This article presents non-similar analysis of Tiwari-Das hybrid nanofluid flow toward the exponentially expanding/shrinking sheet. Aluminum oxide ( A l 2 O 3 ) and copper ( Cu ) nanoparticles have been dispersed in the water. The significance of viscous dissipation, thermal radiation, magnetic fields, and heat sources has been observed in this work. A mathematical system is transmuted into a dimensionless, non-similar form by the utilization of non-similar transformations. The non-similar partial differential system is simulated by employing local non-similarity up to the 3rd order of iteration via bvp4c. The significance of flow constraints versus energy and velocity profiles is demonstrated through figures and tables. The fluid velocity decreases with expanding magnetic field ( M ) and injection parameters ( S ) . Energy profile grows as radiation ( Rd ) and heat generating ( Q ) parameter increases. The thermal profile is thought to be diminished by an expansion in the Prandtl number ( Pr ) . Stretching parameter ( λ ) increases cause a reduction in the temperature profile, whereas the heat profile grows as the Eckert parameter ( Ec ) increases. For particular values of the skin friction ( C f ) and Nusselt number ( Nu ) , numerical values are produced using local similarity and local non-similarity approaches. The findings indicate that skin friction decreases as the magnetic parameter ( M ) rises, but an expansion of the Prandtl number creates a growth in the Nusselt number. Excellent agreement between the current work and the published article is discovered in limiting cases.