This numerical investigation intends to present the impact of nanoparticles volume fraction, Casson, and magnetic force on natural convection in the boundary layer region of a horizontal cylinder in a Casson nanofluid under constant heat flux boundary conditions. Methanol is considered as a host Casson fluid. Graphite oxide (GO), single and multiple walls carbon nanotubes (SWCNTs and MWCNTs) nanoparticles have been incorporated to support the heat transfer performances of the host fluid. The Keller box technique is employed to solve the transformed governing equations. Our numerical findings were in an excellent agreement with the preceding literature. Graphical results of the effect of the relevant parameters on some physical quantities related to examine the behavior of Casson nanofluid flow were obtained, and they confirmed that an augmentation in Casson parameter results in a decline in local skin friction, velocity, or temperature, as well as leading to an increment in local Nusselt number. Furthermore, MWCNTs are the most efficient in improving the rate of heat transfer and velocity, and they possess the lowest temperature.

This work aimed to establish a numerical simulation of kerosene oil as a host Casson fluid flowing around a cylindrical shape with an applied magnetic field crossing through it, under constant wall temperature boundary conditions. Nanoparticles of zinc, aluminum, and titanium oxides were included to reinforce its thermal characteristics. The governing model was established based on the Tiwari and Das model. Graphical and numerical results for correlated physical quantities were gained through the Keller Box method, with the assistance of MATLAB software (9.2). The combined convection ($\lambda >0 \& \lambda <0$), magnetic parameter ($M>0$), Casson parameter ($\beta >0$), and nanosolid volume fraction ($0.1\le \chi \le 0.2$) were the parameter ranges considered in this study. According to the current findings, the growth of mixed convection parameter or volume fraction of ultrafine particles contributes to boosting the rate of energy transport, skin friction, and velocity distribution. Zinc oxide–kerosene oil has the highest velocity and temperature, whatever the parameters influencing it.

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.

A computational simulation of Williamson fluid flowing around a spherical shape in the case of natural convection is carried out. The Lorentz force and constant wall temperature are taken into consideration. In addition, upgrader heat transfer catalysts consisting of multi-walled carbon tubes, molybdenum disulfide, graphene oxide, and molybdenum disulfide are employed. The Keller box approach is used to solve the mathematical model governing the flow of hybrid Williamson fluid. To validate our findings, the key parameters in the constructed model are set to zero. Next, the extent of the agreement between our results and published results is observed. Numerical and graphical results that simulate the impressions of key parameters on physical quantities related to energy transmission are obtained, discussed, and analyzed. According to the results of this study, increasing the value of the Weissenberg number causes an increase in both the fluid temperature and drag force, while it also leads to a decrease in both the velocity of the fluid and the rate of energy transmission. Increasing the magnetic field intensity leads to a reduction in the rate of heat transfer, drag force, and fluid velocity while it has an appositive effect on temperature profiles.

Accurately modeling transport phenomena in melted nanofluids is a pivotal challenge for advancing technologies like high-density electronic cooling due to the strong coupling between phase change, nanoparticle dynamics, and external fields. This study introduces a novel hybrid framework that synergistically combines spectral collocation methods with multiple linear regression analysis. This framework is applied to the specific case of a magnetized, radiative ternary hybrid nanofluid past a shrinking cylinder. Current results reveal that increases in nanoparticle volume fractions escalates angular velocity while diminishing linear velocity and temperature. The micropolar factor reduces the magnitude of the Nusselt number. Enhancing melting at the cylindrical surface inhibits heat transmission and drag force. Regression analysis further identifies shrinkage and radiation as the primary controllers of thermal efficiency, while the magnetic parameter exerts dominance over drag force in this melting regime. This framework provides a powerful diagnostic tool for designing complex thermal systems where multiple physics interact.