An integral equation basic to the BGK model for flow in a cylindrical tube

  • Authors:

  • L. B. Barichello;M. Camargo;Paul Rodrigues;C. E. Siewert

  • Affiliations:

  • Instituto de Matemática Universidade Federal do Rio Grande do Sul 91509-900 Porto Alegre, RS Brasil;Programa de Pós-Graduação em Engenharia Mecânica Universidade Federal do Rio Grande do Sul Brasil and Departamento de Ciências Exatas e da Terra Universidade Regional Inte ...;Programa de Pós-Graduação em Engenharia Mecânica Universidade Federal do Rio Grande do Sul Brasil and Departamento de Ciências Exatas e da Terra Universidade Regional Inte ...;Mathematics Department North Carolina State University Raleigh, NC

  • Venue:
  • Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
  • Year:
  • 2002

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Abstract

The classical BGK model for describing the flow of a rarefied gas in a cylindrical tube is used as a starting point for developing an equivalent integral-equation formulation of the considered class of problems. While the problems of Poiseuille flow and thermal creep in a cylindrical tube have already been well solved in terms of a pseudo problem obtained from an integral-equation definition of the problems, the development of the relevant integral equation is given here for a larger class of problems. In particular it is noted that a general inhomogeneous source term in the balance equation and a general inhomogeneous term in the boundary condition are both included in the considered model, and, as a special case, the integral-equation formulation for the case of specular reflection at the surface of the tube is also developed.