By David H. West and Gregory Yablonsky (Eds.)
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Additional info for Advances in Chemical Engineering
The lacking special description of the Gibbs phase rule in MEIS that should be met automatically in case of its validity is very important for solution of many problems on the analysis of multiphase, multicomponent systems. Indeed, without information (at least complete enough) on the process mechanism (for coal combustion, for example, it may consist of thousands of stages), it is impossible to specify the number of independent reactions and the number of phases. , the dimensionality of the studied system.
M. Kaganovich et al. maximization of an isolated system including a hydraulic network and its environment. , in the network. From the “physico-economic” standpoint convergence of the cho sen method can be explained by the fact that it naturally represents the tendency of an open system with fixed conditions of interaction with the environment to equilibrium, which corresponds to minimum production of both physical and economic entropy. , a physical mechanism. Thus, in this case the model of equilibrium thermodynamics—MEIS solves the problem of self-organization, ordering of the “physico-economic” system that is referred as a rule to the area of applications of nonequilibrium thermodynamics or synergetics.
Then condition (15) is excluded and model (13)–(17) is replaced by the model that corresponds to the Kirchhoff theorem of mini mum heat production (Kirchhoff, 1848): find min X Pbr i xi i subject to Ax ¼ Q; Pbr i ¼ i xi ; i ¼ 1; … ; np : g ð21Þ In this case the second derivatives of the Lagrange function L¼ np X i¼1 i xþ1 i À m À1 X 0 j @ j¼1 X 1 aij xi A j2Ij with the above supposition on the form of closing relations @2L ! 0: ¼ ð þ 1Þ i xÀ1 i @x2i ð22Þ Hence, the extremum L(x) is the point of minimum.
Advances in Chemical Engineering by David H. West and Gregory Yablonsky (Eds.)