In this article, the effects of a Casson Nanofluid boundary layer flow, over an inclined extending surface with Soret and Dufour, is scrutinized. The model used in this study is based on the Buongiorno model of the thermal efficiencies of the fluid flows in the presence of Brownian motion and thermophoresis properties. The non-linear problem for Casson Nanofluid flow over an inclined channel is modeled to gain knowledge on the heat and mass exchange phenomenon, by considering important flow parameters of the intensified boundary layer. The governing non-linear partial differential equations are changed to non-linear ordinary differential equations and are afterward illustrated numerically by the Keller-Box scheme. A comparison of the established results, if the incorporated effects are lacking, is performed with the available outcomes of Khan and Pop [1] and recognized in a nice settlement. Numerical and graphical results are also presented in tables and graphs.

In this article, we present a numerical analysis of the energy and mass transport behavior of microrotational flow via Riga plate, considering suction or injection and mixed convection. The thermal stratified parameters of nanofluid are captured using an interpretation of the well-known Keller box model, which helps us to determine the characteristic properties of the physical parameters. The formulated boundary layer equations (nonlinear partial differential equations) are transformed into coupled ODEs with nonlinearities for the stratified controlled regimes. The impact of embedded flow and all physical quantities of practical interest, such as velocity, temperature, and concentration profile, are inspected and presented through tables and graphs. We found that the heat transfer on the surface decreases for the temperature stratification factor as mass transfer increases. Additionally, the fluid velocity increases as the modified Hartmann number increases.

The study of nanofluids has become a key research area in mathematics, physics, engineering, and materials science. Nowadays, nanofluids are widely used in many industrial applications to improve thermophysical properties such as thermal conductivity, thermal diffusivity, convective heat transfer, and viscosity. This article discusses the effects of heat generation/absorption and chemical reaction on magnetohydrodynamics (MHD) flow of Williamson nanofluid over an inclined stretching surface. The impact of Williamson factor on velocity field is investigated numerically using Keller box analysis (KBA). Suitable similarity transformations are used to recover ordinary differential equations (ODEs) from the boundary flow equations. These ordinary differential equations are addressed numerically. The numerical computations revealed that energy and species exchange decrease with rising values of magnetic field. Moreover, it is found that increasing the chemical reaction parameter increases the Nusselt number and decreases skin friction. Further, the effect of Lewis parameter diminishes energy transport rate. In the same vein, it is also observed that increasing the inclination can enhance skin friction, while the opposite occurred for the energy and species transport rate. As given numerical computations demonstrate, our results are in reasonable agreement with the reported earlier studies.

Brownian motion and thermophoresis diffusions are the fundamental ideas of abnormal upgrading in thermal conductivity via binary fluids (base fluid along with nanoparticles). The influence of Brownian motion and thermophoresis are focused on in the Buongiorno model. In this problem, we considered the Buongiorno model with Brownian motion and thermophoretic effects. The nonlinear ordinary differential equations are recovered from the partial differential equations of the boundary flow via compatible similarity transformations and then employed to the Keller-box scheme for numerical results. The physical quantities of our concern including skin friction, Nusselt number, and Sherwood number along with velocity, temperature and concentration profile against involved effects are demonstrated. The impacts of the involved flow parameters are drawn in graphs and tabulated forms. The inclination effect shows an inverse relation with the velocity field. Moreover, the velocity profile increases with the growth of the buoyancy effect.

The investigation of heat and mass transport properties of the flow is a key research area in mathematics, physics, engineering, and computer science. This article focuses on studying the heat and mass transport phenomenon for micropolar nanofluid flow generated by a vertical stretching Riga plate. It is assembled by including a spanwise-aligned array of alternating electrodes and permanent magnets. This technique produces electromagnetic hydrodynamic behavior in flow. Our aim for this article is to examine the influences of Brownian motion and thermophoresis on a Riga plate. We also explore the micro-rotational effects of the particles. The flow behavior of the modeled problem has also been computed numerically and presented by the graph. It is verified that the numerical computations show a good approval with the reported earlier studies. The velocity profile is computed and presented by the graph, which shows direct correspondence with the modified Hartmann number. We also show that energy and mass flux rates increase by increasing modified Hartmann numbers. The results also revealed that concentration distribution diminishes for larger values of Brownian motion, whereas temperature distribution portrays increases for larger values of both Brownian motion and thermophoresis. Moreover, it is found that concentration distribution shows direct relation with thermophoretic impact.

The principal objective of the current study is to analyze the Brownian motion and thermophoretic impacts on micropolar nanofluid flow over a nonlinear inclined stretching sheet taking into account the Soret and Dufour effects. The compatible similarity transformations are applied to obtain the nonlinear ordinary differential equations from the partial differential equations. The numerical solution of the present study obtained via the Keller-Box technique. The physical quantities of interest are skin friction, Sherwood number, and heat exchange, along with several influences of material parameters on the momentum, temperature, and concentration are elucidated and clarified with diagrams. A decent settlement can be established in the current results with previously published work in the deficiency of incorporating effects. It is found that the growth of the inclination and nonlinear stretching factor decreases the velocity profile. Moreover, the growth of the Soret effect reduces the heat flux rate and wall shear stress.