The flow and heat transfer of non-Newtonian nanofluids has an extensive range of applications in oceanography, the cooling of metallic plates, melt-spinning, the movement of biological fluids, heat exchangers technology, coating and suspensions. In view of these applications, we studied the steady Marangoni driven boundary layer flow, heat and mass transfer characteristics of a nanofluid. A non-Newtonian second-grade liquid model is used to deliberate the effect of activation energy on the chemically reactive non-Newtonian nanofluid. By applying suitable similarity transformations, the system of governing equations is transformed into a set of ordinary differential equations. These reduced equations are tackled numerically using the Runge–Kutta–Fehlberg fourth-fifth order (RKF-45) method. The velocity, concentration, thermal fields and rate of heat transfer are explored for the embedded non-dimensional parameters graphically. Our results revealed that the escalating values of the Marangoni number improve the velocity gradient and reduce the heat transfer. As the values of the porosity parameter increase, the velocity gradient is reduced and the heat transfer is improved. Finally, the Nusselt number is found to decline as the porosity parameter increases.

A mathematical model is proposed to describe the flow, heat, and mass transfer behaviour of a non-Newtonian (Jeffrey and Oldroyd-B) fluid over a stretching sheet. Moreover, a similarity solution is given for steady two-dimensional flow subjected to Buongiorno’s theory to investigate the nature of magnetohydrodynamics (MHD) in a porous medium, utilizing the local thermal non-equilibrium conditions (LTNE). The LTNE model is based on the energy equations and defines distinctive temperature profiles for both solid and fluid phases. Hence, distinctive temperature profiles for both the fluid and solid phases are employed in this study. Numerical solution for the nonlinear ordinary differential equations is obtained by employing fourth fifth order Runge–Kutta–Fehlberg numerical methodology with shooting technique. Results reveal that, the velocity of the Oldroyd-B fluid declines faster and high heat transfer is seen for lower values of magnetic parameter when compared to Jeffry fluid. However, for higher values of magnetic parameter velocity of the Jeffery fluid declines faster and shows high heat transfer when compared to Oldroyd-B fluid. The Jeffery liquid shows a higher fluid phase heat transfer than Oldroyd-B liquid for increasing values of Brownian motion and thermophoresis parameters. The increasing values of thermophoresis parameter decline the liquid and solid phase heat transfer rate of both liquids.

Radiation and chemical reaction effects on the steady boundary layer flow of MHD Williamson fluid through porous medium toward a horizontal linearly stretching sheet in the presence of nanoparticles are investigated numerically. Adequate similarity transformations are used to derive a set of nonlinear ordinary differential equations governing the flow. The resultant nondimensionalized boundary value problem is solved numerically by Runge–Kutta–Fehlberg fourth–fifth order method with Shooting technique. The profiles for velocity, temperature and concentration, which are controlled by a number of thermo-physical parameters, are presented graphically. Based on these plots the conclusions are given, and the obtained results are tested for their accuracy

The current article explores the impact of magnetic effect on the Casson nanoliquid flow over a curved stretching sheet with the influence of chemical reaction. Further, the heat and mass transference characteristics are analyzed by means of Brownian motion, exponential heat source and thermophoresis effects. Governing equations of the described flow problem are transformed into ordinary differential equations by means of similarity variables. These reduced equations are numerically solved by Runge-Kutta-Fehlberg fourth-fifth (RKF 45) order scheme with shooting method. Results reveal that, the escalating values of curvature parameter improves the velocity gradient whereas, converse trend is detected in thermal gradient.

The current study explores the nanofluid flow and heat transfer properties by exposing it to a slippery surface. The effect of radiation, heat source, porous medium, and viscous dissipation are also comprised in this analysis. The arising partial differential equations from boundary layer equations of the second grade nanoliquid model are reformed into non-linear ordinary differential equations using suitable transformations. The solution of these equations is then cracked by means of shooting numerical scheme. In this investigation, we used two different types of nanoparticles, Alumina (Al ₂ O ₃ ) and Copper (Cu), along with a non-Newtonian Engine Oil (EO) as based liquid. The valuable finding of this scrutiny is that the comparative heat transference rate of Cu-EO second grade nanofluids gradually more increases as compared to Al ₂ O ₃ -EO nanofluids. Results reveal that, the parameters have a massive effect on the heat transfer very close to the wall and are slightly away from the wall. The escalation in nanoparticle volume fraction and second grade parameters declines the velocity profile.