A new formulation for the second law of thermodynamics for the case of thin surfaces

A new formulation for the second law of thermodynamics was proposed (1973) [1 - 5] by means of the combination of two Clausius-Dühem-Truesdell type inequalities. This formulation deals with a thin surface, each side of which has its own temperature and entropy. So, the formulation contains two entropies, two internal temperature fields, and two external temperature fields. Apart from the theory of shells this elaboration of the second law of thermodynamics is also useful for the solid-state physics when studying the influence of skin effects on properties of solids, as well as for the description of interfaces between different phases of a solid.
  1. Zhilin P.A. Mechanics of Deformable Surfaces. The Danish Center for Appl. Math and Mech. Report N 89. 1975. P. 1-29.
  2. Zhilin P.A. Mechanics of Deformable Cosserat Surfaces and Shell Theory. The Danish Center for Appl. Math and Mech. Annual report, 1975.
  3. Zhilin P.A. Mechanics of deformable enriched surfaces // Transactions of the 9th Soviet conference on the theory of shells and plates. Leningrad, “Sudostroenie”. 1975. P. 48-54. (In Russian.)
  4. Zhilin P.A. Mechanics of Deformable Directed Surfaces. Int. J. Solids Structures. 1976. Vol. 12. P. 635-648.
  5. Zhilin P.A. Applied mechanics. Foundations of shells theory. Tutorial book. St. Petersburg State Polytechnical University. 2006. 167 p. (In Russian.)