Stimulated by thermal optimization in magnetic materials process engineering, the present investigation investigates theoretically the entropy generation in mixed convection magnetohydrodynamic (MHD) flow of an electrically-conducting nanofluid from a vertical cylinder. The mathematical model includes the effects of viscous dissipation, second order velocity slip and thermal slip, has been considered. The cylindrical partial differential form of the two-component non-homogenous nanofluid model has been transformed into a system of coupled ordinary differential equations by applying similarity transformations. The effects of governing parameters with no-flux nanoparticle concentration have been examined on important quantities of interest. Furthermore, the dimensionless form of the entropy generation number has also been evaluated using homotopy analysis method (HAM). The present analytical results achieve good correlation with numerical results (shooting method). Entropy is found to be an increasing function of second order velocity slip, magnetic field and curvature parameter. Temperature is elevated with increasing curvature parameter and magnetic parameter whereas it is reduced with mixed convection parameter. The flow is accelerated with curvature parameter but decelerated with magnetic parameter. Heat transfer rate (Nusselt number) is enhanced with greater mixed convection parameter, curvature parameter and first order velocity slip parameter but reduced with increasing second order velocity slip parameter. Entropy generation is also increased with magnetic parameter, second order slip velocity parameter, curvature parameter, thermophoresis parameter, buoyancy parameter and Reynolds number whereas it is suppressed with first order velocity slip parameter, Brownian motion parameter and thermal slip parameter.

受磁性材料工艺工程中的热优化刺激，本研究从理论上研究了来自垂直圆柱体的导电纳米流体的混合对流磁流体动力学（MHD）流中的熵产生。已经考虑了数学模型，包括粘性耗散，二阶速度滑移和热滑移的影响。通过应用相似变换，两组分非均质纳米流体模型的圆柱偏微分形式已转换为耦合常微分方程组。在重要的目标量上已经检查了无助焊剂纳米粒子浓度控制参数的影响。此外，熵生成数的无量纲形式也已使用同伦分析方法（HAM）进行了评估。本分析结果与数值结果（校正方法）具有良好的相关性。发现熵是二阶速度滑移，磁场和曲率参数的增加函数。温度随着曲率参数和磁参数的增加而升高，而温度随着混合对流参数的降低而降低。流量通过曲率参数加速，但通过磁参数减速。更大的混合对流参数，曲率参数和一阶速度滑移参数可提高传热速率（努塞尔数），而二阶速度滑移参数可提高传热速率（努塞尔数）。熵的产生也随着磁参数的增加而增加，