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Öğe Controlling the Power-Law Fluid Flow and Heat Transfer Under the External Magnetic Field Using the Flow Index and the Hartmann Number(World Scientific Publ Co Pte Ltd, 2020) Evcin, Cansu; Uğur, Ömür; Tezer Sezgin, MünevverThe 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.Öğe Determining the optimal parameters for the MHD flow and heat transfer with variable viscosity and Hall effect(Pergamon-Elsevier Science Ltd, 2018) Evcin, Cansu; Uğur, Ömür; Tezer Sezgin, MünevverThe 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 using mixed finite element method for the MHD and energy equations. The control formulations with the Hall and viscosity parameters, the Hartmann and Brinkmann number are given to regain the desired velocity and temperature of the MHD flow. (C) 2018 Elsevier Ltd. All rights reserved.Öğe Identifying the mixed and forced convection flow with transverse magnetic field(Wiley-V C H Verlag Gmbh, 2024) Evcin, CansuOptimal control of the steady, laminar, magnetohydrodynamics (MHD) mixed convection flow of an electrically conducting fluid is considered under the effect of the transverse magnetic field in a square duct. The viscous and Joule dissipations are included and the flow is driven by a constant pressure gradient. The triple nonlinear set of momentum, induction, and energy equations are solved in dimensionless form by using the mixed finite element method (FEM) with the implementation of Newton's method for nonlinearity with the discretize-then-linearize approach. Accordingly, FEM solutions are obtained for various values of the problem parameters to ensure the efficiency of the underlying scheme. This study aims to investigate the problem of controlling the steady flow by using the physically significant parameters of the problem as control variables in the case of a mixed convection flow. In this respect, classification of the type of convection, forced or free, is achieved by controlling the Grashof number (Gr). Besides, single and pairwise controls with Hartmann number (M), Prandtl number (Pr), and magnetic Reynolds number (Rm) are also used to regain the prescribed fluid behaviors and required magnetic field. Control simulations are conducted with the sequential-least-squares-programming (SLSQP) algorithm in the optimization.Öğe Optimal placement of the multiple magnetic sources for the MHD flow in a rectangular duct(Springer, 2023) Evcin, Cansu; Uğur, Ö.; Tezer-Sezgin, M.In this paper, we consider the optimal control of the fully developed, steady, laminar, unidirectional flow of an incompressible electrically conducting fluid in a long channel of rectangular cross-section (duct). The magnetic field is generated by thin wires carrying electric current and placed along, below and/or above the channel, forming magnetic sources at the bottom and top walls of the duct. Control problem is designed to find the optimal placement of magnetic sources by using the axis coordinates of the sources as control variables to achieve the desired fluid behavior. Optimality conditions are obtained via adjoint method following discretize-then-optimize procedure. Optimization is performed by a gradient-based algorithm with bounds on the controls. The coupled system of magnetohydrodynamic (MHD) flow equations is solved by using FEM with quadratic elements. Control simulations are conducted by one, two and multiple sources for various values of the Hartmann number. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.Öğe Time varying control of magnetohydrodynamic duct flow(Elsevier Ltd, 2021) Evcin, Cansu; Uğur, Ö.; Tezer Sezgin, MünevverOptimal 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. FEM solutions are obtained for various values of the Hartmann number, Reynolds number, magnetic Reynolds number and for several types of time dependence of applied magnetic field at transient level and steady-state. In this study, we aim to control the unsteady MHD flow by using the time varying coefficient function f(t) in the applied magnetic field B0(t)=B0f(t) as a control function. In addition, control problem is designed to involve the determination of the optimal parameters of the system (Reynolds number, magnetic Reynolds number and the angle ?) regarded as control variables. In the optimization, a discretize-then-optimize approach with a gradient based algorithm is followed. Cost function is designed to regain the prescribed velocity and induced magnetic field profiles as well as the smooth control function with respect to time. Controls are investigated for the regularization parameters included in the cost function. Optimal solutions are achieved for several states of the flow considering Hartmann number and at the time level where the flow stabilizes. © 2021 Elsevier Masson SAS
