2D regimes of non-fourier convection

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Abstract

In this work, we investigate the 2D flow in a rectangular cavity subject to both vertical and horizontal temperature gradients. The linearized model is studied and the effect of thermal relaxation, as described by the Maxwell-Cattaneo law of heat conduction is examined. To this end, a spectral numerical model is created based on a Galerkin expansion. The basis is the Cartesian product of systems of beam functions and trigonometric functions. The natural modes of the system are derived for both the Fourier and non-Fourier models. The results are compared to earlier works for the plain Fourier law. Our computations show that for the same set of parameters, the Maxwell-Cattaneo law yields modes which are quantitatively different from the Fourier. It is found that the real parts of the eigenvalues increase with the Straughan number Sg, which quantifies the non-Fourier effects. This confirms the destabilizing effect of the MC-law on the convective flow.

Original languageEnglish
Title of host publicationApplication of Mathematics in Technical and Natural Sciences - Proceedings of the 2nd International Conference, AMiTaNS'10
Pages282-290
Number of pages9
Volume1301
DOIs
Publication statusPublished - 2010
Event2nd International Conference on Application of Mathematics in Technical and Natural Sciences, AMiTaNS'10 - Sozopol, Bulgaria
Duration: 21 Jun 201026 Jun 2010

Other

Other2nd International Conference on Application of Mathematics in Technical and Natural Sciences, AMiTaNS'10
CountryBulgaria
CitySozopol
Period21/06/1026/06/10

Keywords

  • 2-D linear stability
  • beam functions
  • Non-Fourier heat conduction
  • two-gradient convection

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  • Cite this

    Papanicolaou, N. C. (2010). 2D regimes of non-fourier convection. In Application of Mathematics in Technical and Natural Sciences - Proceedings of the 2nd International Conference, AMiTaNS'10 (Vol. 1301, pp. 282-290) https://doi.org/10.1063/1.3526624