In this paper, we present a theoretical study of the combined effects of activation energy and binary chemical reaction in an unsteady mixed convective flow over a boundary of infinite length. The current study incorporates the influence of the Brownian motion, thermophoresis and viscous dissipation on the velocity of the fluid, temperature of the fluid and concentration of chemical species. The equations are solved numerically to a high degree of accuracy using the spectral quasilinearization method. Brownian motion was noted as the main process by which the mass is transported out of the boundary layer. The effect of thermophoretic parameter seems to be contrary to the expected norm. We expect the thermophoretic force to ‘push’ the mass away from the surface thereby reducing the concentration in the boundary layer, however, concentration of chemical species is seen to increase in the boundary layer with an increase in the thermophoretic parameter. The use of a heated plate of infinite length increased the concentration of chemical species in the boundary layer. The Biot number which increases and exceeds a value of one for large heated solids immersed in fluids increases the concentration of chemical species for its increasing values.

This paper presents a formulation for simulating magnetohydrodynamic three-dimensional convective flow and heat transfer in a nanofluid by incorporating the complete viscous dissipation function in the energy equation. A novel feature of this investigation of entropy generation and dual solutions is the use of the spectral quasilinearization method to solve the conservation equations. The results are compared with exact solutions or higher order solutions and a good agreement is achieved. The accuracy is determined by calculation of residual errors and the method of solution is shown to produce smaller residual errors than those achieved by the fifth-order Runge-Kutta Fehlberg method for nonlinear differential equations. The dual solutions for different Prandtl number, and Brownian motion and thermophoresis parameters are shown graphically and discussed. It is found that the temperature profiles as well as thermal boundary layer thickness increase with the Brownian motion parameter for first and the second solutions. The temperature profiles increase with the thermophoresis parameter for the first and second solutions. The entropy generation increases with the Reynolds number. Highlights Combined effects of entropy generation and MHD nanofluid are proposed. Spectral quasi-linearization method (SQLM) is used for computer simulations. Use axisymmetric stretching/shrinking sheet for dual solution. Validate the accuracy and convergence using residual error analysis.