<p>Thermal performance is significantly better in hybrid nanofluids compared to traditional nanofluids and leading to advancements in industrial processes, medical equipment, and nanomaterials engineering. The ongoing study explores the hybridized fluid flow dynamics over a bidirectional stretching surface, emphasizing their thermal flow properties under various impacts. The study explores not only achieving higher heat conduction compared to traditional nanofluids but also highlights the shape effects capabilities offered by the single-walled and multi-walled carbon nanotube nanoparticle combination in water. The partial differential equations concerning momentum and energy transport have been rendered into a set of ordinary differential equations using a similarity transformation. The transformed nonlinear dimensionless ODEs were solved using the <i>bvp5c</i> solver, a boundary-value problem tool available in MATLAB, and the obtained profiles were further refined and validated using MATLAB’s bvp5c solver. The visualizations represent the results for flows, heat transmission characteristics, which are obtained via the utilization of many important physical features. The present numerical data were validated by comparing special cases of the model with former published results, and display admirable agreement. Outcomes reveal that both hybrid volume fraction and nanoparticle rotation strengthen the axial velocity but damp transverse motion, showing a directional partiality in momentum transport. The temperature fields are remarkably raised by increasing the Biot number, radiation, hybrid nanoparticle concentration, and heat source factor, depicting the hybrid nanofluid’s thermal performance. These findings are applicable in the cooling of rotating machinery, microchannel thermal systems, solar collectors, and nano-manufacturing technologies.</p>