This article investigates the classical entropy generation in cooled slabs. Two types of materials are assumed for the slab: homogeneous material and FGM (functionally graded material). For the homogeneous material, the thermal conductivity is assumed to be a linear function of temperature, while for the FGM slab the thermal conductivity is modeled to vary in accordance with the rule of mixtures. The boundary conditions are assumed to be convective and radiative concurrently, and the internal heat generation of the slab is a linear function of temperature. Using the DIM (differential transformation method) and resultant temperature fields from the DIM, the local and total entropy generation rates within slabs are derived. The effects of physically applicable parameters such as the thermal conductivity parameter for the homogenous slab, beta, the thermal conductivity parameter for the FGM slab, gamma, gradient index, j, internal heat generation parameter, Q, Biot number at the right side, Nc(2), conduction radiation parameter, Nr(2), dimensionless convection sink temperature, delta, and dimensionless radiation sink temperature, eta, on the local and total entropy generation rates are illustrated and explained. The results demonstrate that considering temperature- or coordinate-dependent thermal conductivity and radiation heat transfer at both sides of the slab have great effects on the entropy generation. (C) 2013 Elsevier Ltd. All rights reserved.