Identifying the mixed and forced convection flow with transverse magnetic field

Abstract

AbstractOptimal 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.