | 2024-03-11T05:49:21Z |
| format | Article |
| id | doaj.art-791f56576d1e420ca3007fe4dbca51e0 |
| institution | Directory Open Access Journal |
| issn | 2673-7264 |
| language | English |
| last_indexed | 2024-03-11T05:49:21Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Thermo |
| spelling | doaj.art-791f56576d1e420ca3007fe4dbca51e02023-11-17T14:12:18ZengMDPI AGThermo2673-72642023-02-013114817510.3390/thermo3010010Natural Convection Heat Transfer from an Isothermal PlateAubrey Jaffer0Independent Researcher, Waltham, MA 02452, USAUsing boundary-layer theory, natural convection heat transfer formulas that are accurate over a wide range of Rayleigh numbers (<i>Ra</i>) were developed in the 1970s and 1980s for vertical and downward-facing plates. A comprehensive formula for upward-facing plates remained unsolved because they do not form conventional boundary-layers. From the thermodynamic constraints on heat-engine efficiency, the novel approach presented here derives formulas for natural convection heat transfer from isothermal plates. The union of four peer-reviewed data-sets spanning <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi>R</mi><mi>a</mi><mo><</mo><msup><mn>10</mn><mn>12</mn></msup></mrow></semantics></math></inline-formula> has 5.4% root-mean-squared relative error (RMSRE) from the new upward-facing heat transfer formula. Applied to downward-facing plates, this novel approach outperforms the Schulenberg (1985) formula’s 4.6% RMSRE with 3.8% on four peer-reviewed data-sets spanning <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mn>10</mn><mn>6</mn></msup><mo><</mo><mi>R</mi><mi>a</mi><mo><</mo><msup><mn>10</mn><mn>12</mn></msup></mrow></semantics></math></inline-formula>. The introduction of the harmonic mean as the characteristic length metric for vertical and downward-facing plates extends those rectangular plate formulas to other convex shapes, achieving 3.8% RMSRE on vertical disk convection from Hassani and Hollands (1987) and 3.2% from Kobus and Wedekind (1995).https://www.mdpi.com/2673-7264/3/1/10natural convectionheat engineCarnot efficiency |
| spellingShingle | Aubrey Jaffer Natural Convection Heat Transfer from an Isothermal Plate Thermo natural convection heat engine Carnot efficiency |
| title | Natural Convection Heat Transfer from an Isothermal Plate |
| title_full | Natural Convection Heat Transfer from an Isothermal Plate |
| title_fullStr | Natural Convection Heat Transfer from an Isothermal Plate |
| title_full_unstemmed | Natural Convection Heat Transfer from an Isothermal Plate |
| title_short | Natural Convection Heat Transfer from an Isothermal Plate |
| title_sort | natural convection heat transfer from an isothermal plate |
| topic | natural convection heat engine Carnot efficiency |
| url | https://www.mdpi.com/2673-7264/3/1/10 |
| work_keys_str_mv | AT aubreyjaffer naturalconvectionheattransferfromanisothermalplate |