Fully HOC Scheme for Mixed Convection Flow in a Lid-Driven Cavity Filled with a Nanofluid (Advances in Applied Mathematics and Mechanics, 2018)
A fully higher-order compact (HOC) finite difference scheme on the9-point two-dimensional (2D) stencil is formulated for solving thesteady-state laminar mixed convection flow in a lid-driven inclinedsquare enclosure filled with water-$Al_2O_3$ nanofluid. Twocases are considered depending on the direction of temperaturegradient imposed (Case I, top and bottom; Case II, left and right).The developed equations are given in terms of the streamfunction-vorticity formulation and are non-dimensionalized and thensolved numerically by a fourth-order accurate compact finitedifference method. Unlike other compact solution procedure inliterature for this physical configuration, the present method isfully compact and fully higher-order accurate. The fluid flow, heattransfer and heat transport characteristics were illustrated bystreamlines, isotherms and averaged Nusselt number. Comparisons withpreviously published work are performed and found to be in excellentagreement. A parametric study is conducted and a set of graphicalresults is presented and discussed to elucidate that significantheat transfer enhancement can be obtained due to the presence ofnanoparticles and that this is accentuated by inclination of theenclosure at moderate and large Richardson numbers.