The classical Merkin and Needham’s wall-jet problem was studied for copper-titanium dioxide/water hybrid nanofluid with the effects of suction/injection and thermal energy. The governing equations were converted into non-linear ordinary differential equations by using proper similarity transformations. These equations were then solved analytically for the hybrid nanofluid flow and temperature distribution in hypergeometric function. Therefore, we have obtained expressions for both the reduced skin friction coefficient and reduced Nusselt number.

It was found that the upper-branch and lower-branch solutions are possible only for suction. Further in the case of regular fluid, i.e. the solid volume fractions are zeros, the current results are in a very good agreement with those in the literature. Moreover, it was shown that copper-nanoparticle volume fraction plays a very important role in variation of the velocity. Furthermore, adding nanoparticles of copper to the nanofluid titanium dioxide/water cools/warms the resulting hybrid nanofluid on increasing some of the involved parameters.

研究了经典的Merkin和Needham的壁喷射问题，研究了铜/二氧化钛/水混合纳米流体的吸力/喷射力和热能的影响。通过使用适当的相似性变换，将控制方程转换为非线性常微分方程。然后针对超几何函数中的混合纳米流体流动和温度分布解析求解这些方程。因此，我们获得了减小的皮肤摩擦系数和减小的努塞尔数的表达式。

发现上支和下支解决方案仅可能用于抽吸。此外，在常规流体的情况下，即固体体积分数为零，当前结果与文献中的结果非常一致。此外，已表明铜纳米颗粒的体积分数在速度变化中起着非常重要的作用。此外，将铜的纳米颗粒添加到纳米流体二氧化钛/水中在增加一些涉及的参数时冷却/加热所得的杂化纳米流体。