This research work was the statistical and numerical investigation of heat transfer rate on MHD Jeffery–Hamel (J–H) ternary hybrid nanofluid flow. Moreover, the flow is under the influence of thermal radiation, MHD, variable thermal conductivity \(k_{{{\text{thnf}}}} \left( T \right)\) , stretchable–shrinkable inclined walls and temperature jump effects. In this situation, there are nanoparticles considered (i.e., \({\text{Fe}}_{3} {\text{O}}_{4} - {\text{ZnO}} - {\text{UO}}_{2}\) ). The purpose of this paper is to investigate the mechanisms by which hybrid nanofluids influence the skin friction coefficient ( \(C_{{\text{f}}}\) ) and heat transfer characteristics inside magnetohydrodynamic (MHD) systems. Additionally, a rise in the amount of hybrid nanofluids results in an increase in the viscosity, which in turn results in an increase in the skin friction coefficient. However, at the same time, the skin friction coefficient reduces as the Hartmann number values grow because turbulence decreases in proportion to the increase. The findings of the research demonstrate that the concentration of hybrid nanofluids and the intensity of magnetic fields interact in a complex way to impact fluid dynamics. According to the results of the study, optimizing the management of these parameters so as to minimize friction loss and maximize the performance of MHD applications is necessary. This research study provides quantitative and qualitative outcomes that improve comprehension of MHD hybrid nanofluid applications in practical settings. Analysis results demonstrate that the skin friction coefficient ( \(C_{{\text{f}}}\) ) together with Nusselt number (Nu) increases substantially as Reynolds number reaches 210 through optimal conditions when using 6% hybrid nanofluid concentration. The statistical findings based on ANOVA establish that predictor variables exert a very strong effect on \(C_{{\text{f}}}\) values (p-value = 0.000), but Nu values exhibit varying measurement significance patterns due to the complexity of heat transfer mechanisms. This qualitative part of the research demonstrates that ternary hybrid nanofluids deliver enhanced heat exchange performance through efficient nanomaterials that boost thermal conductivity and minimize stream resistance.
