| Summary: | The problem of a steady flow and heat transfer past a permeable moving thin needle in a hybrid nanofluid is examined in this study. Here, we consider copper (Cu) and alumina (Al<sub>2</sub>O<sub>3</sub>) as hybrid nanoparticles, and water as a base fluid. In addition, the effects of thermophoresis and Brownian motion are taken into consideration. A similarity transformation is used to obtain similarity equations, which are then solved numerically using the boundary value problem solver, bvp4c available in Matlab software (Matlab_R2014b, MathWorks, Singapore). It is shown that heat transfer rate is higher in the presence of hybrid nanoparticles. It is discovered that the non-uniqueness of the solutions is observed for a certain range of the moving parameter <inline-formula> <math display="inline"> <semantics> <mi>λ</mi> </semantics> </math> </inline-formula>. We also observed that the bifurcation of the solutions occurs in the region of <inline-formula> <math display="inline"> <semantics> <mrow> <mi>λ</mi> <mo><</mo> <mn>0</mn> </mrow> </semantics> </math> </inline-formula>, i.e., when the needle moved toward the origin. Furthermore, we found that the skin friction coefficient and the heat transfer rate at the surface are higher for smaller needle sizes. A reduction in the temperature and nanoparticle concentration was observed with the increasing of the thermophoresis parameter. It was also found that the increase of the Brownian motion parameter leads to an increase in the nanoparticle concentration. Temporal stability analysis shows that only one of the solutions was stable and physically reliable as time evolved.
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