Research on boundary layer flow and heat transfer has been growing since their importance in industrial and technological processes has been recognized. The boundary layer flow over a horizontally and vertically slender (thin) needle with irregular size has created interest among researchers due to its infinite use in biomimetics field, biomedical, aerodynamics, and engineering purposes. The intention here is to study the two-dimensional steady hybrid nanofluid over a slender horizontal needle with water as its base, copper (cu), and alumina oxide (Al₂O₃) as the combination of nanoparticles in the presence of hydromagnetic and slip effect in the flow. A partial differential equation (PDEs) was set to govern the fluid flow model. Through similarity requirement, the PDE is transformed into ordinary differential equations (ODEs) and analysed using bvp4c in MATLAB 2019a. The influence of hydromagnetic (MHD), M, slip effect, σ, needle thickness, c, and nanoparticle volume fraction, φ on velocity, f ′ (η), temperature, θ(η), skin friction coefficient, C_f and local Nusselt number, Nu_x are clearly presented. Throughout the study, it shows that duality of solutions presents in a certain range when ԑ_c < ԑ ≤ − 1 and unique solution at ԑ > − 1. The range on the dual solutions broadens as σ increased, which contradicts with M and c that decreases as both of these values increased. Hence, a stability analysis is imposed. The reduction on skin friction between the needle and fluid can been seen when values of M, σ and c increased. Meanwhile, it also noted that the heat transfer rate on the needle surface increased drastically when σ is increased while opposite trait is found for M and c. hybrid nanofluid possesses better results in increasing the C_f and heat transfer rate compared to nanofluid.

由于边界层流动和传热在工业和技术过程中的重要性已得到认可，因此对其的研究一直在增长。由于其在仿生领域，生物医学，空气动力学和工程目的中的无限使用，边界层流过水平和垂直细长（细）针的大小不规则，引起了研究人员的兴趣。本文的目的是研究细长的水平针头上的二维稳定杂化纳米流体，该针头上以水，铜（cu）和氧化铝（Al ₂ O ₃）作为纳米粒子的组合，在流体中存在水磁和滑移效应的情况下。设置了偏微分方程（PDE）来控制流体流动模型。通过相似性要求，将PDE转换为常微分方程（ODE）并使用MATLAB 2019a中的bvp4c进行分析。磁流体（MHD）的影响下，中号，防滑效果，σ，针厚度，Ç，和纳米颗粒体积分数，φ上速度，˚F  '（η），温度，θ（η），皮肤的摩擦系数，Ç _˚F和本地努塞尔特数Nu _x清晰呈现。整个研究中，它显示的解决方案呈现了在一定范围内的是对偶时ԑ _ç  <  ԑ  ≤ - 1，在独特的解决方案ԑ  > - 1。在双解决方案变宽为σ增加的范围，这与用中号和Ç那随着这两个值的增加而减小。因此，进行了稳定性分析。当M，σ和c的值增加时，可以看到针头与液体之间皮肤摩擦的减少。同时，还注意到当σ增大时，针表面上的传热速率急剧增加，而M和c则具有相反的特性。混合纳米流体具有在提高更好的结果Ç _˚F相比纳米流体和传热速率。