effect of magnetic field intensity on hydrodynamic entrance length and nusselt number

The present study is a numerical investigation of the laminar flow and convective heat transfer of water/copper ferrofluid inside a horizontal tube in the presence of a uniform magnetic field# the effect of magnetic field intensity on hydrodynamic entrance length and nusselt number was investigated# all studies were performed at reynolds number of 100, the volume fraction of 5% and hartmann numbers of 0, 20, 50, 80# the results obtained indicated that with the increase of hartmann number, the thickness of the boundary layer decreases and hydrodynamic entrance length increases# also with the increase of hartmann number, nusselt number increases and wall temperature decreases#