Double-diffusive convection flows of a binary mixed electrically conducting fluid in the presence of a uniform horizontal magnetic field and heat source are investigated numerically in a rectangular cavity with, the upper and lower walls being insulated and impermeable and the left and right walls being constant temperatures and concentrations. A high accuracy compact scheme, which is fourth-order accuracy in space and third-order accuracy in time, is applied to solve the problems based on the stream functionvorticity formulation of Navier-Stokes equation. Numerical simulations are carried out in a wide range of Hartmann number (Ha), Lewis number (Le), Rayleigh number (Ra) and the heat generation or absorption coefficient (phi) at the Prandtl number Pr = 0.025 for the electrically conducting fluid such as molten gallium in the rectangular cavity with the aspect ratio 2. The computed results show that the oscillatory behavior would disappear with the increase of the strength of the magnetic field, and the total kinetic energy in the cavity is inhibited proportionally to (1 - lambda)(2)Ra(2)Ha(-beta), where beta is between 3.5 and 4, under the strong magnetic field and weak heat source. In addition, asymptotic solutions of the average Nusselt and Sherwood numbers on the left and right walls in the presence of very strong magnetic field, which only dependent on phi, are deduced and proved by the present numerical results. (C) 2017 Elsevier Ltd. All rights reserved.