Abstract
Focusing on the Fourier fluids in the liquid state, which are characterized by linear thermal constitutive equation and low compressibility, this short note proposes a discrete approach based on the elementary scales, which allows removing the so-called Fourier paradox in classical continuum thermomechanics. As a corollary, the adopted line of reasoning allows highlighting some features on the elementary scales.
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References
Serrin J (1959) Mathematical principles of classical fluid mechanics. In: Flügge S, Truesdell CA (eds) Fluid Dynamics I/Strömungsmechanik I, Handbuch der Physik. Springer, Berlin, pp 125–263
Meyer RE (1971) Introduction to mathematical fluid dynamics. John Wiley, New York
Bear J (1972) Dynamics of fluids in porous media. Elsevier, New York
Auriault J-L (2005) Homogenization theory applied to porous media. Poromechanics 3:113–120
Verga AD (1982) Irreversible thermodynamics in a radiating fluid. Astrophys J 260:286–298
Auriault J-L (2017) The paradox of Fourier heat equation: a theoretical refutation. Int J Eng Sci 118:82–88. https://doi.org/10.1016/j.ijengsci.2017.06.006
Cimmelli VA (2009) Different thermodynamic theories and different heat conduction laws. J Non-Equilib Thermodyn 34:299–333. https://doi.org/10.1515/JNETDY.2009.016
Gallavotti G (2002) Foundations of fluid dynamics. Springer, Berlin, Heidelberg
Panton R (2013) Incompressible flow. Wiley, Hoboken
Pekař M, Samohýl I (2014) The thermodynamics of linear fluids and fluid mixtures. Springer, Cham
Fernando HJ (Ed.). (2012). Handbook of environmental fluid dynamics, volume one: overview and fundamentals. CRC Press, Boca Ranton
Landau LD, Lifshitz EM (2000) Fluid Mechanics. Butterworth Heinemann, Oxford
Cattaneo C (1948) Sulla conduzione del calore. Atti Sem Mat Fis Univ Modena 3:83–101
Jou D, Casas-Vázquez J, Lebon G (1999) Extended irreversible thermodynamics revisited (1988–98). Rep Prog Phys 62:1035–1142
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Di Nucci, C., Celli, D., Fischione, P. et al. Elementary scales and the lack of Fourier paradox for Fourier fluids. Meccanica 57, 251–254 (2022). https://doi.org/10.1007/s11012-021-01444-x
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DOI: https://doi.org/10.1007/s11012-021-01444-x