Chapter 11 - Entropy-Generation Minimization in Steady-State Heat Conduction

Abstract

This chapter discusses that the boundary-value problems of diffusional heat-transfer processes are usually formulated based on the first law of thermodynamics. To obtain the same result when the method of irreversible thermodynamics is applied, an additional assumption that the temperature gradient values over the whole domain are reasonably small must be introduced. Based on the 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. As a result, the 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. The minimization of entropy generation in heat-conduction process is always possible by introducing additional heat sources. The most important conclusion derived from the presented theoretical considerations is directly connected with the solution of the boundary-value problems for solids with temperature-dependent heat-conduction coefficients. In such cases, additional internal heat sources can be arbitrarily chosen as positive or negative. It makes it possible to extend practical applications presented in literature by Bejan. The problem of heat conduction in anisotropic solids is also discussed in the chapter.