Finite element simulations of inclined magnetic field and mixed convection in an enclosure with periodically heated walls in the presence of an obstacle

Abstract

The current manifestation is utilized to explicate the inspiration of combined convection flows in a cavity with a square cylinder placed at the center of the cavity having coordinates (0.5, 0.5). To be more specific, right- and left-sided vertical walls are kept cold, and the lower wall is to be heated in uniform and non-uniform manners, while the upper horizontal wall is moved with a constant velocity ULid and is thermally adiabatic. The obstacle is treated as cold as well as thermally adiabatic, and the no-slip velocity boundary conditions are specified at its surface. For the purpose of computing the velocity profile and temperature, a space including the quadratic polynomials (P2) is chosen; however, the pressure has been approximated using a linear ( P1 ) finite element space of functions. The Newton technique is used to perform the computations needed to solve the discrete systems of non-linear algebraic equations. The non-linear iterations are terminated at residual below 10–6, whereas the inner core linear solver is based on Gaussian elimination with special reordering of unknowns. To show the consistency of the implemented numerical technique, the parametric study is designed based on the most relevant non-dimensional parameters, namely, the Grashof number Gr ranging from 102 to 105, the Hartmann number Ha changing from 0 to 50, and the Reynolds number Re varying from 10 to 200. Computations in the forms of velocity streamlines and isotherm contour profiles are adorned. In addition, the production of temperature disparities is associated with an increase in Nuavg as Re increases. In contrast, a diminishing aptitude in kinetic energy is observed due to the creation of Lorentz forces.