Lattice Boltzmann simulation of MHD mixed convection in a lid-driven square cavity with linearly heated wall

Solving of mhd flow by the lattice boltzmann method, utilizing classical equations has beeninvestigated by presenting mhd mixed convection in a lid-driven cavity by a linearly heated wall. thehartmann number varied from ha d 0 to 100; furthermore, the study has been conducted for richardsonnumbers (ri) from 0.01 to 100, while the directions of the magnetic field were investigated for  d 0,and 90,. results show that the augmentation of richardson number causes heat transfer to increase, asthe heat transfer decreases by the increment of hartmann number for various richardson numbers andthe directions of the magnetic field. the highest decline of heat transfer on the linearly heated wall wasfound at  d 0, for richardson numbers of ri d 100 and ha d 100. on the other hand, the least effectof the magnetic field is observed at ri d 0:01 from ha d 25 to 100 for both directions on the linearlyheated wall. moreover, the magnetic field influences heat transfer marginally at  d 90, against  d 0,,which changes dramatically. heat transfer on the heated wall at the bottom of the cavity behaves like thelinearly heated wall regarding the effect of the magnetic field.