A finite volume technique based double diffusive natural convection of power-law fluid in an enclosure has been studied numerically in the presence of magnetic field due to different physical parameters such as Rayleigh number (Ra), Lewis number (Le), Hartmann number (Ha) and Prandtl number (Pr). The flow is generated by the combined mechanism of a time periodic thermal and solutal gradient acts along the vertical walls. The combined buoyancy effect due to thermal and species diffusion plays a key role on the flow characterisation. The study dealt with the effect of pertinent parameters on fluid flow, heat and mass transfer in case of a laminar flow regime. The apparent power law indices and magnetic field strengths are varied using the non-Newtonian power law forms. The relevant results are presented in terms of streamlines, isotherms, isoconcentrations, average Nusselt number, Sherwood number and total entropy generation with the variation of power law index (n) from 0.2 to 1.8, Ra from 10(4) to 10(5), Ha from 0 to 20, Pr from 1 to 5 and buoyancy ratio (N) from -1 to 1. The entropy generation and Bejan number are determined to analyze the thermodynamic optimization of the conjugate double diffusive convection. It is observed that the average Nusselt and Sherwood number shows linear variation with the increase of amplitudes of the imposed sinusoidal temperature and concentration gradient and the fluctuation is found to be trivial. Also the results indicate that the power law index variation influences largely the rate of heat and mass transfer and average entropy generation. The magnetic field strength increases the strength of the fluid flow and also strongly supported by the increased values of n. It is found that with the decrement of flow behavior index n the buoyancy effect and the hydrodynamic behavior of the fluid is getting increased. (C) 2018 Elsevier Ltd. All rights reserved.