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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 .