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In this study, the Spectral Relaxation Method (SRM) is used to solve the coupled highly nonlinear system of partial differential equations due to an unsteady flow over a stretching surface in an incompressible rotating viscous fluid in presence of binary chemical reaction and Arrhenius activation energy. The velocity, temperature and concentration distributions as well as the skin-friction, heat and mass transfer coefficients have been obtained and discussed for various physical parametric values. The numerical results obtained by (SRM) are then presented graphically and discussed to highlight the physical implications of the simulations.

a b s t r a c tIn this study convection from an inverted cone in a porous medium with cross-diffusion is studied numerically. Diffusion-thermo and thermo-diffusion effects are assumed to be significant. The governing equations are transformed into nonlinear ordinary differential equations and then solved numerically using a shooting method together with a sixth order Runge-Kutta method. Verification of the accuracy and correctness of the results is achieved by solving the equations using an independent linearisation method. The effects of the Dufour and the Soret parameters are investigated. The results for the skin friction, Nusselt number and the Sherwood number are presented graphically and in tabular form.

a b s t r a c tThe problem of double-diffusive convection and cross-diffusion in a Maxwell fluid in a horizontal layer in porous media is re-examined using the modified Darcy-Brinkman model. The effect of Dufour and Soret parameters on the critical Darcy-Rayleigh numbers is investigated. Analytical expressions of the critical Darcy-Rayleigh numbers for the onset of stationary and oscillatory convection are derived. Numerical simulations show that the presence of Dufour and Soret parameters has a significant effect on the critical Darcy-Rayleigh number for over-stability. In the limiting case some previously published results are recovered.

We study the effect of thermophoresis on boundary layer magneto-nanofluid flow over a stretching sheet. The model includes the effects of Brownian motion and cross-diffusion effects. The governing partial differential equations are transformed to a system of ordinary differential equations and solved numerically using a spectral linearisation method. The effects of the magnetic influence number, the Prandtl number, Lewis number, the Brownian motion parameter, thermophoresis parameter, the modified Dufour parameter and the Dufour-solutal Lewis number on the fluid properties as well as on the heat, regular and nano mass transfer coefficients are determined and shown graphically.