text: Department of Mathemmatics, Central University of Rajasthan, Ajmer, India
  A numerical study has been performed to analyze the effect of radial magnetic ﬁeld on free convective ﬂow of an electrically conducting and viscous incompressible ﬂuid over the ramped moving vertical cylinder with ramped type temperature and concentration considered at the surface of vertical cylinder. The governing partial differential equations which describe the ﬂow formation have been solved numerically by using implicit ﬁnite difference method of Crank-Nicolson type. The simulation results of the considered model have been shown graphically. One of the interesting result of our analysis is that the local as well as average skin-friction, Nusselt number and Sherwood number have increasing tendency in time interval (0,1), thereafter these quantities decrease. We have also compared the case of ramped type boundary conditions with that of constant boundary conditions with help of table. The advantage of taking ramped type boundary conditions is that initial heat transfer rate and mass transfer rate are minimum in this case.