1D dynamics of a second-grade viscous fluid in a constricted tube

Tom 81 / 2008

Fernando Carapau, Adélia Sequeira Banach Center Publications 81 (2008), 95-103 MSC: Primary 76A05; Secondary 76M25. DOI: 10.4064/bc81-0-6


Using a one-dimensional hierarchical model based on the Cosserat theory approach to fluid dynamics we can reduce the full 3D system of equations for the axisymmetric unsteady motion of a non-Newtonian incompressible second-grade viscous fluid to a system of equations depending on time and on a single spatial variable. From this new system we obtain the steady relationship between average pressure gradient and volume flow rate over a finite section of a straight constricted tube, and the corresponding equation for the wall shear stress.


  • Fernando CarapauDept. Matemática and CIMA/UE
    Universidade de Évora
    Rua Romão Ramalho 59
    7001 Évora, Portugal
  • Adélia SequeiraDept. Matemática and CEMAT/IST
    Instituto Superior Técnico
    Universidade Técnica de Lisboa
    Av. Rovisco Pais
    1049 Lisboa, Portugal

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