Abstract In recent times, the mixture of liquids has been referred to as ‘‘hybrid modelling.” Ternary hybrid models are advantageous for different systems such as production industries, aerosol particle processing, and experimental instrument design, to name a few. The regulating partial differential equation (PDE) for nonlinear systems is changed into a system of associate nonlinear (ODE) In this study, ordinary differential equations report utilizing new similarity scaling symmetry transformations produced via Lie group transformations analysis. Using a BVP4C with a shooting method approach, the resulting system is numerically resolved (MATLAB). For Cases: 1 CNT, Graphene, Aluminium oxide, Cases: 2 Cooper oxide, Magnesium oxide, and Zirconium oxide with different nanosized particle morphologies including platelet, cylindrical, and spherical, the rate of heat transmission and the magnetohydrodynamic flow of incompressible fluid friction were studied. It is observed that Nusselt number transfer is having more transmission rate in case-1 Al2o3 ðÞ þ GNT þ CNT with water than in case-2 Mgo þ Zro2 Cuo with water ðÞ , This shows that, þ