The addition of nanoparticles is one of the modern scientific techniques to improve the heat transfer enhancement. However, micropolar fluid model is not examined under nanoparticles effects. The addition of nanoparticles in a micropolar fluid, make the mixture more complex as compare to conventional nanofluids. The innovative micropolar nanofluid model is introduced to explore nanofluid characteristics under microstructure and inertial effects. In this study, steady laminar 2D natural convection flow of copper (Cu) and alumina (Al₂O₃) suspended micropolar nanofluid over a solid sphere with constant surface heat flux is investigated. The governing partial differential equations are transformed into dimensionless form and then solved numerically using an implicit finite difference scheme known as Keller-box method. The behaviors of different parameters on temperature, velocity and angular velocity have been examined graphically for both Cu/Al₂O₃-water and Cu/Al₂O₃-kerosene oil. From graphical results, it is found that temperature and velocity fields of Al₂O₃-water have higher values as compared to Al₂O₃-kerosene oil.

Many physical aspects emerging from the local structure and micromotions of liquid particles can be studied by utilizing the governing model of micropolar liquid. It has the ability to explain the behavior of a wide range of real fluids, including polymeric solutions, liquid crystals, lubricants, and animal blood. This earned it a major role in the treatment of many industrial and engineering applications. Radiative heat transmission induced by a combined convection flow of micropolar fluid over a solid sphere, and its enhancement via nanoparticle oxides, are investigated in this study. An applied magnetic field and a constant wall temperature are also considered. The Tiwari–Das model is used to construct the mathematical model. An approximate numerical solution is included using the Keller box method, in which its numerical calculations are performed via MATLAB software, to obtain numerical results and graphic outputs reflecting the effects of critical parameters on the physical quantities associated with heat transfer. The investigation results point out that a weakness in the intensity of the magnetic field, or an increment in the nanoparticle volume fraction, causes an increment in velocity. Raising the radiation parameter promotes energy transport, angular velocity, and velocity.

This numerical analysis aims to observe and analyze the combined convection characteristics of the micropolar tri-hybrid nano-liquid that moves around a cylindrical object, and, in addition, to compare its thermal behavior to that of hybrid and mono nano-fluids. For this purpose, the problem is modeled by developing the Tiwari and Das models, then the governing model is converted into dimensionless expressions, and finally, the problem is solved using the Keller box approximation. The current findings are compared with previously published results to show that the present method is sufficiently accurate for physical and engineering applications. By examining and analyzing the extent to which skin friction, the Nusselt number, velocity, angular velocity, and temperature are affected by some critical factors, the following points are revealed: A greater value of the micropolar and magnetic factors can result in curtailing the heat transmission rate, velocity, and angular velocity. Higher values of the mixed convection factor can contribute to a better rate of energy transfer and can grant the micropolar tri-hybrid nano-liquid a higher velocity. Regardless of the influencing factors, the maximum value of all considered physical groups is achieved by using ternary hybrid nano-liquids.

The assumptions that form our focus in this study are water or water-ethylene glycol flowing around a horizontal cylinder, containing hybrid nanoparticles, affected by a magnetic force, and under a constant wall temperature, in addition to considering free convection. The Tiwari–Das model is employed to highlight the influence of the nanoparticles volume fraction on the flow characteristics. A numerical approximate technique called the Keller box method is implemented to obtain a solution to the physical model. The effects of some critical parameters related to heat transmission are also graphically examined and analyzed. The increase in the nanoparticle volume fraction increases the heat transfer rate and liquid velocity; the strength of the magnetic field has an adverse effect on liquid velocity, heat transfer, and skin friction. We find that cobalt nanoparticles provide more efficient support for the heat transfer rate of aluminum oxide than aluminum nanoparticles.

This analysis focuses on extending and developing some previous studies of energy transport through nanofluids to include the states of combined convection flow of a Williamson hybrid nanofluid that flows around a cylinder. Mathematical models that simulate the behavior of these upgraded nanofluids are constructed by expanding the Tiwari and Das model, which are then solved numerically via Keller box approaches. The accuracy of the results is emphasized by comparing them with the previous published outcomes. Nanosolid volume fraction $0\le \chi \le 0.1,$ combined convection $-1\le \lambda \le 5,$ radiation factor $0.1\le R\le 6,$ Weissenberg number $0.2\le We\le 0.9,$ and magnetic factor $0.1\le M\le 1$ are the factors that have been taken into consideration to examine the energy transfer performance of Williamson hybrid nanofluid. Numerical and graphical outcomes are obtained using MATLAB, analyzed, and discussed in depth. According to the outcomes, the Weissenberg number reduces energy transfer and friction forces. Both the combined convective coefficient and the radiation factor improved the rate of energy transfer and increased the velocity of the host fluid. The fluid velocity and rate of energy transfer can be reduced by increasing the magnetic factor. The nanoparticle combination of silver and aluminum oxide (Ag-Al₂O₃) has demonstrated superiority in enhancing the energy transfer rate and velocity of the host fluid.