A numerical study of mixed convection in a square enclosure from a heating element to a cold moving wall is performed under the isothermal heating conditions. The heater is placed at the bottom boundary and the cold upper wall moves horizontally towards right side with constant velocity. The lateral walls are insulated. The study includes the thermal performance of nanofluid for various shaped obstacles kept at center of the enclosure. The application of hydro-magnetism with uniform and constant magnetic intensity throughout the bottom wall is considered. The heat convection is studied at two Richardson number (0.01 and 10), four percentage volume of silver nanoparticles (0%, 2%, 5%, and 8%) and four Hartmann number (0, 10, 20, and 50). Grashof number, Prandtl number, and Reynolds number have a constant value of 104, 6.2 and 100 respectively. The obtained results indicate the suppression of heat fluxes with increasing intensity of magnetic field whereas it increases with increasing Richardson number and percentage volume of the nano-material in the base fluid.