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

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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 ...
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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...
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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...

Citation Formats

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.