A numerical investigation of unsteady magnetohydrodynamic mixed convective boundary layer flow of a nanofluid over an exponentially stretching sheet in porous media, is presented. The transformed, non-similar conservations equations are solved using a robust, explicit, finite difference method (EFDM). A detailed stability and convergence analysis is also conducted. The regime is shown to be controlled by a number of emerging thermophysical parameters i.e. combined porous and hydromagnetic parameter (R), thermal Grashof number (G _r ), species Grashof number (G _m ), viscosity ratio parameter (Λ), dimensionless porous media inertial parameter (∇), Eckert number (E _c ), Lewis number (L _e ), Brownian motion parameter (N_b) and thermophoresis parameter (N_t). The flow is found to be accelerated with increasing thermal and species Grashof numbers and also increasing Brownian motion and thermophoresis effects. However, flow is decelerated with increasing viscosity ratio and combined porous and hydromagnetic parameters. Temperatures are enhanced with increasing Brownian motion and thermophoresis as are concentration values. With progression in time the flow is accelerated and temperatures and concentrations are increased. EFDM solutions are validated with an optimized variational iteration method. The present study finds applications in magnetic nanomaterials processing.

This paper investigates combined heat and mass transfer by mixed magneto-convective flow of an electrically conducting flow along a moving radiating vertical flat plate with hydrodynamic slip and thermal convective boundary conditions. The governing transport equations are converted into a system of coupled nonlinear ordinary differential equations with prescribed boundary conditions using similarity variables developed by Lie group theory. The transformed nondimensional boundary value problem is then solved numerically with MAPLE13 quadrature. Excellent correlation with previous nonmagnetic, no-slip studies is achieved. Surface shear stress function and local Nusselt number (heat transfer gradient at the wall) are increased with Richardson number, whereas local Sherwood number is found to initially decrease then subsequently increase. The “thermally thick” scenario (Biot number > 0.1) is investigated and increasing Biot number is observed to enhance shear stress function (skin friction), local Nusselt number, and local Sherwood number. Increasing thermal radiation flux increases thermal boundary layer thickness as does increasing the magnetic field effect. Increasing hydrodynamic slip parameter reduces skin friction but enhances local Nusselt and Sherwood numbers. The study has applications in high-temperature polymeric synthesis and magnetic field flow control.

Peristaltic motion of a non-Newtonian Carreau fluid is analyzed in a curved channel under the long wavelength and low Reynolds number assumptions, as a simulation of digestive transport. The flow regime is shown to be governed by a dimensionless fourth-order, nonlinear, ordinary differential equation subject to no-slip wall boundary conditions. A well-tested finite difference method based on an iterative scheme is employed for the solution of the boundary value problem. The important phenomena of pumping and trapping associated with the peristaltic motion are investigated for various values of rheological parameters of Carreau fluid and curvature of the channel. An increase in Weissenberg number is found to generate a small eddy in the vicinity of the lower wall of the channel, which is enhanced with further increase in Weissenberg number. For shear-thinning bio-fluids (power-law rheological index, n < 1) greater Weissenberg number displaces the maximum velocity toward the upper wall. For shear-thickening bio-fluids, the velocity amplitude is enhanced markedly with increasing Weissenberg number.

Transient mixed convective laminar boundary layer flow of an incompressible, viscous, dissipative, electrically conducting nanofluid from a continuously stretching permeable surface in the presence of magnetic field and thermal radiation flux is studied. The model used for the unsteadiness in the momentum, temperature, and concentration fields is based on the time-dependent stretching velocity and surface temperature and concentration. Similarity transformations are used to convert the governing time-dependent nonlinear boundary layer equations for momentum, thermal energy, and concentration to a system of nonlinear ordinary coupled differential equations with appropriate boundary conditions. The transformed model is shown to be controlled by a number of thermophysical parameters, namely the magnetic parameter, thermal convective parameter, mass convective parameter, suction parameter, radiation-conduction parameter, Eckert number, Prandtl number, Lewis number, Brownian motion parameter, thermophoresis parameter, and the unsteadiness parameter. Numerical solutions are obtained with the robust Nactsheim–Swigert shooting technique together with Runge–Kutta sixth-order iteration schemes. Comparisons with previously published work are performed and are found to be in excellent agreement. The effects of selected parameters on velocity, temperature, and concentration distributions and furthermore on skin friction coefficients, heat transfer rate (Nusselt number), and mass transfer rate (Sherwood number) are presented graphically. The current study has applications in high-temperature nano-technological materials processing.