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Unsteady flow of Bingham fluid in a two dimensional elastic domain

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The main goal of this work is to study an initial boundary value problem relating to the unsteady flow of a rigid, viscoplastic, and incompressible Bingham fluid in an elastic bounded domain of $\mathbb{R}^{2}$. By using the approximation sequences of the Faedo-Galerkin method together with the regularization techniques, we obtain the results of the existence and uniqueness of local solutions.

Abstract

The main goal of this work is to study an initial boundary value problem relating to the unsteady flow of a rigid, viscoplastic, and incompressible Bingham fluid in an elastic bounded domain of $\mathbb{R}^{2}$. By using the approximation sequences of the Faedo-Galerkin method together with the regularization techniques, we obtain the results of the existence and uniqueness of local solutions.

참고문헌 (13)

  1. E. C. Bingham, "An investigation of the laws of plastic flow", Bull. Bur. Stand, 13, pp.309~353 (1916)
  2. E. C. Bingham, "Fluidity and Plasticity", pp.215~218 (1922), McGraw-Hill
  3. R. B. Bird, "Dynamics of polymeric liquids, vol. 1" (1977), Wiley-Interscience
  4. R. B. Bird, "The rheology and flow of viscoplastic materials", Rev. Chem. Eng, 1, pp.1~70 (1983)
  5. Y. L. Chen, "Couette-Poiseuille flow of Bingham fluids between two porous parallel plates with slip conditions", J. Non-Newton. Fluid Mech, 153, pp.1~11 (2008)
  6. R. Darby, "How to predict the friction factor for flow of Bingham plastics", Chem. Eng, 28, pp.59~61 (1981)
  7. J. -L. Lions, "Quelques m´ethodes de r´esolutions des probl`emes aux limites non lin´eaires" (1969), Dunod Gauthier-villars
  8. K. F. Liu, "Slow spreading of a sheet of Bingham fluid on an inclined plane", J. Fluid Mech, 207, pp.505~529 (2006)
  9. T. Min, "Laminar convective heat transfer of a Bingham plastic in a circular pipe. II. numerical approach-hydro-dynamically developing flow and simultaneously developing flow", Int. J. Heat Mass Transf, 40, pp.3689~3701 (1997)
  10. J. G. Oldroyd, "A rational formulation of the equations of plastic flow for a Bingham solid", Proc. Cambridge Philos. Soc, 43, pp.100~105 (1947)
  11. A. Parvin, "Unsteady MHD viscous incompressible Bingham fluid flow with hall current", model, Meas. Control B, 84, pp.38~48 (2015)
  12. D. A. S. Rees, "Unsteady thermal boundary layer flows of a Bingham fluid in a porous medium following a sudden change in surface heat flux", Int. J. Heat Mass Transf, 93, pp.1100~1106 (2016)
  13. L. Sreekala, "Effects on unsteady MHD flow of a non-Newtonian fluid through a porous medium with uniform suction and injection", IOSR J. Mech. Civ. Eng, 11, pp.55~64 (2014)

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