On the minimum entropy production in steady state heat conduction processes

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.