In this analysis, the mixed convection boundary layer MHD flow of non-Newtonian Carreau fluid subjected to Soret and Dufour effects over a moving vertical plate is studied. The governing flow equations are converted into a set of non-linear ordinary differential equations using suitable transformations. For numerical computations, bvp4c in MATLAB package is used to solve the resulting equations. Impacts of various involved parameters, such as Weissenberg number, power-law index, magnetic parameter, thermal buoyancy parameter, solutal buoyancy parameter, thermal radiation, Dufour number, Soret number and reaction rate parameter, on velocity, temperature and concentration are shown through figures. Also, the local skin-friction coefficient, local Nusselt number and local Sherwood number are calculated and shown graphically and in tabular form for different parameters. Some important facts are revealed during the investigation. The temperature and concentration show decreasing trends with increasing values of power-law index, whereas velocity shows reverse trend and these trends are more prominent for larger values of Weissenberg number. For stronger magnetic field, velocity decreases, while the temperature and concentration increase. It was also found that for shear thinning fluid the drag coefficient exhibits an increasing character when Weissenberg number increases, but for shear thickening fluid the drag coefficient shows the contrary nature. For small values of Dufour number, heat transfer rate enhances with increasing Soret number, but for higher values of Dufour number it slightly dies down with Soret number and the mass transfer rate reacts oppositely. In addition, due to increasing chemical reaction rate, the concentration and velocity decrease.

Entropy generation analysis in steady two-dimensional, viscous, incompressible forced convective Falkner–Skan flow of Maxwell nanofluid over a static wedge embedded in a porous medium with temperature-dependent viscosity is examined. The Buongiorno’s model has been utilised, to get the flow governing higher-order coupled nonlinear partial differential equations (PDEs) from mass, momentum, energy and concentration conservations. Suitable transformations have been done to convert governing PDEs into the coupled non-linear ODEs along with no-slip boundary conditions, which are then solved using the MATLAB programme bvp4c. The influences of diverse flow governing parameters on various flow properties and quantities of physical interest are displayed in graphical mode and discussed. It is found that entropy generation reduces only with Eckert number (Ec), while more entropy is generated for pressure gradient parameter $(m)$, local Deborah number ($\beta$), variable viscosity parameter ($\delta$) and permeability parameter ($K$). Entropy generation due to heat transfer irreversibility is prominent with increase in $m$ and $\delta$, but it is not so for other parameters. The drag force on the wedge surface become stronger with $\beta$ and $m$, but it reduces with $\delta$. Rates of heat transfer and mass transfer enhance with $m$ and $\delta$. In addition, surface drag force and heat transfer rate diminish with Brownian motion parameter ($Nb$) and thermophoresis parameter ($Nt$).

Two-dimensional forced convective steady boundary layer flow of non-Newtonian Eyring–Powell nanofluid over a moving plate in a porous medium in the presence of a parallel free-stream is investigated. The governing coupled non-linear partial differential equations (PDEs) along with boundary conditions are transformed into a set of non-linear coupled ordinary differential equations (ODEs) by using appropriate transformations. The obtained non-linear ODEs with modified boundary conditions are converted into a system of first-order ODEs whichare solved using the classical and efficient shooting method. Dual solutions for velocity, temperature and nanoparticle concentration distributions for Eying–Powell fluids similar to Newtonian fluid in some special flow situations are obtained, when the plate and free-stream are moving along mutually opposite directions. The stability analysis of the obtained solutions is performed and it is found that the upper branch solutions are physically stable, while lowerbranch solutions are unstable. The impacts of different dimensionless physical parameters on velocity, temperature and nanoparticle concentration are reported in the form of graphs and tables. An important result is obtained and itreveals that the ‘dual solutions’ character has been destroyed if resistance due to the porous medium is raised up to a definite level (i.e., permeability parameter K > 0.07979), though the range of existence of unique solution becomes larger with further increase of resistance due to porous medium. It is also observed that heat transfer rate diminishes with increasing thermophoresis parameter, Brownian diffusion parameter and Lewis number in all the cases, whereas mass transfer rate enhances with thermophoresis parameter (for dual solutions), Brownian diffusionparameter (for unique solutions) and Lewis number (for unique solutions). Further, skin-friction coefficient, i.e., the surface drag force, increases with permeability parameter, suction/injection parameter and decreases with Eyring–Powell fluid parameter. Also, increments in permeability parameter and the suction/injection parameter lead to the delay in the boundary layer separation. The critical values of velocity ratio parameter beyond which the boundarylayer separation appears are − 0.5476432, − 0.5987132, − 0.704862, − 0.816944, − 0.9365732, − 0.96179102, − 1.057104, − 1.062004, − 1.09222, − 1.115824, − 1.193413, − 1.591023 and − 1.898366 for K = 0, 0.01, 0.03, 0.05, 0.07, 0.074, 0.08, 0.082, 0.085, 0.09, 0.1, 0.15 and 0.2, respectively.