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General Aspects of Thermodynamical Modeling

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Solving Problems in Thermal Engineering

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Abstract

Solving a thermal problem means a solution of a mathematical model that governs the process and describes its time evolution. The thermodynamic background of these mathematical models is discussed in the present chapter. There are two building blocks of such a model. The first block consists the well-known balance equations such as the mass, momentum, and energy. The second one is the so-called constitutive relation, which tells us ‘how a material behaves’. This chapter is about their thermodynamic background.

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Notes

  1. 1.

    We note here that there are so-called ‘regularization techniques’ which stabilize the behavior and yield parabolic models [10].

  2. 2.

    Or using the usual convention: ‘ordinary’ thermodynamics which is about to describe the time evolution without considering any spatial dependence.

  3. 3.

    Only when the internal moment of momenta is absent.

  4. 4.

    Strictly speaking, it is meaningless in a mathematical sense until the definition of a ‘distance’ is given, measuring the ‘interval’ between states in which one is related to equilibrium state.

  5. 5.

    In a more general situation, the mass density \(\rho \) is also present, i.e., \(e=e(T,\rho )\).

  6. 6.

    From a practical point of view, neglecting the T-dependence of \(\lambda \) depends on the material, and theoretically, Eq. (13) is a better model for low temperature situations.

  7. 7.

    We note here that a different representation is also possible since the \(\nabla \frac{1}{T}\) terms can be unified. In this way, the resulting coefficients will be different, too [27].

  8. 8.

    We note that this identification of fluxes and forces is not unique, and it affects the definitions of material parameters.

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    Viktor Józsa & Róbert Kovács

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Józsa, V., Kovács, R. (2020). General Aspects of Thermodynamical Modeling. In: Solving Problems in Thermal Engineering. Power Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-33475-8_2

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