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This paper examines the squeezed hybrid nanofluid flow over a permeable sensor surface with magnetohydrodynamics (MHD) and radiation effects. The alumina (Al₂O₃) and copper (Cu) are considered as the hybrid nanoparticles, while water is the base fluid. The governing equations are reduced to the similarity equations, using the similarity transformation. The resulting equations are programmed in Matlab software through the bvp4c solver to obtain the numerical solutions. It was found that the heat transfer rate was greater for the hybrid nanofluid, compared to the regular nanofluid. It was observed that dual solutions exist for some values of the permeable parameter <i>S</i>. The upper branch solutions of the skin friction coefficient (<inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mrow> <mi mathvariant="italic">Re</mi> </mrow> <mi>x</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msubsup> <msub> <mi>C</mi> <mi>f</mi> </msub> </mrow> </semantics> </math> </inline-formula>) and the heat transfer rate at the surface (<inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mrow> <mi mathvariant="italic">Re</mi> </mrow> <mi>x</mi> <mrow> <mo>−</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msubsup> <mi>N</mi> <msub> <mi>u</mi> <mi>x</mi> </msub> </mrow> </semantics> </math> </inline-formula>) enhance with the added Cu nanoparticle (<inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>φ</mi> <mn>2</mn> </msub> </mrow> </semantics> </math> </inline-formula>) and for larger magnetic strength (<inline-formula> <math display="inline"> <semantics> <mi>M</mi> </semantics> </math> </inline-formula>). Moreover, the values of <inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mrow> <mi mathvariant="italic">Re</mi> </mrow> <mi>x</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msubsup> <msub> <mi>C</mi> <mi>f</mi> </msub> </mrow> </semantics> </math> </inline-formula> decrease, whereas the values of <inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mrow> <mi mathvariant="italic">Re</mi> </mrow> <mi>x</mi> <mrow> <mo>−</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msubsup> <mi>N</mi> <msub> <mi>u</mi> <mi>x</mi> </msub> </mrow> </semantics> </math> </inline-formula> increase for both branches, with the rise of the squeeze flow index (<inline-formula> <math display="inline"> <semantics> <mi>b</mi> </semantics> </math> </inline-formula>). Besides, an increment of the heat transfer rate at the sensor surface for both branches was observed in the presence of radiation (<inline-formula> <math display="inline"> <semantics> <mi>R</mi> </semantics> </math> </inline-formula>). Temporal stability analysis was employed to determine the stability of the dual solutions, and it was discovered that only one of them was stable and physically reliable as time evolves.