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In current days, hybrid models have become more essential in a wide range of systems, including medical treatment, aerosol particle handling, laboratory instrument design, industry and naval academia, and more. The influence of linear, nonlinear, and quadratic Rosseland approximations on 3D flow behavior was explored in the presence of Fourier fluxes and Boussinesq quadratic thermal oscillations. Ternary hybrid nanoparticles of different shapes and densities were also included. Using the necessary transformation, the resulting partial differential system is transformed into a governing ordinary differential system, and the solution is then furnished with two mixed compositions (Case-Ⅰ and Case-Ⅱ). Combination one looked at aluminum oxide (Platelet), graphene (Cylindrical), and carbon nanotubes (Spherical), whereas mixture two looked at copper (Cylindrical), copper oxide (Spherical), and silver oxide (Platelet). Many changes in two mixture compositions, as well as linear, quadratic, and nonlinear thermal radiation situations of the flow, are discovered. Case-1 ternary combinations have a wider temperature distribution than Case-2 ternary mixtures. Carbon nanotubes (Spherical), graphene (Cylindrical), and aluminum oxide (Platelet) exhibit stronger conductivity than copper oxide (Spherical), copper (Cylindrical), and silver oxide (Platelet) in Case 1. (Platelet). In copper oxide (Spherical), copper (Cylindrical), and silver (Platelet) compositions, the friction factor coefficient is much higher. The combination of liquids is of great importance in various systems such as medical treatment, manufacturing, experimental instrument design, aerosol particle handling and naval academies, etc. Roseland's quadratic and linear approximation of three-dimensional flow characteristics with the existence of Boussinesq quadratic buoyancy and thermal variation. In addition, we combine tertiary solid nanoparticles with different shapes and densities. In many practical applications such as the plastics manufacturing and polymer industry, the temperature difference is remarkably large, causing the density of the working fluid to vary non-linearly with temperature. Therefore, the nonlinear Boussinesq (NBA) approximation cannot be ignored, since it greatly affects the flow and heat transport characteristics of the working fluid. Here, the flow of non-Newtonian elastomers is controlled by the tension of an elastic sheet subjected to NBA and the quadratic form of the Rosseland thermal radiation is studied.
Sajjan et al. (Sat,) studied this question.