This paper investigates the Newtonian heating effect on nanofluid flow over a nonlinear permeable stretching/shrinking sheet near the region of stagnation point. Only two important mechanisms on the transportation of nanoparticles in base fluid are discussed: the Brownian motion and thermophoresis. This physical problem is modelled using the Buongiorno (ASME J. Heat Transfer 128, 240 (2006) model in terms of nonlinear governing partial differential equations and transformed into dimensionless ordinary differential equations by using similarity transformation and the solution is calculated using the numerical scheme known as the Chebyshev spectral collocation method. The main interest of this study is the region of the boundary layer where viscous effects are dominant. Dual solutions are reported against the shrinking parameter in which the first solution is stable due to positive eigenvalues and the second is unstable due to negative eigenvalues and ranges of these solutions are effected by the suction parameter which is discussed using graphs and tables. The effects of dimensionless parameters, namely, velocity ratio, suction, Schmidt number, Prandtl number, thermophoresis and Brownian motion on temperature and concentration profiles, skin friction coefficient and Nusselt number are also shown using graphs. For the validity of the applied scheme, a comparison is established with published studies in the limiting case. Through the results, it is concluded that temperature and concentration increase by increasing the values of the thermophoresis parameter and the opposite behaviour is observed in the case of Brownian motion and Schmidt number. Skin friction coefficient, Nusselt and Sherwood numbers increase on increasing the suction parameter. Also, an enhancement in temperature and concentration profiles is observed in the presence of Newtonian heating parameter.

The advanced thermal characteristics of nanomaterials allow better heat transfer efficiency in engineering, industrial and technological processes. In this report, the outcome of a comparative analysis between the dynamics of blood carrying Cu nanoparticles and blood carrying single-walled carbon nanotubes (SWCNTs) due to the stretching and rotation of two disks at various levels of rotation, stretching, power-law index and heat source/sink is presented. By using appropriate similarity variables, the leading partial differential equations (PDEs)are altered into one-dimensional equations (ODEs). The resulting ODEs are handled using the shooting method. The impact of governing parameters on the boundary layer profiles is analysed graphically. Fluid velocity gets enhanced in three dimensions during the rotation of the disk, but they predict different behaviours for the stretching parameters of the upper and lower disks. The temperature decays for power-law index, rotation and stretching parameters. Also,the rates of heat transfer are more extensive for shear-thinning. Finally, the effects of the Cu–blood(blood) nanofluid are dominant over the base fluid (blood) and SWCNTs–blood nanofluid.

The optimised flow of nanofluids is quite essential to improve the thermal mechanism of various reacting materials. The entropy generation phenomenon is essential to avoid heat losses in thermal transport systems, heating processes and various engineering devices. In this theoretical analysis, the aspects of entropy generation is presented for time-independent second-grade nanomaterials for disk flow which shows rotating behaviours. The second-grade constitutive relations result in highly nonlinear differential equations. The effects of MHD, nonlinear radiation and chemical reaction are manifested in momentum, heat and concentration equations. Precise numerical treatmentfor a wide range of non-Newtonian fluid parameters was adopted to tackle the resulting similarity equations. The fluctuation against the heat transfer system, wall shear stress and mass changing phenomenon were also calculatedand examined for various parametrical values. The interesting Chebyshev spectral collocation numerical simulations were performed to present the solution. This research finds that the entropy generation and Bejan number show thesame trend for temperature and concentration difference parameters, whereas an opposite trend can be seen for the fluid and magnetic parameters. Also, entropy generation increases for diffusion parameter and Brinkman number,but Bejan number shows two trends.