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This study investigates the nanofluid flow towards a shrinking cylinder consisting of Al₂O₃ nanoparticles. Here, the flow is subjected to prescribed surface heat flux. The similarity variables are employed to gain the similarity equations. These equations are solved via the bvp4c solver. From the findings, a unique solution is found for the shrinking strength <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mo>≥</mo><mo>−</mo><mn>1</mn></mrow></semantics></math></inline-formula>. Meanwhile, the dual solutions are observed when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>λ</mi><mi>c</mi></msub><mo><</mo><mi>λ</mi><mo><</mo><mo>−</mo><mn>1</mn></mrow></semantics></math></inline-formula>. Furthermore, the friction factor <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msubsup><mi>e</mi><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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msubsup><mi>e</mi><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 with the rise of Al₂O₃ nanoparticles <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula> and the curvature parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>. Quantitatively, the rates of heat transfer <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msubsup><mi>e</mi><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 up to 3.87% when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula> increases from 0 to 0.04, and 6.69% when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> increases from 0.05 to 0.2. Besides, the profiles of the temperature <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>θ</mi><mrow><mo>(</mo><mi>η</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and the velocity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>’</mo><mrow><mo>(</mo><mi>η</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> on the first solution incline for larger <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>, but their second solutions decline. Moreover, it is noticed that the streamlines are separated into two regions. Finally, it is found that the first solution is stable over time.