In this paper, an analysis of the first and second laws of thermodynamics is presented to show the effects of MHD flow on the distributions of velocity, temperature and entropy generation between two concentric rotating cylinders. The flow inside the gap is assumed to be steady state and laminar for an incompressible, viscous, and Newtonian fluid. The walls of the cylinders are kept at different constant temperatures. Governing equations in cylindrical coordinates are simplified and analytically solved to obtain the local and average (overall) entropy generation rate. Due to the nature of the problem, the velocity distribution in the annulus becomes as the modified Besse! functions I-1(MR) and K-1(MR). Therefore, to obtain the temperature field, the expansions of the modified Bessel functions I-1(MR) and K-1(MR), with 3 terms, are employed in the energy equation. The results are presented for various values of Hartmann number (M), radius ratio (Pi), group parameter (Omega/Br), and Brinkman number (Br). (C) 2012 Elsevier Ltd. All rights reserved.