<p>The increasing demand for engineering and biomedical systems is driven by innovative approaches that enhance the heat transfer mechanism. Hybrid nanofluid comprised of several nanoparticles suspended in conventional fluids has presented as promising elements in recent applications such as solar collectors, microchannel cooling systems, and targeted drug delivery. The present analysis is the synergetic inclusion of copper (Cu) and titanium dioxide (TiO₂) nanoparticles in conventional liquid water which has presented substantial improvements in thermal properties and radiative heat transport phenomena. Also, the study focuses on the predictive modeling of the Nusselt number in natural convection of Cu/TiO₂–water bi-hybridized fluid through a vertical surface with additional heat source. Further, the model accounts for the interactions of thermal radiation which is vital in simulating real-life thermal systems subject to high energy flux. The governing system describing the momentum and energy balance is converted into ordinary system using similarity transformation, and then, exact analytical method such as Laplace transform technique is deployed in handling the model. Further, as a novel approach, to predict the local Nusselt for the variation multiple factors a multilayered artificial neural network is trained using the simulated data. The ANN is designed with a back-propagation learning algorithm incorporating Levenberg–Marquardt optimization to minimize prediction errors and ensure the effective properties. The observation reveals that with a best performance of 0.077754 the model shows its best fitting predictive design for the heat transfer rate. However, with <i>R</i> value of 0.67194 the distribution of the Nusselt number for the factors utilized shows its significant result.</p>