THERMOPHORESIS AND BROWNIAN MOTION EFFECTS ON NATURAL CONVECTION HEAT AND MASS TRANSFER OF FRACTIONAL OLDROYD-B NANOFLUID

We investigated the effects of Brownian motion and thermophoresis on unsteady convection heat and mass transport of nanofluid, where the fractional Oldroyd-B model is employed in the constitutive relation. The nonlinear boundary layer governing equations not only have multi-term time fractional derivatives, but also possess special mixed time space operators in the convection velocity term. Numerical solutions were obtained by finite difference method combined with L1-algorithm. The effects of fractional derivative parameters (α, 0 ~ 0.5; β, 0.2 ~ 1), Brownian motion number (Nb, 0.3 ~ 0.9), and thermophoresis number (Nt, 0.1 ~ 0.9) are discussed in detail. Results indicate that thermophoresis and Brownian motion had a strong influence on the heat and mass transfer of nanofluid. With an increased thermophoresis number, the temperature profiles rose significantly, while the enhancement of Brownian motion led to the decline of the concentration. The intersection points of the velocity profiles demonstrate that the fractional viscoelastic nanofluid had a relaxation response in the velocity transport process.