Study of Heat Transfer under the Impact of Thermal Radiation, Ramped Velocity, and Ramped Temperature on the MHD Oldroyd-B Fluid Subject to Noninteger Differentiable Operators
This theoretical study explores the impact of heat generation/absorption with ramp wall velocity and ramp wall temperature on the magnetohydrodynamic (MHD) time-dependent Oldroyd-B fluid over an unbounded plate embedded in a porous surface. The mathematical analysis of fractional governing partial d...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/8890820 |
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| author | Syed Tauseef Saeed Ilyas Khan Muhammad Bilal Riaz Syed Muhammad Husnine |
| author_facet | Syed Tauseef Saeed Ilyas Khan Muhammad Bilal Riaz Syed Muhammad Husnine |
| author_sort | Syed Tauseef Saeed |
| collection | DOAJ |
| description | This theoretical study explores the impact of heat generation/absorption with ramp wall velocity and ramp wall temperature on the magnetohydrodynamic (MHD) time-dependent Oldroyd-B fluid over an unbounded plate embedded in a porous surface. The mathematical analysis of fractional governing partial differential equations has been established using systematic and powerful techniques of Laplace transform with its numerical inversion algorithms. The fractionalized solutions have been traced out separately through all fractional differential operators. Nondimensional parameters along with Laplace transformation are used to find the solution of temperature and velocity profiles. Fractional time derivatives are used to analyze the impact of fractional parameters (memory effect) on the dynamics of the fluid. While making a comparison, it is observed that the fractional-order model is the best to explain the memory effect as compared to classical models. The obtained solutions are plotted graphically for different values of physical parameters. Our results suggest that the velocity profile decreases by increasing the effective Prandtl number. Furthermore, the existence of an effective Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity. |
| format | Article |
| id | doaj-art-a5f5ec16623844f1a63609a6367e5461 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-a5f5ec16623844f1a63609a6367e54612025-02-03T01:20:21ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/88908208890820Study of Heat Transfer under the Impact of Thermal Radiation, Ramped Velocity, and Ramped Temperature on the MHD Oldroyd-B Fluid Subject to Noninteger Differentiable OperatorsSyed Tauseef Saeed0Ilyas Khan1Muhammad Bilal Riaz2Syed Muhammad Husnine3Department of Science & Humanities, National University of Computer and Emerging Sciences, Lahore Campus 54000, Lahore, PakistanDepartment of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi ArabiaDepartment of Mathematics, University of Management and Technology, Lahore 54000, PakistanDepartment of Science & Humanities, National University of Computer and Emerging Sciences, Lahore Campus 54000, Lahore, PakistanThis theoretical study explores the impact of heat generation/absorption with ramp wall velocity and ramp wall temperature on the magnetohydrodynamic (MHD) time-dependent Oldroyd-B fluid over an unbounded plate embedded in a porous surface. The mathematical analysis of fractional governing partial differential equations has been established using systematic and powerful techniques of Laplace transform with its numerical inversion algorithms. The fractionalized solutions have been traced out separately through all fractional differential operators. Nondimensional parameters along with Laplace transformation are used to find the solution of temperature and velocity profiles. Fractional time derivatives are used to analyze the impact of fractional parameters (memory effect) on the dynamics of the fluid. While making a comparison, it is observed that the fractional-order model is the best to explain the memory effect as compared to classical models. The obtained solutions are plotted graphically for different values of physical parameters. Our results suggest that the velocity profile decreases by increasing the effective Prandtl number. Furthermore, the existence of an effective Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity.http://dx.doi.org/10.1155/2020/8890820 |
| spellingShingle | Syed Tauseef Saeed Ilyas Khan Muhammad Bilal Riaz Syed Muhammad Husnine Study of Heat Transfer under the Impact of Thermal Radiation, Ramped Velocity, and Ramped Temperature on the MHD Oldroyd-B Fluid Subject to Noninteger Differentiable Operators Journal of Mathematics |
| title | Study of Heat Transfer under the Impact of Thermal Radiation, Ramped Velocity, and Ramped Temperature on the MHD Oldroyd-B Fluid Subject to Noninteger Differentiable Operators |
| title_full | Study of Heat Transfer under the Impact of Thermal Radiation, Ramped Velocity, and Ramped Temperature on the MHD Oldroyd-B Fluid Subject to Noninteger Differentiable Operators |
| title_fullStr | Study of Heat Transfer under the Impact of Thermal Radiation, Ramped Velocity, and Ramped Temperature on the MHD Oldroyd-B Fluid Subject to Noninteger Differentiable Operators |
| title_full_unstemmed | Study of Heat Transfer under the Impact of Thermal Radiation, Ramped Velocity, and Ramped Temperature on the MHD Oldroyd-B Fluid Subject to Noninteger Differentiable Operators |
| title_short | Study of Heat Transfer under the Impact of Thermal Radiation, Ramped Velocity, and Ramped Temperature on the MHD Oldroyd-B Fluid Subject to Noninteger Differentiable Operators |
| title_sort | study of heat transfer under the impact of thermal radiation ramped velocity and ramped temperature on the mhd oldroyd b fluid subject to noninteger differentiable operators |
| url | http://dx.doi.org/10.1155/2020/8890820 |
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