The flow and heat transfer characteristics of both single-wall and multi-wall carbon nanotubes (CNTs) with water and kerosene as base fluid on a moving plate with slip effect are studied numerically. By employing similarity transformation, governing equations are transformed into a set of nonlinear ordinary equations. These equations are solved numerically using the bvp4c solver in Matlab which is a very efficient finite difference method. The influence of numerous parameters such as nanoparticle volume fraction, velocity ratio parameter and first order slip parameter on velocity, temperature, skin friction and heat transfer rate are further explored and discussed in the form of graphical and tabular forms. The results reveal that dual solutions exist when the plate and free stream move in the opposite direction and slip parameter was found to widen the range of the possible solutions. However, skin friction coefficients decrease, whereas the heat transfer increases in the presence of slip parameter. Single-wall carbon nanotubes (SWCNTs) give higher skin friction and heat transfer compared to multi-wall carbon nanotubes (MWCNTs) due to the fact that they have higher density and thermal conductivity. A stability analysis is carried out to determine the stability of the solutions obtained.

Purpose: This paper aims to discuss a stability analysis on Cu-Al₂O₃/water nanofluid having a radiation and suction impacts over a rotating stretching/shrinking sheet. Design/methodology/approach: The partial differential equations are converted into nonlinear ordinary differential equations using similarity transformation and then being solved numerically using built in function in Matlab software (bvp4c). The effects of pertinent parameters on the temperature and velocity profiles together with local Nusselt number and skin friction are reported. Findings: Compared to previously published studies, the current work is noticed to be in good deal. The analysis further shows that the non-unique solutions exist for certain shrinking parameter values. Hence, a stability analysis is executed using a linear temporal stability analysis and concluded that the second solution is unstable, while the first solution is stable. The effect of suction parameter is observed to be significant in obtaining the solutions. The improvement of the local skin friction and the decrease of the local Nusselt number on the shrinking surface are observed with the increment of the copper nanoparticle volume fractions. Originality/value: The originality of current work is the numerical solutions and stability analysis of hybrid nanofluid in rotating flow. This work has also resulted in producing the non-unique solutions for the shrinking sheet, and a stability analysis has also been executed for this flow showing that the second solution is unstable, while the first solution is stable. This paper is therefore valuable for engineers and scientist to get acquainted with the properties of the flow, its behavior and the way to predict it. The authors admit that all the findings are original and were not published anywhere else.

The intent of this research was to present numerical solutions to homogeneous–heterogeneous reactions of the magnetohydrodynamic (MHD) stagnation point flow of a Cu-Al₂O₃/water hybrid nanofluid induced by a stretching or shrinking sheet with a convective boundary condition. A proper similarity variable was applied to the system of partial differential equations (PDEs) and converted into a system of ordinary (similarity) differential equations (ODEs). These equations were solved using Matlab’s in-built function (bvp4c) for various values of the governing parameters numerically. The present investigation considered the effects of homogeneous–heterogeneous reactions and magnetic field in the hybrid nanofluid flow. It was observed that dual solutions were visible for the shrinking sheet, and an analysis of stability was done to determine the physically realizable in the practice of these solutions. It was also concluded that hybrid nanofluid acts as a cooler for some increasing parameters. The magnetohydrodynamic parameter delayed the boundary layer separation; meanwhile, the nanoparticle volume fraction quickened the separation of the boundary layer that occurred. In addition, the first solution of hybrid nanofluid was found to be stable; meanwhile, the second solution was not stable. This study is therefore valuable for engineers and scientists to get acquainted with the properties of hybrid nanofluid flow, its behavior and the way to predict it.