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An application of the Entropy Generation Minimization principle allows new formulation of the boundary and initial boundaryvalue problems. Applying Euler-Lagrange variational formalism new mathematical form of heat conduction equation describing steady-state processes have been derived. Mathematical method presented in the paper can also be used for any diffusion heat and mass transfer process. Linear and non-linear problems with internal heat sources have been analyzed.

Entropy generation minimization in steady-state and transient diffusional heat conduction processes Part I – Steady-state boundary value problem