Buongiorno’s model for double-diffusive mixed convective stagnation-point flow of a nanofluid considering diffusiophoresis effect of binary base fluid

Abstract

The development of double-diffusive mixed convective boundary layer flow of a nanofluid near stagnation point region over a vertical surface has been investigated. Buongiorno’s model is used to incorporate the effects of Brownian motion and thermophoresis for the nanofluid, when the base fluid of the nanofluid is itself a binary fluid such as salty water. In addition the thermal energy equations include regular diffusion and cross-diffusion terms. Using the local similarity method, it is shown that a set of suitable similarity transformations reduces the non-linear coupled PDEs governing on the problem into a set of non-linear coupled ODEs. The analysis shows that velocity, temperature, solutal concentration and nanoparticle concentration profiles in the respective boundary layers depend on ten dimensionless physical parameters, namely the mixed convection parameter λ, the regular double-diffusive buoyancy parameter Nc, the nanofluid buoyancy ratio Nr, the Brownian motion parameter Nb, the thermophoresis parameter Nt, the modified Dufour parameter Nd, the regular Schmidt number Sc, the nanofluid Schmidt number Scn, Prandtl number Pr, and the Dufour-solutal Lewis number Ld. The results are presented in graphical form illustrating the effects of these parameters on boundary layer behavior. A sensitivity analysis of model is tabulated where the difference in each graph can be quantified in terms of root mean square deviation (RMSD) with respect to that with the default parameters. These results are supplemented with the data for the reduced Nusselt number and the two reduced Sherwood numbers, one for the solute and the other for the nanoparticles. It is found that for assisting flow regime the reduced Nusselt number is a decreasing function of each of Nr,NbandNt, and an increasing function of each of λ,NcandNd. The results demonstrate that the highest heat transfer rate is obtained for the situation that the thermophoresis effects are negligible. Moreover, a reduction in the reduced Sherwood number of nanoparticle is observed with increase in each of NcandNt, while this quantity increases with Nb.