Double-diffusive natural convective flow in a rectangular enclosure with the shortest sides being insulated and impermeable is investigated numerically. Constant temperatures and concentration are imposed along the longest sides of the enclosure. Laminar regime is considered under steady-state condition. The transport equations for continuity, momentum, energy are solved using the finite volume technique. The numerical results are reported for the effect of thermal Rayleigh number on the contours of streamline, temperature, and concentration. In addition, results for the average Nusselt and Sherwood numbers are presented and discussedfor various parametric conditions. This study is done for constant Prandtl number, Pr = 0.7; aspect ratio, A = 2 and Lewis number, Le =2. Computations are carried out for thermal Rayleighnumber ranging from 103ranging from -40 F 40, buoyancy ratio ranging from -5 N 5 and the Hartmann number ranging from 0 Ha 70 to 5 x 105, dimensionless heat generation and absorption coefficients.