On the basis of minimum entropy generation principle, a new formulation of the boundary value problems is proposed. Applying Euler-Lagrange variational formalism, a new mathematical form of heat conduction equation with additional heat source terms has been derived. To obtain a unique solution a special mathematical form of boundary conditions for 2D and 3D problems is required. As a result, entropy generation rate of the process can significantly be reduced, which leads to the decrease of the irreversibility ratio according to the Gouy-Stodola theorem. Minimization of entropy generation in heat conduction process is always possible by introducing additional heat sources. (C) 2004 Elsevier Ltd. All rights reserved.