The chemically reactive unsteady 3D Sisko fluid flow over a bidirectional stretched surface in the presence of nonlinear thermal radiation and magnetic field is considered. The numerical scrutiny of the transformed nonlinear ODEs is performed with the help of a numerical technique known as bvp4c. The mechanism of heat and mass transfer by the applications of chemical reaction and radiation is presented using temperature and concentration graphs. A remarkable enhancing results are estimated in the presence of nonlinear thermal radiation parameter $R_{d}$ and temperature ratio parameter $\theta_{w}$ for the temperature field. Another significant decreasing outcomes are found while plotting the concentration profile with variation of homogeneous and heterogeneous parameters ($k_{1}, k_{2}$). Computational results of the local skin friction and local Nusselt number are tabulated under the influence of physical parameters which governs the flow. Decrease in skin friction with varying values of $\lambda$ is observed. On the other hand, the impact of $R_{d}$ and $\theta_{w}$ on the tabular values of local Nusselt number is found in increasing order. All the graphical results and tabular values are illustrated while testing both cases of power-law fluids including pseudoplastic (0 & lt; n & lt; 1) and dilatant (n & gt; 1) behaviours. A comparison of the bvp4c and shooting technique with RK-45 Fehlberg is presented which shows excellent agreement. Additionally, the present results are compared with the results in the existing literature and both are found to be in very good correlation.

The rheology of Burgers nanofluid flow over a stretching cylinder with convective transport of thermal and solutal energy is studied in the present article. The relaxation and retardation properties of viscoelastic fluid are examined for flow field and energy distribution. Moreover, the thermophoretic and Brownian forces are also incorporated in the phenomena of thermal and solutal energy distribution. The thermal conductivity of the fluid is taken as temperature dependent. The homotopy analysis method (HAM) is adopted to solve the governing ordinary differential equations (ODEs). The impact of physical parameters on the flow field and energy transport is depicted using graphs. The outcomes proved that both thermophoretic and Brownian forces significantly boosted the temperature field but in the case of concentration field these show conflicting behaviour. The Burgers parameter of viscoelastic fluid enhances the thermal and solutal conduction in the fluid and decreases the fluid velocity. Moreover, due to the increase in temperature-dependent thermal conductivity, the transport of energy increases. The outcomes of this study are validated by comparing numerical data with some previous studies.

Nanofluids can be engineered as per requirements and have applications in microelectronic, therapeutic activities, hybrid-mechanical machineries, aeronautics zones, thermonuclear storehouses, shielding of miscellaneous engines etc. Here, the aspects of new mass flux theory in magneto Carreau nanofluid with convectiveand variable connectivity have been studied. Additionally, nonlinear properties of mixed convection are examined. The shear thinning–thickening properties are analysed by utilising bvp4c algorithm for influential variables.The fluid temperature increases with thermophoresis and variable conductivity parameters. The outcomes of thermophoresis and Brownian motion parameters have conflicting influences on concentration field.