###### Abstract  
The mathematical model of the two-dimensional steady stagnation-point flow over a stretching or shrinking sheet of nanofluid in the presence of the Soret and Dufour effects and of second-order slip at the boundary was considered in this paper. The partial differential equations were transformed into the ordinary differential equations by applying a suitable similarity transformation. The numerical results were obtained by using bvp4c codes in Matlab. The skin friction coefficient, heat transfer coefficient, mass transfer coefficient, as well as the velocity, temperature, and concentration profiles were presented graphically for different values of slip parameters, Soret effect, Dufour effect, Brownian motion parameter, and thermophoresis parameter. A dual solution was obtained in this present paper. The presence of the slip parameters (first- and second-order slip parameters) was found to expand the range of solutions. However, the presence of the slip parameters led to a decrease in the skin friction coefficient, whereas the heat transfer coefficient increased. Besides that, a larger Soret effect (smallest Dufour effect) led to the decrement of the heat transfer coefficient. The effects of the Brownian motion and thermophoresis parameters on the heat transfer coefficient were also studied in this paper. A stability analysis was performed in this paper to verify the stability of the solutions obtained. stability analysis; second-order slip; Soret and Dufour effects; nanofluids; stretching/shrinking 2018 8 642 (2018)  
thermophoresis in nanofluids. The proposed model has been implemented by [PERSON] and [PERSON] [5], [PERSON] and [PERSON] [6], [PERSON] et al. [7], [PERSON] et al. [8], [PERSON] et al. [9], [PERSON] et al. [10], and [PERSON] et al. [11]. Later, the boundary condition of the Buongiorno model was modified by [PERSON] and [PERSON] [12; 13] resulting in a revised model. These researchers improved the Buongiorno model by extending it to the case where the nanofluid particles fraction on the boundary is controlled passively rather than actively. [PERSON] et al. [14] reported the flow past a stretching/shrinking sheet with suction in a nanofluid using the revised model. Different approaches have been made by [PERSON] et al. [15] to present a numerical simulation of the natural convection in an enclosure filled with nanofluid when the cylindrical block is heated. Furthermore, several works on solving nanofluid problems using the lattice Boltzmann method were reported by [PERSON] [16] and [PERSON] et al. [17; 18]. [PERSON] et al. [19] experimentally investigated the effects of the solid volume fraction and thermal conductivity of nanofluids. The consideration of the slip conditions at the boundary in certain cases should not be ignored, such as in rarefied gas flows in micro-scale devices and low-pressure situations [20; 21; 22]. The new formulation of the second-order slip flow was provided by [PERSON] [23] using the kinetic theory. The new slip model has then been used by [PERSON] et al. [24] and [PERSON] and [PERSON] [25]. [PERSON] et al. [26] analyzed the [PERSON]'s model over a stretching sheet with no-linear Navier boundary condition. The second-order slip flow and heat transfer over a permeable shrinking surface embedded in a porous medium and in mixed convection flow were reported by [PERSON] et al. [27] and [PERSON] and [PERSON] [28], respectively. The work by [PERSON] et al. [29] described the second-order slip embedded in a porous medium when the viscous dissipation was taken into account over a permeable stretching sheet. [PERSON] et al. [30] studied the effect of a magnetic field on second- order slip flow in a nanofluid over a stretching/shrinking sheet with radiation. [PERSON] et al. [31] applied the new slip model and temperature jump to an axisymmetric stagnation-point flow over a stretching/shrinking surface. The application in industrial processes involving slip velocity can be found in polymer solutions and emulsions process in the oil industry.