In thermosfluid dynamics, free convection flows external to di erent geometries, such as cylinders, ellipses, spheres, curved walls, wavy plates, cones, etc., play major role in various industrial and process engineering systems. The thermal buoyancy force associated with natural convection flows can play a critical role in determining skin friction and heat transfer rates at the boundary. In thermal engineering, natural convection flows from cylindrical bodies has gained exceptional interest. In this article, we mathematically evaluate an entropy analysis of magnetohydrodynamic third-grade convection flows from permeable cylinder considering velocity and thermal slip effects. The resulting non-linear coupled partial di erential conservation equations with associated boundary conditions are solved with an e cient unconditionally stable implicit finite di erence Keller-Box technique. The impacts of momentum and heat transport coe cients, entropy generation and Bejan number are computed for several values of non-dimensional parameters arising in the flow equations. Streamlines are plotted to analyze the heat transport process in a two-dimensional domain. Furthermore, the deviations of the flow variables are compared with those computed for a Newtonian fluid and this has important implications in industrial thermal material processing operations, aviation technology, di erent enterprises, energy systems and thermal enhancement of industrial flow processes. © 2018 Polish Academy of Sciences. All rights reserved.