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Controlling the power law fluid flow and heat transfer under the external magnetic field using the flow index and the Hartmann number
Date
2018-10-01
Author
Evcin, Cansu
Uğur, Ömür
Tezer, Münevver
Metadata
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The direct and optimal control solution of laminar fully developed, steady Magnetohydrodynamics (MHD) flow of an incompressible, electrically conducting power-law non-Newtonian fluid in a square duct is considered with the heat transfer. The fluid is subjected to an external uniform magnetic field as well as a constant pressure gradient. The apparent fluid viscosity is both a function of the unknown velocity and the flow index which makes the momentum equation nonlinear. Viscous and Joule dissipation terms are also included. The direct problem is solved by using Galerkin finite element method (FEM) with mixed finite elements and the control problem approach is the discretize-then-optimize procedure. The control formulations with the flow index parameter and the Hartmann number are given to regain the desired velocity profile and temperature isolines of the MHD flow.
Subject Keywords
MHD
,
FEM
,
Variable viscosity
,
Optimal control
,
Heat transfer
URI
https://www.worldscientific.com/doi/abs/10.1142/S0219876218501438
https://hdl.handle.net/11511/81469
Journal
International Journal of Computational Methods
DOI
https://doi.org/https://doi.org/10.1142/S0219876218501438
Collections
Graduate School of Applied Mathematics, Article
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Controlling the power law fluid flow and heat transfer under the external magnetic field using the flow index and the Hartmann number
Evcin, Cansu; Uğur, Ömür; Tezer, Münevver (2018-10-01)
The direct and optimal control solution of laminar fully developed, steady Magnetohydrodynamics (MHD) flow of an incompressible, electrically conducting power-law non-Newtonian fluid in a square duct is considered with the heat transfer. The fluid is subjected to an external uniform magnetic field as well as a constant pressure gradient. The apparent fluid viscosity is both a function of the unknown velocity and the flow index which makes the momentum equation nonlinear. Viscous and Joule dissipation terms ...
Determining the optimal parameters for the MHD flow and heat transfer with variable viscosity and Hall effect
EVCİN, CANSU; Uğur, Ömür; Tezer, Münevver (2018-09-15)
The direct and optimal control solution of the laminar, fully developed, steady MHD flow of an incompressible, electrically conducting fluid in a duct is considered together with the heat transfer. The flow is driven by a constant pressure gradient and an external uniform magnetic field. The fluid viscosity is temperature dependent varying exponentially and the Hall effect, viscous and Joule dissipations are taken into consideration. The control problem is solved by the discretize-then-optimize approach usi...
The BEM Solutions of MHD Flow and Heat Transfer in a Rectangular Duct with Temperature Dependent Viscosity
Kaya, Elif Ebren; Tezer, Münevver (2019-01-01)
The steady, laminar, fully developed magnetohydrodynamic (MHD) flow of an incompressible, electrically conducting fluid with temperature dependent viscosity is studied in a rectangular duct together with its heat transfer. Although the induced magnetic field is neglected due to the small Reynolds number, the Hall effect, viscous and Joule dissipations are taken into consideration. The momentum and the energy equations are solved iteratively. Firstly, the momentum equation is solved by using the boundary ele...
Time varying control of magnetohydrodynamic duct flow
Evcin, Cansu; Uğur, Ömür; Tezer, Münevver (2021-09-01)
Optimal control of the unsteady, laminar, fully developed flow of a viscous, incompressible and electrically conducting fluid is considered under the effect of a time varying magnetic field B0(t) applied in the direction making an angle with the y–axis. Thus, the coefficients of convection terms in the Magnetohydrodynamics (MHD) equations are also time-dependent. The coupled time-dependent MHD equations are solved by using the mixed finite element method (FEM) in space and the implicit Euler scheme in time....
The application of BEM to MHD flow and heat transfer in a rectangular duct with temperature dependent viscosity
Ebren Kaya, Elif; Tezer, Münevver ( EC LTD.; 2018-07-11)
The steady, laminar, fully developed MHD flow of an incompressible, electrically conducting fluid with temperature dependent viscosity is studied in a rectangular duct together with its heat transfer. Although the induced magnetic field is neglected due to the small Reynolds number, the Hall effect, viscous and Joule dissipations are taken into consideration. The momentum equation for the pipe-axis velocity and the energy equation are solved iteratively. Firstly, the momentum equation is solved by using the...
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C. Evcin, Ö. Uğur, and M. Tezer, “Controlling the power law fluid flow and heat transfer under the external magnetic field using the flow index and the Hartmann number,”
International Journal of Computational Methods
, 2018, Accessed: 00, 2021. [Online]. Available: https://www.worldscientific.com/doi/abs/10.1142/S0219876218501438.