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.

Unsteady laminar boundary-layer flows of a nanofluid past a stretching sheet with thermal radiation in the presence of magnetic field have been studied numerically. The non-similar momentum, energy and concentration equations have been obtained by using non-dimensional variables. The non-similar equations are presented here which depends on the useful parameters of the model. The obtained equations have been solved by explicit finite difference method with stability and convergence analysis. The velocity, temperature and nanoparticles volume fraction profiles as well as the average Shear stress, Nusselt number and Sherwood number at the sheet are discussed for the different values of important parameters with different time steps

The perspective of this paper is to characterize a Casson type of Non-Newtonian fluid flow through heat as well as mass conduction towards a stretching surface with thermophoresis and radiation absorption impacts in association with periodic hydromagnetic effect. Here heat absorption is also integrated with the heat absorbing parameter. A time dependent fundamental set of equations, i.e. momentum, energy and concentration have been established to discuss the fluid flow system. Explicit finite difference technique is occupied here by executing a procedure in Compaq Visual Fortran 6.6a to elucidate the mathematical model of liquid flow. The stability and convergence inspection has been accomplished. It has observed that the present work converged at, P_r ≥ 0.447 indicates the value of Prandtl number and L_e ≥ 0.163 indicates the value of Lewis number. Impact of useful physical parameters has been illustrated graphically on various flow fields. It has inspected that the periodic magnetic field has helped to increase the interaction of the nanoparticles in the velocity field significantly. The field has been depicted in a vibrating form which is also done newly in this work. Subsequently, the Lorentz force has also represented a great impact in the updated visualization (streamlines and isotherms) of the flow field. The respective fields appeared with more wave for the larger values of magnetic parameter. These results help to visualize a theoretical idea of the effect of modern electromagnetic induction use in industry instead of traditional energy sources. Moreover, it has a great application in lung and prostate cancer therapy.