Entropy generation, which is available exergy destruction, is an important subject in fields of energy management and thermal engineering. With the fast-growing rate of composite media applications in both industries and academic researches, it is necessary to study these media from the second law of thermodynamics point of view. In this work, three fundamental composite media, i.e., composite walls, cylinders and spheres, are considered. The thermal contact resistance between two layers of each medium is considered to be non-zero, and the effect of the radiation heat loss from the second layer, i.e., the outer layer of the composite system, is taken into account. Thermal conductivities are assumed temperature-dependent. Temperature-independent internal heat generation within each layer is considered. The system of non-linear ordinary differential equations is solved with a combined analytical numerical technique. Assuming temperature-independent thermal conductivities and neglecting the radiation effect, the system of ordinary equations can be solved with an exact analytical technique. Finding the solution of the temperature distribution and local entropy generation rate with this exact analytical procedure, provides a practical tool to check the correctness and accuracy of the combined analytical numerical solution for general problems, i.e., with the radiation effect and temperature-dependent thermal conductivities. Thereafter, temperature distribution, local and total entropy generation rates are plotted for number of parameters for three considered composite geometries. It is found that assuming zero thermal contact resistance overestimates the total entropy generation rate within these composite media. Depending on the value of parameters, it is or is not possible to find an optimum value for the radiation parameter to minimize the total entropy generation rate within these media. (C) 2014 Elsevier Ltd. All rights reserved.