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On the Nondimensionalization Process in Complex Problems: Application to Natural Convection in Anisotropic Porous Media

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  • I. Alhama
  • M. Cánovas
  • F. Alhama

Abstract

The nondimensionalization of the equations governing a given problem is a direct, relatively easy, and low-cost way to provide interesting information, the dimensionless groups that rule the problem and define its final patterns of solution. In complex problems, however, this technique frequently does not provide the precise and complete set of monomials we are looking for. The use of discrimination in the process of nondimensionalization, the detailed application of which is explained in this paper, always leads to a minimum set of parameters, which, separately, determine the solution of the problems. In addition, the physical meaning and order of magnitude of these discriminated monomials are also provided by the discrimination. The technique is applied to the coupled problem of natural convection between horizontal plates heated from below, containing an anisotropic porous medium.

Suggested Citation

  • I. Alhama & M. Cánovas & F. Alhama, 2014. "On the Nondimensionalization Process in Complex Problems: Application to Natural Convection in Anisotropic Porous Media," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-13, June.
    • Handle: RePEc:hin:jnlmpe:796781
    DOI: 10.1155/2014/796781
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    Cited by:

    1. Manuel Conesa & Juan Francisco Sánchez-Pérez & Gonzalo García-Ros & Enrique Castro & Julio Valenzuela, 2023. "Normalization Method as a Potent Tool for Grasping Linear and Nonlinear Systems in Physics and Soil Mechanics," Mathematics, MDPI, vol. 11(20), pages 1-19, October.

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