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

Abstract

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–Al $$_2$$ O $$_3$$ 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 ( $$0 \le \phi \le 0.04$$ ), Reynolds number ( $$1 \le Re \le 500$$ ), Richardson number ( $$0.01 \le Ri \le 100$$ ), Hartmann number ( $$0 \le Ha \le 50$$ ) and the size of the inner solid ( $$0.1 \le D \le 0.7$$ ). The other parameters: the Prandtl number, Lewis number, Schmidt number, ratio of Brownian to thermophoretic diffusivity and the normalized temperature parameter, are fixed at $$Pr=4.623$$ , $$Le=3.5\times 10^{5}$$ , $$Sc=3.55\times 10^{4}$$ , $$N_{\mathrm{BT}}=1.1$$ and $$\delta =155$$ , respectively. The inclination of the magnetic field is fixed at $$\gamma =\frac{\pi }{4}$$ . 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.