In this study, the lattice Boltzmann method is used to explore the double-diffusive natural convection within a shallow enclosure with a built-in rectangular blockage at its geometric center. The enclosure is exposed to an external magnetic field. One of the enclosure walls is subjected to linearly/sinusoidal heating and concentration conditions. The rectangular blockage is at higher temperature and concentration conditions. Numerical experimentation is executed for a range of parameters such as Rayleigh number (Formula presented.), Lewis number (Formula presented.), buoyancy ratio (Formula presented.), aspect ratio of the enclosure (Formula presented.), aspect ratio of the built-in blockage (Formula presented.), and Hartmann number (Formula presented.). The working fluid is assumed to be liquid metal (sodium–potassium alloy, (Formula presented.)). The complex interaction of flow parameters with the nonuniform heating and concentration conditions has been explored. Higher heat and mass transfer (HMT) rates are noticed for the sinusoidal temperature and concentration profile compared to linear for a given (Formula presented.). (Formula presented.) and (Formula presented.) showed enhancement by (Formula presented.), and (Formula presented.) for sinusoidal temperature and concentration profile of the enclosure as compared to linear for (Formula presented.). The increase in the blockage and the enclosure aspect ratio shows augmentation in the HMT rate. The consequences of the study are also summarized in terms of empirical correlations of the (Formula presented.) and (Formula presented.) numbers showing functional dependence on the considered range of parameters. © 2022 Wiley Periodicals LLC.