This article investigates the unsteady flow and heat transfer in a nanofluid over a stretching/shrinking sheet with injection/suction effects to overcome the deficiency found in the previous model that was to control the nanoparticles fraction actively. Besides, this study controls the nanoparticles volume fraction on the boundary passively rather than actively in order to make the model physically more realistic with zero flux at the surface. This approach makes the Buongiorno's nanofluid model more effective for the plate problems in reality. The governing partial differential equations are transformed into ordinary differential equations via the similarity transformation and are then solved numerically using the bvp4c function. Effects of different flow parameters on the velocity profile, the temperature distribution, the skin friction coefficient and the local Nusselt number are deliberated in detail. Dual solutions are observed for the stretching/shrinking sheet and suction/injection parameter in some certain range. Stability analysis is conceived to check the reliability and stability of the solutions. The local Nusselt number is estimated through multiple linear and quadratic regressions. A comparison is made to validate the obtained results. Results indicate that the first solution is stable and physically realizable as compared to the second solution either fluid flow is under suction or injection effect. The Brownian motion parameter is not significant, and the local Nusselt number is almost independent of the Brownian motion parameter, but it depicts decreasing behavior for the Schmidt number and the thermophoresis parameter for suction and opposite behavior for the injection case. The rise in the suction parameter causes the streamlines to get closer to each other while for the impermeable case, the oncoming flow is the same as for the stagnation point flow.

本文研究了具有注射/抽吸作用的拉伸/收缩片材上的纳米流体中的非稳态流动和传热，从而克服了先前模型中发现的主动控制纳米颗粒比例的不足。此外，本研究被动地而不是主动地控制边界上的纳米粒子体积分数，以使模型在表面上的通量为零时在物理上更真实。这种方法使Buongiorno的纳米流体模型对实际中的板问题更有效。控制的偏微分方程通过相似变换转换为常微分方程，然后使用bvp4c函数进行数值求解。不同流量参数对速度分布，温度分布，详细讨论了皮肤摩擦系数和局部Nusselt数。在一定范围内观察到拉伸/收缩片材和抽吸/注射参数的双重解决方案。可以进行稳定性分析以检查解决方案的可靠性和稳定性。通过多个线性和二次回归来估计局部Nusselt数。进行比较以验证所获得的结果。结果表明，与第二种解决方案相比，无论是流体流处于抽吸作用还是注入作用，第一解决方案都是稳定且可物理实现的。布朗运动参数并不重要，并且本地Nusselt数几乎与布朗运动参数无关，但它描述了Schmidt数的下降行为和吸力的热泳参数，以及注射情况的相反行为。吸力参数的增加导致流线彼此靠近，而对于不渗透的情况，迎面而来的流量与停滞点流相同。