The current research relates to numerical analysis of the unsteady MHD mixed convective flow over a curved stretching surface. The Dufour and Soret effects, chemical reaction and joule heating are accounted into the flow together with the thermal and velocity slip effects. The governing partial differential equations of the flow which are in curvilinear coordinates are transformed into ordinary differential equations by using suitable similarity transformations. The numerical results are obtained using the MATLAB built-in solver bvp4c. The stability of the numerical technique has been verified and compared with the available literatures. The resultant boundary layer flow field parameters and the parameters of engineering interest have been presented graphically along with tabular data. The results thus obtained show that the surface drag significantly drops by about 9.4% and 23.4% respectively upon enlargement of the curvature parameter (0.5 ≤ K ≤ 0.7) and velocity slip parameter (0.4 ≤ λ ≤ 0.6) at the stretching surface. The thermal boundary layer thickness and heat transfer rate also tend to be drastically depleted as lesser heat gets transferred from the curve surface to the fluid. Incrementing the unsteadiness parameter (0.5 ≤ δ ≤ 1) significantly improves the heat and mass transfer rates by about 13.5% and 13% respectively. It is also found that the rates of heat and mass transfer can be increased by enhancing the Dufour and Soret effects respectively.