Mixed convection in alumina-water nanofluid filled lid-driven square cavity with an isothermally heated square blockage inside with magnetic field effect: Introduction

In this work, mixed convection in alumina-water nanofluid filled lid-driven square cavity with an isothermally heated square blockage inside with magnetic field effect has been examined. All the walls of the cavity are at rest except top wall. A square blockage with isothermal heating is maintained at the centre of the cavity. Vertical side walls are adiabatic and bottom wall is kept at some hot temperature. Flow is generated due to motion of top wall and buoyancy forces that are produced in cavity due to temperature gradient. Governing equations are discretized in space using Galerkin finite element method and time discretization is performed using Crank-Nicolson scheme. Newton method is used to cope with discretized nonlinear systems of equations and Gaussian elimination method has been applied to solve the associated linear subproblems in each nonlinear iteration at each time level. Analysis has been performed on numerical results in the form of streamlines, isotherms, tables and some useful plots. Influence of emerging parameters on the flow, in specific ranges such as Reynolds number (1⩽Re⩽200), Richardson number (0.01⩽Ri⩽10), Hartmann number (0⩽Ha⩽100), Eckert number (0⩽Ec⩽0.01) as well as nanoparticles volume fraction (0⩽ϕ⩽0.2) are investigated and findings are very closely comparable to the previous analysis for the special cases in the literature. Calculations of average Nusselt number, entropy generation as well as average temperature in the cavity will be our focus of interest in this study.