MHD mixed convection and entropy generation of water-alumina nanofluid flow in a double lid driven cavity with discrete heating

摘要

In the present study, entropy generation due to mixed convection in a partially heated square double lid driven cavity filled with Al_2O_3-water nanofluid under the influence of inclined magnetic field is numerically investigated. At the lower wall of the cavity two heat sources are fixed, with the condition that the remaining part of the bottom wall is kept insulated. Top wall and vertically moving walls are maintained at constant cold temperature. Buoyant force is responsible for the flow along with the two moving vertical walls. Governing equations are discretized in space using LBB-stable finite element pair Q_2/P_1~(disc) which lead to 3rd and 2nd order accuracy in the L_2-norm for the velocity/temperature and pressure, respectively and the fully implicit Crank-Nicolson scheme of 2nd order accuracy is utilized for the temporal discretization. The discretized systems of nonlinear equations are treated by using the Newton method and the associated linear subproblems are solved by means of Guassian elimination method. Numerical results are presented and analyzed by means of streamlines, isotherms, tables and some useful plots. Impacts of emerging parameters on the flow, in specific ranges such as Reynolds number (1 ≤ Re ≤ 100), Richardson number (1 ≤ Ri ≤ 50), Hartman number (0 ≤ Ha ≤ 100), solid volume fraction (0 ≤ φ ≤ 0.2) as well as the angles of inclined magnetic field (0° ≤ γ ≤ 90°) are investigated and the findings are exactly of the same order as that of the previously performed analysis. Calculation of average Nusselt number, entropy generation due to heat transfer, fluid friction and magnetic field, total entropy generation, Bejan number and kinetic energy are the main focus of our study.