Investigation of boundary stresses on MHD flow in a convergent/divergent channel: An analytical and numerical study
This study investigates the boundary stresses prescribed by the traction boundary condition on an incompressible magnetohydrodynamic Jeffery-Hamel flow of viscous fluid. The governing partial differential equations are transformed to a nonlinear ordinary differential equation (ODE) by the transforma...
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| Published in | Alexandria engineering journal Vol. 61; no. 6; pp. 4479 - 4490 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Elsevier B.V
01.06.2022
Elsevier |
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| ISSN | 1110-0168 |
| DOI | 10.1016/j.aej.2021.10.004 |
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| Abstract | This study investigates the boundary stresses prescribed by the traction boundary condition on an incompressible magnetohydrodynamic Jeffery-Hamel flow of viscous fluid. The governing partial differential equations are transformed to a nonlinear ordinary differential equation (ODE) by the transformation obtained from continuity equation. We have modeled traction boundary conditions to solve the problem. We have not imposed flow symmetry condition and applied prescribed flow rate condition. We have computed analytical and numerical solutions of the problem. We have developed modified Adomian decomposition method based on Daun-Rach Approach (DRA) for general nonlinear third order ODE subject to Robin’s and integral boundary conditions. The governing equation is solved using the developed scheme. The Mathematica routine, NDSolve, is used to obtain numerical solution by first approximating the constant flow rate condition by Gauss-Lobatto integration formula of four and five points as well as by trapezoidal rule. Analytical and numerical results are compared and found in good agreement. The slip and no-slip scenarios are observed both for inertial and non-inertial flows. The back flow occurs both for convergent and divergent channel geometries. Flow bifurcations and boundary layer get strengthened due to presence of boundary stresses. The symmetric and asymmetric natures of flow are also captured due to presence of boundary stresses. |
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| AbstractList | This study investigates the boundary stresses prescribed by the traction boundary condition on an incompressible magnetohydrodynamic Jeffery-Hamel flow of viscous fluid. The governing partial differential equations are transformed to a nonlinear ordinary differential equation (ODE) by the transformation obtained from continuity equation. We have modeled traction boundary conditions to solve the problem. We have not imposed flow symmetry condition and applied prescribed flow rate condition. We have computed analytical and numerical solutions of the problem. We have developed modified Adomian decomposition method based on Daun-Rach Approach (DRA) for general nonlinear third order ODE subject to Robin’s and integral boundary conditions. The governing equation is solved using the developed scheme. The Mathematica routine, NDSolve, is used to obtain numerical solution by first approximating the constant flow rate condition by Gauss-Lobatto integration formula of four and five points as well as by trapezoidal rule. Analytical and numerical results are compared and found in good agreement. The slip and no-slip scenarios are observed both for inertial and non-inertial flows. The back flow occurs both for convergent and divergent channel geometries. Flow bifurcations and boundary layer get strengthened due to presence of boundary stresses. The symmetric and asymmetric natures of flow are also captured due to presence of boundary stresses. |
| Author | Ali, Nasir Saif, Rai Sajjad Asghar, Zaheer |
| Author_xml | – sequence: 1 givenname: Zaheer surname: Asghar fullname: Asghar, Zaheer email: zaheerasghar@pieas.edu.pk organization: Centre for Mathematical Sciences, Pakistan Institute of Engineering and Applied Sciences, Nilore Islamabad 45650, Pakistan – sequence: 2 givenname: Rai Sajjad surname: Saif fullname: Saif, Rai Sajjad organization: Department of Humanities and Sciences, School of Electrical Engineering and Computer Science (SEECS), National University of Sciences and Technology (NUST), Islamabad, Pakistan – sequence: 3 givenname: Nasir surname: Ali fullname: Ali, Nasir organization: Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan |
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| Keywords | Modified adomian decomposition method Traction boundary conditions Gauss-Lobatto integration Jeffery-Hamel flow |
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| Title | Investigation of boundary stresses on MHD flow in a convergent/divergent channel: An analytical and numerical study |
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