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Skin friction coefficient c p Specific heat (J kg −1 K −1) f Dimensionless stream function g Dimensionless microrotation function j Micro-inertia density k Thermal conductivity of fluid (W m −1 K −1) K n Knudsen number ι = min[ 1 K n , 1] M Magnetic parameter N Microrotation component normal to xy-plane (s −1) n Microrotation parameter Nu x Local Nusselt number Pr Prandtl number q w Surface heat flux (W m −2) Re x Local Reynolds number T Temperature of the fluid inside the boundary layer (K) T w Temperature at the surface of the sheet (K) T ∞ Ambient temperature (K) u, v Velocity component along x-and y-direction (m s −1) Greeks α Momentum accommodation coefficient β Material parameter γ First order slip parameter δ Second order slip parameter η Dimensionless similarity variable θ Dimensionless temprature µ Coefficient of dynamic viscosity (Pas) υ Coefficient kinematic viscosity of (m 2 s −1) σ Electrical conductivity ψ Stream function (m 2 s −1) The molecular mean free path (m) Thermal diffusivity (m 2 s −1) ρ Fluid density (kg m −3

The present study scrutinizes slip effects and stagnation point flows of upperconvected Maxwell fluid past a stretching sheet. The non-linear ordinary differential equations are obtained from the governing partial differential equations and solved using implicit finite difference method. The impacts of non-dimensional governing parameters such as Brownian motion parameter, velocity ratio, velocity slip parameter, suction/injection parameter, Lewis numbers, upper-convected Maxwell parameter, magnetic field, thermophoresis parameter, chemical reactions parameter, thermal slip parameter, solutal slip parameter, and heat source parameter on the velocity field, heat and mass transfer characteristics are discussed and presented through graphs. The values of local Sherwood number, local Nusselt number, and skin friction coefficient are discussed and presented through tables. The results indicate that when the magnetic field is intensified, it reduces velocity profiles and raises temperature and concentration profiles. Moreover, with an upsurge in velocity slip parameter, the local Nusselt number and local Sherwood number diminish.

The present study examines the effect of induced magnetic field and convective boundary condition on magnetohydrodynamic (MHD) stagnation point flow and heat transfer due to upper-convected Maxwell fluid over a stretching sheet in the presence of nanoparticles. Boundary layer theory is used to simplify the equation of motion, induced magnetic field, energy and concentration which results in four coupled non-linear ordinary differential equations. The study takes into account the effect of Brownian motion and thermophoresis parameters. The governing equations and their associated boundary conditions are initially cast into dimensionless form by similarity variables. The resulting system of equations is then solved numerically using fourth order Runge-Kutta-Fehlberg method along with shooting technique. The solution for the governing equations depends on parameters such as, magnetic, velocity ratio parameter B, Biot number Bi, Prandtl number Pr, Lewis number Le, Brownian motion Nb, reciprocal of magnetic Prandtl number A, the thermophoresis parameter Nt, and Maxwell parameter β. The numerical results are obtained for velocity, temperature, induced magnetic field and concentration profiles as well as skin friction coefficient, the local Nusselt number and Sherwood number. The results indicate that the skin friction coefficient, the local Nusselt number and Sherwood number decrease with an increase in B and M parameters. Moreover, local Sherwood number -ϕ 0 (0) decreases with an increase in convective parameter Bi, but the local Nusselt number -θ 0 (0) increases with an increase in Bi. The results are displayed both in graphical and tabular form to illustrate the effect of the governing parameters on the dimensionless velocity, induced magnetic field, temperature and concentration. The numerical results are compared and found to be in good agreement with the previously published results on special cases of the problem.

The problem of two-dimensional steady laminar MHD boundary layer flow past a wedge with heat and mass transfer of nanofluid embedded in porous media with viscous dissipation, Brownian motion, and thermophoresis effect is considered. Using suitable similarity transformations, the governing partial differential equations have been transformed to nonlinear higher-order ordinary differential equations. The transmuted model is shown to be controlled by a number of thermophysical parameters, viz. the pressure gradient, magnetic, permeability, Prandtl number, Lewis number, Brownian motion, thermophoresis, and Eckert number. The problem is then solved numerically using spectral quasilinearization method (SQLM). The accuracy of the method is checked against the previously published results and an excellent agreement has been obtained. The velocity boundary layer thickness reduces with an increase in pressure gradient, permeability, and magnetic parameters, whereas thermal boundary layer thickness increases with an increase in Eckert number, Brownian motion, and thermophoresis parameters. Greater values of Prandtl number, Lewis number, Brownian motion, and magnetic parameter reduce the nanoparticles concentration boundary layer.