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 |
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Multidisciplinary Digital Publishing Institute
2023
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| Online Access: | https://hdl.handle.net/1721.1/148015 |
| _version_ | 1826206441654976512 |
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| author | Jaffer, Aubrey |
| author_facet | Jaffer, Aubrey |
| author_sort | Jaffer, Aubrey |
| collection | MIT |
| 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 | 2024-09-23T13:29:20Z |
| format | Article |
| id | mit-1721.1/148015 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T13:29:20Z |
| publishDate | 2023 |
| publisher | Multidisciplinary Digital Publishing Institute |
| record_format | dspace |
| spelling | mit-1721.1/1480152023-02-11T03:24:11Z Natural Convection Heat Transfer from an Isothermal Plate Jaffer, Aubrey 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). 2023-02-10T16:11:46Z 2023-02-10T16:11:46Z 2023-02-03 2023-02-10T14:28:32Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/148015 Thermo 3 (1): 148-175 (2023) PUBLISHER_CC http://dx.doi.org/10.3390/thermo3010010 Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ application/pdf Multidisciplinary Digital Publishing Institute Multidisciplinary Digital Publishing Institute |
| spellingShingle | Jaffer, Aubrey Natural Convection Heat Transfer from an Isothermal Plate |
| 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 |
| url | https://hdl.handle.net/1721.1/148015 |
| work_keys_str_mv | AT jafferaubrey naturalconvectionheattransferfromanisothermalplate |