An efficient analytical approach with novel integral transform to study the two-dimensional solute transport problem
The q-homotopy analysis method (q-HAM) in combine with the novel integral transform known as Elzaki transform (ET) leads to an efficient analytical technique called, the q-homotopy analysis Elzaki transform method (q-HAETM). In the present study, the two- dimensional advection–dispersion (AD) proble...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-04-01
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| Series: | Ain Shams Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090447922001897 |
| _version_ | 1827979935750291456 |
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| author | M. Sunitha Fehmi Gamaoun Amal Abdulrahman Naveen Sanju Malagi Sandeep Singh Rekha Javare Gowda R.J. Punith Gowda |
| author_facet | M. Sunitha Fehmi Gamaoun Amal Abdulrahman Naveen Sanju Malagi Sandeep Singh Rekha Javare Gowda R.J. Punith Gowda |
| author_sort | M. Sunitha |
| collection | DOAJ |
| description | The q-homotopy analysis method (q-HAM) in combine with the novel integral transform known as Elzaki transform (ET) leads to an efficient analytical technique called, the q-homotopy analysis Elzaki transform method (q-HAETM). In the present study, the two- dimensional advection–dispersion (AD) problem is investigated using an analytical technique q-HAETM. These equations are mainly used to describe the fate of pollutants in aquifers. The analytical solutions to the AD equations are more interesting since they serve as benchmarks against which numerical solutions can be compared. The novelty of the work is to discuss the two-dimensional (2D) solute transport problem in the fractional sense. The reliability and the efficiency of the considered algorithm are demonstrated by employing the 2D fractional solute transport problem. The solute concentration profile is shown in terms of surface plots. The comparison of the exact solution and the approximate solution is done by the 2D plots. The numerical approximate error solutions are presented for different fractional orders. q-HAETM offers us to modulate the range of convergence of the series solution using ℏ, called auxiliary parameter or convergence control parameter. By performing appropriate numerical simulations in comparison with other existing techniques, the effectiveness and reliability of the considered technique are validated. The obtained findings show that the proposed method is very gratifying and examines the complex challenges that arise in science and innovation. |
| first_indexed | 2024-04-09T21:45:45Z |
| format | Article |
| id | doaj.art-8deb41a96b4c4c2182774cd8ea5c0d9a |
| institution | Directory Open Access Journal |
| issn | 2090-4479 |
| language | English |
| last_indexed | 2024-04-09T21:45:45Z |
| publishDate | 2023-04-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Ain Shams Engineering Journal |
| spelling | doaj.art-8deb41a96b4c4c2182774cd8ea5c0d9a2023-03-25T05:10:40ZengElsevierAin Shams Engineering Journal2090-44792023-04-01143101878An efficient analytical approach with novel integral transform to study the two-dimensional solute transport problemM. Sunitha0Fehmi Gamaoun1Amal Abdulrahman2Naveen Sanju Malagi3Sandeep Singh4Rekha Javare Gowda5R.J. Punith Gowda6Department of Mathematics and statistics, University College for women Koti, Hyderabad, IndiaDepartment of Mechanical Engineering, College of Engineering, King Khalid University, Abha 61421, Saudi ArabiaDepartment of Industrial Engineering, College of Engineering, King Khalid University, Abha 61421, Saudi ArabiaDepartment of Studies and Research in Mathematics, Davangere University, Davangere, IndiaDepartment of Civil Engineering and University Centre for Research & Development, Chandigarh University, Mohali-140413, Punjab, IndiaDepartment of Mathematics, Cambridge Institute of Technology, Bangalore 560036, Karnataka, IndiaDepartment of Studies and Research in Mathematics, Davangere University, Davangere, India; Corresponding author.The q-homotopy analysis method (q-HAM) in combine with the novel integral transform known as Elzaki transform (ET) leads to an efficient analytical technique called, the q-homotopy analysis Elzaki transform method (q-HAETM). In the present study, the two- dimensional advection–dispersion (AD) problem is investigated using an analytical technique q-HAETM. These equations are mainly used to describe the fate of pollutants in aquifers. The analytical solutions to the AD equations are more interesting since they serve as benchmarks against which numerical solutions can be compared. The novelty of the work is to discuss the two-dimensional (2D) solute transport problem in the fractional sense. The reliability and the efficiency of the considered algorithm are demonstrated by employing the 2D fractional solute transport problem. The solute concentration profile is shown in terms of surface plots. The comparison of the exact solution and the approximate solution is done by the 2D plots. The numerical approximate error solutions are presented for different fractional orders. q-HAETM offers us to modulate the range of convergence of the series solution using ℏ, called auxiliary parameter or convergence control parameter. By performing appropriate numerical simulations in comparison with other existing techniques, the effectiveness and reliability of the considered technique are validated. The obtained findings show that the proposed method is very gratifying and examines the complex challenges that arise in science and innovation.http://www.sciencedirect.com/science/article/pii/S20904479220018972D solute transport problemElzaki transformq-homotopy analysis method |
| spellingShingle | M. Sunitha Fehmi Gamaoun Amal Abdulrahman Naveen Sanju Malagi Sandeep Singh Rekha Javare Gowda R.J. Punith Gowda An efficient analytical approach with novel integral transform to study the two-dimensional solute transport problem Ain Shams Engineering Journal 2D solute transport problem Elzaki transform q-homotopy analysis method |
| title | An efficient analytical approach with novel integral transform to study the two-dimensional solute transport problem |
| title_full | An efficient analytical approach with novel integral transform to study the two-dimensional solute transport problem |
| title_fullStr | An efficient analytical approach with novel integral transform to study the two-dimensional solute transport problem |
| title_full_unstemmed | An efficient analytical approach with novel integral transform to study the two-dimensional solute transport problem |
| title_short | An efficient analytical approach with novel integral transform to study the two-dimensional solute transport problem |
| title_sort | efficient analytical approach with novel integral transform to study the two dimensional solute transport problem |
| topic | 2D solute transport problem Elzaki transform q-homotopy analysis method |
| url | http://www.sciencedirect.com/science/article/pii/S2090447922001897 |
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