Lie group method for analyzing the generalized heat transfer mathematical model for Lake Tahoe
The one-dimensional time-dependent heat transfer equation in a vertical direction is introduced in terms of a general formula of density and thermal conductivity. One-parameter Lie symmetry group transformation is applied to determine the suitable forms of water density and thermal conductivity base...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818120300036 |
| _version_ | 1819140415517884416 |
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| author | Mina B. Abd-el-Malek Nagwa A. Badran Amr M. Amin Anood M. Hanafy |
| author_facet | Mina B. Abd-el-Malek Nagwa A. Badran Amr M. Amin Anood M. Hanafy |
| author_sort | Mina B. Abd-el-Malek |
| collection | DOAJ |
| description | The one-dimensional time-dependent heat transfer equation in a vertical direction is introduced in terms of a general formula of density and thermal conductivity. One-parameter Lie symmetry group transformation is applied to determine the suitable forms of water density and thermal conductivity based on experimental measurements. The general equation is investigated again using Lie group analysis after substitution by the two possible forms of water density and thermal conductivity from the first part. The obtained partial differential equation is solved numerically using explicit 4th and 5th Runge–Kutta formula or analytically if it is possible assuming the physical parameters of Lake Tahoe in the Sierra Nevada of the United States. The temperature distribution across the lake depth from each case is illustrated graphically to indicate the thermal stratification phenomenon of lakes. |
| first_indexed | 2024-12-22T11:38:12Z |
| format | Article |
| id | doaj.art-80459dc942f04e9db9122b901c8ec6b3 |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-12-22T11:38:12Z |
| publishDate | 2020-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-80459dc942f04e9db9122b901c8ec6b32022-12-21T18:27:21ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812020-12-012100003Lie group method for analyzing the generalized heat transfer mathematical model for Lake TahoeMina B. Abd-el-Malek0Nagwa A. Badran1Amr M. Amin2Anood M. Hanafy3Corresponding author.; Department of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria University, Alexandria 21544, EgyptDepartment of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria University, Alexandria 21544, EgyptDepartment of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria University, Alexandria 21544, EgyptDepartment of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria University, Alexandria 21544, EgyptThe one-dimensional time-dependent heat transfer equation in a vertical direction is introduced in terms of a general formula of density and thermal conductivity. One-parameter Lie symmetry group transformation is applied to determine the suitable forms of water density and thermal conductivity based on experimental measurements. The general equation is investigated again using Lie group analysis after substitution by the two possible forms of water density and thermal conductivity from the first part. The obtained partial differential equation is solved numerically using explicit 4th and 5th Runge–Kutta formula or analytically if it is possible assuming the physical parameters of Lake Tahoe in the Sierra Nevada of the United States. The temperature distribution across the lake depth from each case is illustrated graphically to indicate the thermal stratification phenomenon of lakes.http://www.sciencedirect.com/science/article/pii/S2666818120300036Lie symmetry transformThermal stratification of lakesOne-dimensional heat transfer modelDensity and thermal conductivity of lakesThermal distributionTahoe Lake |
| spellingShingle | Mina B. Abd-el-Malek Nagwa A. Badran Amr M. Amin Anood M. Hanafy Lie group method for analyzing the generalized heat transfer mathematical model for Lake Tahoe Partial Differential Equations in Applied Mathematics Lie symmetry transform Thermal stratification of lakes One-dimensional heat transfer model Density and thermal conductivity of lakes Thermal distribution Tahoe Lake |
| title | Lie group method for analyzing the generalized heat transfer mathematical model for Lake Tahoe |
| title_full | Lie group method for analyzing the generalized heat transfer mathematical model for Lake Tahoe |
| title_fullStr | Lie group method for analyzing the generalized heat transfer mathematical model for Lake Tahoe |
| title_full_unstemmed | Lie group method for analyzing the generalized heat transfer mathematical model for Lake Tahoe |
| title_short | Lie group method for analyzing the generalized heat transfer mathematical model for Lake Tahoe |
| title_sort | lie group method for analyzing the generalized heat transfer mathematical model for lake tahoe |
| topic | Lie symmetry transform Thermal stratification of lakes One-dimensional heat transfer model Density and thermal conductivity of lakes Thermal distribution Tahoe Lake |
| url | http://www.sciencedirect.com/science/article/pii/S2666818120300036 |
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