Mixed convection in horizontal duct flow with transverse magnetic field and heating of side wall

Computational study of mixed convection in a horizontal duct with very strong (Hartmann numbers Ha up to 800) horizontal transverse magnetic field and electrically insulated walls is conducted. Strong constant-rate heating (Grashof numbers Gr up to 109) is applied to one vertical wall, while the other walls are thermally insulated. It is found that in a wide range of Ha and Gr the flow is two-dimensional (uniform in the streamwise direction) and steady-state. No instability to convection rolls aligned with the magnetic field detected recently in a similar duct and pipe with bottom heating is observed. The velocity field is a combination of convection-modified streamwise flow and convection-induced circulation in the transverse plane. The circulation has strong jets near the heated and horizontal walls as prominent features. It is demonstrated that, at a constant Reynolds number, integral characteristics and spatial structure of the flow can be approximately considered as determined by Gr/Ha2 as a single parameter. We also present results of a systematic comparison study of several commonly used grid clustering schemes in their application to wall-bounded flows with strong magnetic fields.