Entropy generation rate which is a tool to measure exergy destruction has attracted considerable attention these years. This work is about temperature and entropy generation rate modeling within cylindrical systems using magnetohydrodynamic (MHD) flow. Two solid co-rotating cylindrical geometries with temperature-dependent thermal conductivities and constant, but different, internal heat generations are considered. The inner one is solid and the outer one is hollow. The MHD flow is within the empty space between these cylindrical geometries. Since the middle geometry is considered as fluid flow, the temperature field is coupled with the velocity field. By obtaining the velocity formula as Bessel functions and approximating it with a series form, and employing a combined analytical-numerical solution technique, the temperature formula within all three components of the system can be formulated. Incorporating the obtained temperature field into the provided fundamental entropy generation rates formulas, the local and volumetric averaged entropy generation rates are calculated. Assuming constant thermal conductivity for all materials, completely analytical solution can be achieved for the considered problem. The accuracy and correctness of the combined analytical-numerical solution technique are checked against available analytical solution. After verification, effects of thermophysical parameters such as magnetic field, Brinkman number, different radii, etc. on the velocity field, temperature distribution and entropy generation rates are examined. (C) 2015 Elsevier Ltd. All rights reserved.