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The significance of the study comes in the fact that it investigates complex fluid dynamics and magnetohydrodynamics phenomena, which have the potential to be applied in a variety of domains, such as physics, engineering, and materials science. Their exceptional physical significance stems from their ability to combine the unique properties of multiple substances to provide the desired functions and performance characteristics. However, in this study, the numerical studies of slip effects on magnetized radiatively hybridized ferrofluid flow with acute magnetic force over stretching/shrinking surface were investigated. The main objective of current research is to examine the influence of solid volume percentage of cobalt ferrite, the sharply oriented magnetic field, and velocity slip factors on the behaviour of skin friction and heat transfer subjected to suction effect. Moreover, the study included an analysis of the behaviour of velocity and temperature profiles in relation to the consideration of the magnetic parameter, the solid volume percentage of cobalt ferrite, the Prandtl number, and the thermal radiation parameter. The equations that regulate the system were converted partial differential equations into ordinary differential equations by making use of the relevant similarity variables, and then, it solved with bvp4c MATLAB software. The boundary requirements are satisfied in particular parameter ranges where dual solutions are achieved. Besides, dual solutions were obtained in shrinking zone. At critical points, the two dual solutions intersect; however, after these points, no further solutions are accessible. The heat transfer rate decreased the velocity slip factor, while it increased the thermal slip factor. In addition, the thickness of the thermal boundary layer increased thermal radiation, while simultaneously reducing the Prandtl number. Besides, the temperature profile improves when the value of cobalt ferrite is higher. In summary, according to stability analysis, he first solution is stable and the second solution is unstable.

There are extensive range of applications related to nuclear industry, industrial manufacturing, science and engineering processing, in which the boundary layer hydromagnetic motion of Casson liquids perform vital role. Casson liquid is a useful liquid in the nuclear industry for optimizing the design and operation of nuclear reactors. Researchers have investigated transfer of heat in liquid motions with linear stratification, which is a phenomenon where the temperature varies linearly with height, affecting various fields such as medical equipment, glass fiber production, electronic devices, polymer sheets, paper production, filaments, and medicine. However, the most discussion of heat transfer problems is to get numerical solutions of a comprehensive Casson liquid model with heat generation described by the BVP4 via shooting method. In this study, a new velocity slip boundary condition is applied at the stretching or shrinking surface. These conditions are grounded in the previously established Buongiorno model, providing a more practical and realistic approach compared to previous study. The time independent Gov. Eqs. changed into a set of couple non-linear ODEs with help of suitable similarity conversions. The equations are evaluating via R-K-F by help of MATLAB software programming. [ABSTRACT FROM AUTHOR]

There are extensive range of applications related to nuclear industry, industrial manufacturing, science and engineering processing, in which the boundary layer hydromagnetic motion of Casson liquids perform vital role. Casson liquid is a useful liquid in the nuclear industry for optimizing the design and operation of nuclear reactors. Researchers have investigated transfer of heat in liquid motions with linear stratification, which is a phenomenon where the temperature varies linearly with height, affecting various fields such as medical equipment, glass fiber production, electronic devices, polymer sheets, paper production, filaments, and medicine. However, the most discussion of heat transfer problems is to get numerical solutions of a comprehensive Casson liquid model with heat generation described by the BVP4 via shooting method. In this study, a new velocity slip boundary condition is applied at the stretching or shrinking surface. These conditions are grounded in the previously established Buongiorno model, providing a more practical and realistic approach compared to previous study. The time independent Gov. Eqs. changed into a set of couple non-linear ODEs with help of suitable similarity conversions. The equations are evaluating via R-K-F by help of MATLAB software programming.

Recent nanotechnology advancements have created a remarkable platform for the development of a better performance of ultrahigh coolant acknowledged as nanofluid for numerous industrial and engineering technologies. The current study aims to examine the boundary-layer cross-flow of Williamson fluid through a rotational stagnation point towards either a shrinking or stretching permeable wall incorporated by a hybrid nanofluid. The shape factors along with the radiation effect are also taken into account. The contained boundary layers are the type of stream-wise by shrinking/stretching process along with the sheet. Employing the suitable transformations, the partial differential equations (PDEs) are transmuted to similarity (ordinary) differential equations (ODEs). The transmuted system of ODEs is worked out by using a built-in package bvp4c in MATLAB for distinct values of pertaining parameters. Dual (first and second branch) outcomes are found for the shrinking surface. The results suggest that the inclusion of hybrid particles uplifts the drag force as well as the heat transfer in both solutions. In addition, the Weissenberg number accelerates the separation. Moreover, the effect of suction permits the friction factor and heat transfer to improve significantly at the porous shrinking/stretching sheet of hybrid nanofluid.

The analysis explores the significance of thermal radiation on mixed convective boundary layer flow of a hybrid (SiO2–MoS2/H2O) nanofluid. The permeability of the stretched/shrinking surface is allowing the wall fluid suction, whereas radiation phenomenon is also incorporated in the presence of thermal convection. The combination of SiO2 nanoparticles and MoS2/H2O nanofluid are being modeled using the analytical nanofluid hybrid model in the present work. The hybrid nanofluid governing equations are transformed utilizing the similarity transformation technique. The transformed boundary value problem, then solved by bvp4c technique in MATLAB software. For specified values of various parameters the numerical results are obtained. The findings indicate dual solutions, up to some amount of stretching/shrinking parameter. The suction parameter decelerates the friction factor and accelerates the heat transfer rate. Also, the temperature augments due to the radiation and nanoparticles volume fraction in both solutions, whereas the velocity declines due to nanoparticles volume fraction.

The purpose of the present paper is to investigate the micropolar nanofluid flow on permeable stretching and shrinking surfaces with the velocity, thermal and concentration slip effects. Furthermore, the thermal radiation effect has also been considered. Boundary layer momentum, angular velocity, heat and mass transfer equations are converted to non-linear ordinary differential equations (ODEs). Then, the obtained ODEs are solved by applying the shooting method and in the results, the dual solutions are obtained in the certain ranges of pertinent parameters in both cases of shrinking and stretching surfaces. Due to the presence of the dual solutions, stability analysis is done and it was found that the first solution is stable and physically feasible. The results are also compared with previously published literature and found to be in excellent agreement. Moreover, the obtained results reveal the angular velocity increases in the first solution when the value of micropolar parameter increases. The velocity of nanofluid flow decreases in the first solution as the velocity slip parameter increases, whereas the temperature profiles increase in both solutions when thermal radiation, Brownian motion and the thermophoresis parameters are increased. Concentration profile increases by increasing N t and decreases by increasing N b . [ABSTRACT FROM AUTHOR]