The steady two-dimensional MHD flow of a Jeffery nanofluid over a stretching sheet in the presence of thermal radiation and heat source has been examined numerically. The Brownian motion and thermophoresis effects have been fused in the nanofluid. Applying similarity transformations, the governing partial differential equations are reduced into a set of non-linear ordinary differential equations and then are solved numerically by using the fourth order Runge-Kutta method along with shooting technique (MATLAB package). The influence of various flow parameters on the velocity, temperature, nanoparticles concentration as well as the skin friction coefficient, Nusselt and Sherwood numbers has been presented and discussed through graphs and tables. It is observed that the thermophoresis parameter N_t shows the increasing nature of temperature for both Newtonian and non-Newtonian nanofluids. Whereas the Deborah number β and ratio of relaxation and retardation times λ show opposite effect on the velocity, temperature and concentration distributions.

A mathematical model is proposed to analyze the impacts of an inclined magnetic field and velocity slip on a hybrid nanoliquid over an exponentially elongated sheet in the presence of thermal heat flux. In this study, single wall and multiwall carbon nanotubes (SWCNT and MWCNT’s) are considered as nanoparticles with water as a base fluid due to their distinctive nanostructures and excellent thermal conductivity in many industrial and engineering applications. The governing equations are converted into ordinary differential equations by employing appropriate similarity transformations and are then solved by utilizing the bvp4c technique with the help of MATLAB software. The influence of various parameters such as magnetic field ( $0\le M\le 2$), velocity slip parameter ( $0\le \lambda \le 1.5$), angle of inclination ( ${30}^o\le \gamma \le {90}^0$), thermal radiation ( $0\le R\le 1.5$), Prandtl number ( $0.71\le Pr\le 10$), the volume fraction of the nanoparticles ( $0.05\le {\varphi }_1,{\varphi }_2\le 0.25$) on fluid velocity and dimensionless temperature are discussed graphically. The fluid momentum and dimensionless temperature are dominant for hybrid nanoliquid against a single wall or multi-wall carbon tubes/water. Also, the heat transfer rate decelerates by increasing the slip parameter and the magnetic parameter.

A mathematical model has been established to study the effect of heat source on magnetohydrodynamic 3D chemically reacting couple stress nanofluid flow generated due to the stretching surface. The flow of the fluid in this analysis is controlled by the effects of Brownian motion and thermophoresis force on the temperature and concentration boundary. Zero nanoparticle mass flux condition is employed at the surface, which specifies that the nanoparticles fraction are submissively measured. The systems of partial differential equations translated into dimensionless expressions by using suitable similarity functions and are then evaluated computationally (by utilizing MATLAB). The influence of different physical parameters on the flow variables is displayed graphically and discussed. It is reviled that the thermal and species boundary layer thickness of the liquid is enhanced due to the rising values of thermal radiation ( $2\le R_d\le 8$) and heat generation ( $0.1\le H\le 0.4$). On the other hand rate of heat transfer and skin-friction coefficient are shown reverse trend with the increase of couple stress values ( $0.1\le K\le 0.4$). The outcomes of present work are matched with the results available in the literature and are found to approve very closely as a limiting case.