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Solving Problems in Thermal Engineering

Part of the book series: Power Systems ((POWSYS))

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Abstract

This chapter focuses on the experimental background of extended constitutive equations, especially on non-Fourier heat conduction. Although these phenomena are not common in engineering practice nowadays, it conveys essential aspects and provides guidance for ‘special’ thermal and coupled problems. It is anticipated that the advanced material models will appear in the commercial codes as the thermal modeling of micro and nano-scaled objects become increasingly important.

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Notes

  1. 1.

    Since the heat flux \(\mathbf q\) becomes a state variable in the generalized equations, independently of the approach, it is worth to mention the possible \(\mathbf q\)-dependence of the material parameters.

  2. 2.

    We refer to it as ‘temperature representation’. If the temperature is eliminated, then it is called ‘heat flux representation’.

  3. 3.

    Naturally, the scaling property appears in large scales, too, but it is less frequent in the practical applications and may be important merely for geological applications.

  4. 4.

    Assuming adiabatic boundary conditions on both sides with non-uniform initial condition to model the initial (and quick) absorption of the heat pulse.

  5. 5.

    As a philosophical question to the Reader: is it possible to interpret the internal variable as a measure of deformation to obtain a hyperbolic heat equation?

  6. 6.

    Recall the Fourier resonance condition!

  7. 7.

    We note here the difference between the apparent and theoretical (calculated) material parameters. It has great importance in some scaling properties that will be discussed at the end of this chapter.

  8. 8.

    In some papers, the MCV equation is considered to be thermodynamically incompatible. In general, this interpretation depends on the space of state variables: one must include the heat flux as an independent variable, then the anomalies around the entropy production disappear.

  9. 9.

    Analogously to the GK equation, it can be interpreted as a nonlocal term.

  10. 10.

    The deformedness in a 1D case is defined as \( D=\ln (l/l_r)\) with \(l_r\) being a relaxed length, characterizing the unloaded state of the material. This is an appropriate thermodynamic state variable. The engineering strain is \(\varepsilon =(l-l_0)/l_0\) in which \(l_0\) is the length at the initial time instant. Since \(\varepsilon \) is a reference time dependent, it is not a good thermodynamic state variable [293]. Unfortunately, D is not directly measurable.

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Józsa, V., Kovács, R. (2020). Nature Knows Better. In: Solving Problems in Thermal Engineering. Power Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-33475-8_5

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