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The present theoretical investigation is conducted on a micropolar fluid medium channel in the presence of mixed and nonlinear convection with the assumptions of thermal radiation and species reactive agents. The nonlinear governing equations, which describe the micropolar fluid flow and energy, are converted into ordinary differential equations using appropriate similarity variables. With the Runge–Kutta–Fehlberg method, the resultant equations are numerically solved. The physical characteristics of flow restrictions over velocity, microrotation, energy, and concentration profile are plotted and discussed. Further, the impact of several dimensionless parameters on Nusselt and Sherwood numbers is investigated and depicted graphically. In addition to observing flow patterns, contour plots of streamlines are plotted and discussed. It is demonstrated that the dimensionless velocity, temperature, and concentration of micropolar fluid have a maximum value at the center of the channel. However, the microrotation velocity of the micropolar fluid has both maxima and minima. The thermal and solutal properties of micropolar fluid influence heat and mass transport rates, that is, mixed convection and buoyancy parameter boost up the local heat transfer at the surface. Finally, Péclet number and chemically reactive parameters boost up the local mass transfer at the surface. [ABSTRACT FROM AUTHOR]

In the current communication, three‐dimensional Williamson fluid flow past a bidirectional inclined stretching plate with novel Hall current, nonuniform heat source/sink, and nth‐order chemical reaction features are investigated. Rosseland's diffusion model is defined for the radiation heat transfer. The nonlinear governing derivative equations satisfying the flow are transmuted to the coupled derivative equations by employing the local similarity quantities and then solved numerically through the Runge–Kutta–Fehlberg method utilizing the shooting quadrature. An inclusive analysis is reported via graphs for the flow rate field, temperature, and concentration distributions for different evolving terms of immense concern. Wall dragging effect and wall heat gradient and wall concentration gradient have been examined, plotted, and described. The detailed geometry reveals that dimensionless velocity field is monotonically rising as the Hall parameter rises. The chemical reaction concentration for the Williamson fluid is enhanced with expanding values of the magnetic field parameter. Transitional values of wall stress components upturn with an increase in Hall parameter while the Williamson term is boosted. Nusselt number is reduced as the Williamson term rises and the Sherwood number enhances with a rising chemical reaction term. The results are verified for limiting cases by comparing with various investigations and found to have excellent accuracy. [ABSTRACT FROM AUTHOR]

The current study focuses on investigating the influence of transverse magnetic field, variable viscosity, buoy-ancy, variable Prandtl number, viscous dissipation, Joulian dissipation, and heat generation on the flow of nanofluids over thin needle moving in parallel stream. The theory of nanofluids that includes the Buongiorno model featured by slip mechanism, such as Brownian motion and thermophoresis, has been implemented. Further, convective boundary condition and zero mass flux condition are considered. The nondimensionally developed boundary layer equations have been solved by Runge–Kutta–Fehlberg method with shooting technique for different values of parameters. The most relevant outcomes of the present study are that the augmented magnetic field strength, viscosity parameter, buoyancy ratio parameter, and the size of the needle undermine the flow velocity, establishing thicker velocity boundary layer while Richardson number and Brownian motion show opposite trend. Another most important outcome is that increase in the size of the needle, viscous dissipation, convective heating, and heat generation upsurges the fluid temperature, leading to improvement in thermal boundary layer. The effects of different natural parameters on wall shear stress and heat and mass transfer rates have been discussed. [ABSTRACT FROM AUTHOR]