A theoretical analysis for magnetohydrodynamic (MHD) mixed convection of non-Newtonian tangent hyperbolic nanofluid flow with suspension dust particles along a vertical stretching sheet is carried out. The current model comprises of non-linear partial differential equations expressing conservation of total mass, momentum, and thermal energy for two-phase tangent hyperbolic nanofluid phase and dust particle phase. Primitive similarity formulation is given to mutate the dimensional boundary layer flow field equations into a proper nonlinear ordinary differential system then Runge-Kutta-Fehlberg method (RKF45 method) is applied. Distinct pertinent parameter impact on the fluid or particle velocity, temperature, concentration, and skin friction coefficient is illustrated. Analysis of the obtained computations shows that the flow field is affected appreciably by the existence of suspension dust particles. It is concluded that an increment in the mass concentration of dust particles leads to depreciate the velocity distributions of the nanofluid and dust phases. The numerical computations has been validated with earlier published contributions for a special cases.

中文翻译：

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两相混合对流纳米流体流过非线性拉伸片的双曲线尘埃切线

对非牛顿切线双曲纳米流体流与悬浮尘埃粒子沿垂直拉伸片的磁流体动力学 (MHD) 混合对流进行了理论分析。当前模型由非线性偏微分方程组成，表示两相切线双曲纳米流体相和尘埃粒子相的总质量、动量和热能守恒。给出原始相似公式将维边界层流场方程变异为适当的非线性常微分系统，然后应用Runge-Kutta-Fehlberg方法（RKF45方法）。说明了对流体或粒子速度、温度、浓度和皮肤摩擦系数的不同相关参数影响。对所得计算结果的分析表明，悬浮尘粒的存在显着影响了流场。结论是尘埃粒子质量浓度的增加导致纳米流体和尘埃相的速度分布下降。数值计算已经通过早期发表的特殊情况的贡献得到验证。