Determining the optimal parameters for the MHD flow and heat transfer with variable viscosity and Hall effect

Abstract 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 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.

[1]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[2]  Kazufumi Ito,et al.  Optimal Control of Thermally Convected Fluid Flows , 1998, SIAM J. Sci. Comput..

[3]  Anders Logg,et al.  Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book , 2012 .

[4]  Pooya Hoseinpoori,et al.  Energy and cost optimization of a plate and fin heat exchanger using genetic algorithm , 2011 .

[5]  M. R. Hajmohammadi,et al.  Optimal design of tree-shaped inverted fins , 2018 .

[6]  H. A. Attia,et al.  MHD flow and heat transfer in a rectangular duct with temperature dependent viscosity and hall effect , 2000 .

[7]  H. Lee,et al.  Optimal control of non-isothermal viscous fluid flow , 2009, Math. Comput. Model..

[8]  I. Pop,et al.  Fully developed magneto convection flow in a vertical rectangular duct , 2011 .

[9]  Karl Kunisch,et al.  Optimal Control for a Stationary MHD System in Velocity-Current Formulation , 2006, SIAM J. Control. Optim..

[10]  Chebyshev Spectral Collocation Method for Unsteady Mhd Flow and Heat Transfer of a Dusty Fluid Between Parallel Plates , 2013 .

[11]  R. Temam,et al.  On some control problems in fluid mechanics , 1990 .

[12]  S. Funke,et al.  The automation of PDE-constrained optimisation and its applications , 2012 .

[13]  M. Ahmed Numerical solution of power law fluids flow and heat transfer with a magnetic field in a rectangular duct , 2006 .

[14]  M. R. Hajmohammadi,et al.  Design and analysis of multi-scale annular fins attached to a pin fin , 2017 .

[15]  M. R. Hajmohammadi Introducing a ψ-shaped cavity for cooling a heat generating medium , 2017 .

[16]  N. Kishan,et al.  Finite Element Analysis of Fully Developed Unsteady MHD Convection Flow in a Vertical Rectangular Duct with Viscous Dissipation and Heat Source/Sink , 2015 .

[17]  L. Hou,et al.  Boundary optimal control of MHD flows , 1995 .

[18]  Peter Deuflhard,et al.  Asymptotic Mesh Independence of Newton's Method Revisited , 2004, SIAM J. Numer. Anal..

[19]  David A. Ham,et al.  Automated Derivation of the Adjoint of High-Level Transient Finite Element Programs , 2013, SIAM J. Sci. Comput..

[20]  M. Gunzburger,et al.  Analysis and discretization of an optimal control problem for the time-periodic MHD equations , 2005 .

[21]  M. Tezer-Sezgin,et al.  FEM solution of natural convection flow in square enclosures under magnetic field , 2013 .

[22]  Z. Ren,et al.  Optimal control for realizing target flow velocity in 1D MHD flow , 2017, 2017 36th Chinese Control Conference (CCC).

[23]  Influence of temperature dependent viscosity on the MHD-channel flow of dusty fluid with heat transfer , 2001 .

[24]  H. A. Attia Influence of temperature-dependent viscosity on the MHD Couette flow of dusty fluid with heat transfer. , 2006 .

[25]  G. Bornia Analysis of optimal control problems for the incompressible MHD equations and implementation in a finite element multiphysics code , 2012 .