Effects of two-phase nanofluid model on MHD mixed convection in a lid-driven cavity in the presence of conductive inner block and corner heater

This paper investigates a steady mixed convection in a lid-driven square cavity subjected to an inclined magnetic field and heated by corner heater with an inserted square solid block. Water-Al2O3 nanofluid fills the cavity based on Buongiorno's two-phase model. A corner heater is configured in the left lower corner of the cavity by maintaining 40% of the bottom and vertical walls at constant hot temperature. The top horizontal wall is moving and maintained at a constant low temperature. The remainder walls are thermally insulated. The governing equations are solved numerically using the finite element method. The governing parameters are the nanoparticles volume fraction (0 <= phi <= 0.04), Reynolds number (1 <= Re <= 500), Richardson number (0.01 <= Ri <= 100), Hartmann number (0 <= Ha <= 50) and the size of the inner solid (0.1 <= D <= 0.7). The other parameters: the Prandtl number, Lewis number, Schmidt number, ratio of Brownian to thermophoretic diffusivity and the normalized temperature parameter, are fixed at Pr = 4.623, Le = 3.5 x 10(5), Sc = 3.55 x 10(4), N-BT = 1.1 and delta = 155, respectively. The inclination of the magnetic field is fixed at gamma = pi/4. Results show that at low Reynolds number, the increase in nanoparticles loading more the 2% becomes useless. It is also found that a big size of the solid block can augment heat transfer in the case of high values of both the Reynolds and Richardson numbers.