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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.

The objective of this paper is to analyze the unsteady incompressible flow of the viscous nanofluid on a contracting surface with viscous dissipation effects. Presented and contrasted are analyses of both multi-wall carbon nanotubes (MWNTs) and single-wall carbon nanotubes (SWNTs). As the common (or base) fluids, kerosene oil and water are utilized. In the existence of first-order thermal and velocity slip conditions, mathematical modeling and analysis are performed. Using the MATLAB software's bvp4c solver tool, numerical solutions to the governing nonlinear modeled problems were obtained. This technique is particularly effective for developing many solutions to highly nonlinear differential equations. In addition, a comparison is done between this study and previously published works. The temperature, velocity, skin friction coefficient and heat-transfer rate have been explored for various significant factors included in the problem statements. In the unsteadiness parameter regime, dual solutions can be found. As the velocity slip parameter is increased, the flow slows down. In comparison to SWCNTs kerosene, MWCNTs kerosene oil has a greater velocity curve for the nanoparticles volume fraction. Increases in volume fraction decrease skin friction, whereas increases in the unsteadiness parameter speed up the drag force. Furthermore, as the Eckert number intensity increases, so do the temperature profiles in both solutions. Finally, the stability study revealed that the initial solution is robust, whereas the breakage in the second solution in the Nusselt number shows singularity, and thus the second solution is considered unstable. [ABSTRACT FROM AUTHOR]

Nonsimilar equations exist in many fluid flow problems and these equations are difficult to be solved using variation of the physical parameters. The key purpose of this study is to find nonsimilarity solution of nanofluid on an exponentially shrunk sheet in the existence of micropolar nanofluid without considerations of the thermal radiation and viscous dissipation effects. The governing partial differential equations (PDEs) are transformed into nonsimilar equations consisting of both ordinary and PDEs. Numerical results of velocity, microrotation, heat and concentration are presented in graphs. The results reveal that fluid particles' velocity decreases nearby surface and increases afterward. The skin friction, heat and concentration transfer rate are also plotted to perceive the phenomena with different physical situations. It can be deduced that wall shear force f ′ ′ (0) is improved by developed effects of micropolar fluid parameter K and reduced by increasing values of Hartmann number M. [ABSTRACT FROM AUTHOR]

This thermal case pronounced the stability framework for stagnation point flow of magnetized alumina and copper nanoparticles with due exponentially shrinking permeable surface. The thermal stability and enhancement of water base liquid had been taken into account with uniform impulsion of hybrid nanomaterials. The induced flow results via exponentially shrinking permeable surface. The similarity transformation simplifies the mathematical model where governing formulated system for hybrid nanofluid is altered into the nondimensional form. A numerical solver called bvp4c is employed in MATLAB software to aid in the problem-solving process, and dual branches have been found. The significance of pertaining parameters associated to the flow model is inspected in view of thermal properties. The findings show that there are two branches for suction strength (S > S c) and magnetic strength (M > M c). The bifurcation values S c and M c reduce for the occurrence of dual branches as the solid volume percentages of copper increase. Furthermore, for the upper branch solutions, the skin friction and heat transfer rate rise as ∅ Cu increases. The temporal stability analysis determines the stability of the dual branches, and it is discovered that only one of them is stable and physically applicable. The presence of suction parameter effectively controls the thermal transportation phenomenon. [ABSTRACT FROM AUTHOR]

Magnetohydrodynamic (MHD) flow of micropolar fluid by including the thermal radiation and convective condition on a shrinking surface in the presence of mass suction effects has been investigated. The momentum, angular momentum and energy equations, and the solutions of these equations are valid for whole Navier stokes, and microrotational and energy equations have been solved exactly. We obtain the solution in the form of an incomplete γ function for the energy equation. The results reveal that dual solutions exist for certain domains of different physical parameters. Furthermore, high suction produces the high effect of drag force, and as a result, coefficient of skin friction increases in the first solution. Stability analysis has been performed and determined that the first solution is more stable. [ABSTRACT FROM AUTHOR]

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