MHD double-diffusive mixed convection of binary nanofluids through a vertical porous annulus considering Buongiorno's two-phase model

Binary nanofluids are prepared using a binary liquid (e.g., salt water) instead of a pure liquid as their host fluid. Double-diffusive convection in this type of nanofluids is a kind of triple-diffusive process, which simultaneously includes diffusions of heat, nanoparticles, and solute. This paper is devoted to double-diffusive mixed convection of binary nanofluids flowing through a vertical porous annulus in the presence of an externally applied radial magnetic field. To simulate the problem, a new mathematical model following the Buongiorno's two-phase model is proposed. The equations are solved numerically by means of the finite-volume method. Thereafter, effects of the involved dimensionless variables on the distributions of stream function, temperature, solute concentration, and nanoparticles fraction as well as the mean values of the Nusselt number and the solute Sherwood number are presented and discussed. Inspection of the results demonstrates the significant contributions of the Peclet number (Pe), the usual Lewis number (Le), and the Soret-solute Lewis number (Ld) on the simulation results. In spite of that, the effects of the Hartmann number (Ha) and the thermophoresis parameter (Nt) on the simulation results are weak, while the consequences of the nanofluid Lewis number (Ln), the double-diffusive ratio (Nc), the buoyancy ratio (Nr), and the Dufour parameter (Nd) on the Nusselt and Sherwood numbers are insignificant.