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.
Highlights
A nanofluid can be defined as the dispersion of nanoparticles into a base fluid in which the collision between the nanoparticles would enhance the thermal conductivity of the fluid
It was clear that a unique solution existed for ε > −1, dual solutions were found for ε c ≤ ε ≤ −1, and no solution was reported for ε < ε c
These three figures indicate that an increase in the slip parameters (σ and δ) caused a decrement in the value of the skin friction coefficient
Summary
A nanofluid can be defined as the dispersion of nanoparticles into a base fluid in which the collision between the nanoparticles would enhance the thermal conductivity of the fluid (see Masuda et al [1]). Zaimi et al [14] reported the flow past a stretching/shrinking sheet with suction in a nanofluid using the revised model. Hakeem 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. Motivated by the above studies, the present paper aims to investigate the effects of Soret and Dufour by following the governing equations proposed by Bhattacharyya et al [36] on the stagnation-point flow of a nanofluid over a stretching/shrinking surface with second-order slip conditions (following the formulated second-order slip model by Wu [23]) at the boundary with the improvised model proposed by Kuznetsov and Nield [12]. The stability solutions were analyzed to determine the stability of the solutions obtained
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