In this study, the Daftardar–Jeffery polynomials are incorporated in the homotopy of the optimal homotopy asymptotic method (OHAM) for solving the generalized Hirota–Satsuma coupled system of Korteweg–de Vries equations. The results are displayed through graphs and tables. The results obtained in this study are also compared with the published work on OHAM, which shows that OHAM-DJ is more explicit, reliable, and an efficient analytical technique. The exactness of the developed method can be improved by performing the higher iterations.

Energy efficiency is the highest need of present times to meet the challenges of global energy demands. Nanofluids have proved to possess dynamic thermal characteristics in many experimental and theoretical studies during recent years. Nowadays, a variety of nanomaterials are accessible, and among these alloys of aluminum, AA7072 and AA7075 are important due to their unique functional characteristics. These alloys are widely used in the engineering of aircraft, spacecraft, buildings, and so on. Aiming to highlight the importance of nanofluids, this article analyses the heat and mass transfer for magnetohydrodynamic hybrid nanofluid flow on a stretching sheet of gyrotactic microorganisms. Additionally, the impacts of chemical reactions, activation energy, Peclet number, thermophoresis, Lewis number, Brownian motion, and thermal radiation are also studied. The governing equations from Partial differential equations into Ordinary differential equations are transformed with the support of resemblance transformations, and the solution is obtained with HAM techniques. The numerical findings are presented in figures and tabular form with the Mathematica program. The obtained results are explained from a physical point of view in detail. An assessment between the proposed and current model is described under specific flow parameter assumptions to validate the analysis. It is revealed that the outcomes are consistent with previous findings. The numbers of engineering importance like skin friction and heat transfer rate are explained for practical relevance. The impacts of nanoparticle loading show interesting results. It is perceived that an escalating trend is noted in the nanoparticle temperature through thermal radiation and thermophoretic parameters.