Symmetric form of the equations of heat transport in a rigid conductor of heat with internal state variables. [Cz.] 2, Alternative symmetric systems

• Autorzy: Larecki W.
• Języki publikacji: EN

Abstrakty

EN

In part 1 of this series, it has been shown that the field equations corresponding to the model of a rigid conductor of heat with (vector) internal state variable subject to the entropy inequality can be represented as the respective system of N + 1 conservation eqations for N unknowns, on which the "main dependency relation" (MDR) is imposed. In this paper (part 2), it is demonstrated how two families of symetric systems corresponding to the consistent system of N conservation equations (family of symmetric systems for original unknowns and the family of N + 1 symmetric conservative systems for transformed unknowns) can be directly derived with the aid of the MDR. The condition of equivalence of simmetric systems to the original system of conservation equations is analysed and alternatively formulated. For the considered model of a rigid conductor of heat, the conditions on free energy that assure symmetric hyperbolicity of simmetric systems are established, and it is shown that they are stronger than the conditions required for equivalence of simmetric systems to the original system of conservation equations. Two alternative symmetric conservative systems are derived for the considered model of a rigid conductor of heat and the conditions of symmetric hyperbolicity for those systems are established with the aid of the relation between convexity (concavity) of the respective generating potentials, and with the aid of the relation between symmetric hyperbolicity of the symmetric systems for original unknowns and symmetric conservative system for the transformed unknowns.

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 1998
• Tom: Vol. 50, nr 2
• Strony: 175--205
• Opis fizyczny: Bibliogr. 15 poz.,

Twórcy

autor

Larecki W.

• Polish Academy of Sciences, Institute of Fundamental Technological Research