Start-up of channel-flow of a Bingham fluid initially at rest

Irene Daprà; Giambattista Scarpi

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2004)

  • Volume: 15, Issue: 2, page 125-135
  • ISSN: 1120-6330

Abstract

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We present an analytical solution of plane motion for a Bingham fluid initially at rest subjected to a suddenly applied constant pressure gradient. Using the Laplace transform we obtain expressions which allow a direct easy calculation of the velocity, of the plug thickness and of the rate of flow as function of time.

How to cite

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Daprà, Irene, and Scarpi, Giambattista. "Start-up of channel-flow of a Bingham fluid initially at rest." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 15.2 (2004): 125-135. <http://eudml.org/doc/252278>.

@article{Daprà2004,
abstract = {We present an analytical solution of plane motion for a Bingham fluid initially at rest subjected to a suddenly applied constant pressure gradient. Using the Laplace transform we obtain expressions which allow a direct easy calculation of the velocity, of the plug thickness and of the rate of flow as function of time.},
author = {Daprà, Irene, Scarpi, Giambattista},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Bingham fluid; Unsteady flow; Channel-flow; heat equation; Laplace transform; series solution},
language = {eng},
month = {6},
number = {2},
pages = {125-135},
publisher = {Accademia Nazionale dei Lincei},
title = {Start-up of channel-flow of a Bingham fluid initially at rest},
url = {http://eudml.org/doc/252278},
volume = {15},
year = {2004},
}

TY - JOUR
AU - Daprà, Irene
AU - Scarpi, Giambattista
TI - Start-up of channel-flow of a Bingham fluid initially at rest
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2004/6//
PB - Accademia Nazionale dei Lincei
VL - 15
IS - 2
SP - 125
EP - 135
AB - We present an analytical solution of plane motion for a Bingham fluid initially at rest subjected to a suddenly applied constant pressure gradient. Using the Laplace transform we obtain expressions which allow a direct easy calculation of the velocity, of the plug thickness and of the rate of flow as function of time.
LA - eng
KW - Bingham fluid; Unsteady flow; Channel-flow; heat equation; Laplace transform; series solution
UR - http://eudml.org/doc/252278
ER -

References

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  1. DUGGINS, R.K., The commencement of flow of a Bingham Plastic fluid. Chem. Eng. Sci., 27, 1972, 1991-1996. 
  2. MITRA, A.K., Impulsively started flow of a Bingham Plastic in a tube. ASME FED, 15, 1984, 23-25. 
  3. HAMMAD, K.J., Unsteady pipe flows of a viscoplastic non-Newtonian fluid: effects of pressure gradient waveform. ASME FED, 247, 1998, 197-204. 
  4. LY, D.P. - BELLET, D., The study of time-dependent pipe flows of inelastic non-newtonian fluids using a multiviscous approximation. J. Non-Newtonian Fluid Mech., 1, 1976, 287-304. Zbl0345.76001
  5. AL KATIB, M.A.M. - WILSON, S.D.R., The development of Poiseuille flow of a yield-stress fluid. J. Non-Newtonian Fluid Mech., 100, 2001, 1-8. Zbl1018.76003
  6. MAKAROV, A.M. - ZHDANOVA, L.A. - POLOZOVA, O.N., Non steady-state flow of a viscoplastic medium in a plane channel. J. Eng. Phys., 22, 1972, 51-55. 
  7. SAFRONCHIK, A.I., Non-steady Flow of a visco-plastic Material between parallel Walls. PMM, 23, 1959, 5, 925-935 (J. Appl. Math. Mech., 23, 1959, 1314-1327). Zbl0098.39305
  8. GLOWINSKI, R., Sur l’écoulement d’un fluide de Bingham dans une conduite cylindrique. J. de Méc., 13, 1974, 601-621. Zbl0324.76004MR371245
  9. HUILGOL, R.R. - MENA, B., On the time estimate for start-up of pipe flows in a Bingham fluid – a proof of the result due to Glowinski, Lions and Trèmoliéres. J. Non-Newtonian Fluid Mech., 94, 2000, 113-118. Zbl0995.76005
  10. ATABEK, H.B., Start-up Flow of a Bingham Plastic in a Circular Tube. ZAMM, 44, 1964, 332-333. Zbl0127.40403MR168234
  11. AMADEI, B. - SAVAGE, W.Z., An analytical solution for transient flow of Bingham viscoplastic materials in rock fractures. Int. J. Rock Mech., 38, 2001, 285-296. 
  12. BIRD, R.B. - DAI, G.C. - YARUSSO, B.J., The Rheology and Flow of viscoplastic Materials. Review in Chemical Engineering, 1, 1983, 1-70. 
  13. BROWN, R.G. - NILSSON, J.W., Introduction to Linear System Analysis. Wiley, New York1962. Zbl0124.17103MR169743

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