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To comprehend the thermal regulation within the conical gap between a disk and a cone (TRHNF-DC) for hybrid nanofluid flow, this research introduces a novel application of computationally intelligent heuristics utilizing backpropagated Levenberg–Marquardt neural networks (LM-NNs). A unique hybrid nanoliquid comprising aluminum oxide, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><msub><mi>l</mi><mn>2</mn></msub><msub><mi>O</mi><mn>3</mn></msub></mrow></semantics></math></inline-formula>, nanoparticles and copper, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><mi>u</mi></mrow></semantics></math></inline-formula>, nanoparticles is specifically addressed. Through the application of similarity transformations, the mathematical model formulated in terms of partial differential equations (PDEs) is converted into ordinary differential equations (ODEs). The BVP4C method is employed to generate a dataset encompassing various TRHNF-DC scenarios by varying magnetic parameters and nanoparticles. Subsequently, the intelligent LM-NN solver is trained, tested, and validated to ascertain the TRHNF-DC solution under diverse conditions. The accuracy of the LM-NN approach in solving the TRHNF-DC model is verified through different analyses, demonstrating a high level of accuracy, with discrepancies ranging from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>10</mn><mrow><mo>−</mo><mn>10</mn></mrow></msup></semantics></math></inline-formula> to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>10</mn><mrow><mo>−</mo><mn>8</mn></mrow></msup></semantics></math></inline-formula> when compared with standard solutions. The efficacy of the framework is further underscored by the close agreement of recommended outcomes with reference solutions, thereby validating its integrity.