This article presents the exact solutions of the velocity and temperature elds for a steady fully developed magnetohydrodynamic ow of a viscous incompressible and electrically conducting uid between two Horizontal concentric cylinders. Using the velocity and temperature eld expressions, we have calculated the entropy generation rate and irreversibility ratio. Our study focuses on the in uence of the Hartmann number, Brinkman number, Pclet number and inner radius on the uid temperature eld, entropy generation rate and irreversibility ratio with the help of graphs and table.