Journal of Engineering Mathematics

, Volume 39, Issue 1, pp 345–366

Asymptotic analysis of the flow of shear-thinning foodstuffs in annular scraped heat exchangers

  • A.D. Fitt
  • C.P. Please
Article

Abstract

The problem of isothermal flow of a shear-thinning (pseudoplastic) fluid in the gap between two concentric cylinders is considered. A pump provides an axial pressure gradient which causes flow down the device. The outer cylinder is fixed and has ‘scrapers’ attached to it to cause flow mixing, whilst the inner cylinder rotates about its axis to provide shear and thus thin the fluid. The goal is to determine the optimal distribution of power between rotation and pumping. Although ostensibly the flow is nonlinear and three-dimensional we show that judicious use of fairly straightforward asymptotic methods can yield a great deal of information about the device, including cross-sectional flow predictions and throughput results. Furthermore, these results are derived for a variety of different flow conditions. Some numerical calculations are carried out using a commercial CFD code. These show good agreement with the asymptotic analysis.

asymptotic analysis food industry lubrication theory shear-thinning fluids slow flow. 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    N. Hall-Taylor, A model for the behaviour of scraped surface heat exchangers. Internal Report, Crown Chemtech Ltd., July (1995).Google Scholar
  2. 2.
    N. Hall-Taylor, Experimental results for the rheology pastes and spreads. Internal Report, Crown Chemtech Ltd., January (1998).Google Scholar
  3. 3.
    G. Astarita and G. Marrucci, Principles of Non-Newtonian Fluid Mechanics. London: McGraw-Hill (1974) 289pp.Google Scholar
  4. 4.
    M.W. Johnson and S. Mangkoesoebroto, Analysis of lubrication theory for the power law fluid. J. Tribology, Trans. ASME 115 (1993) 71–77.Google Scholar
  5. 5.
    T.R. Lin, Thermal elastohydrodynamic lubrication of rolling and sliding contacts with a power law fluid. Wear 154 (1992) 77–93.Google Scholar
  6. 6.
    D. Prasad and R.P. Chhabra, Thermal and normal squeezing effects in lubrication of rollers by a power-law fluid. Wear 145 (1991) 61–76.Google Scholar
  7. 7.
    J.M. Wang and Jin, The optimum design of the Rayleigh slider bearing with a power law fluid. Wear 129 (1989) 1–11.Google Scholar
  8. 8.
    P. Szabo and O. Hassager, Flow of viscoplastic fluids in eccentric annular geometries. J. Non-Newtonian Fluid Mech. 45 (1992) 149–169.Google Scholar
  9. 9.
    S.H. Bittleston and O. Hassager, Flow of viscoplastic fluids in a rotating concentric annulus. J. Non-Newtonian Fluid Mech. 42 (1992) 19–36.Google Scholar
  10. 10.
    R.H. Warring, Pumps: Selection, Systems and Applications, 2nd Ed. Morden, Surrey: Trade & Technical Press Ltd. (1984) 271pp.Google Scholar
  11. 11.
    V.S. Lobanoff and R.R. Ross, Centrifugal Pumps, Design and Application. Houston, Texas: Gulf Publications (1985) 374pp.Google Scholar
  12. 12.
    J. Davidson and O. von Bertele, Process Pump Selection. UK: Professional Engineering Publishing (2000) 202pp.Google Scholar
  13. 13.
    M.J.D. Powell, A hybrid method for nonlinear algebraic equations, In: P. Rabinowitz, (ed.) Numerical Methods for Nonlinear Algebraic Equations, Gordon & Breach (1970) pp. 45–48.Google Scholar
  14. 14.
    R.T. Fenner, On local solutions to non-Newtonian viscous flows. Int. J. Non-Linear Mechanics 10 (1975) 207–214.Google Scholar
  15. 15.
    S.J. Chapman, A.D. Fitt and C.P. Please, Extrusion of power-law shear-thinning fluids with small exponent. Int. J. Non-Linear Mechanics 32 (1997) 187–199.Google Scholar
  16. 16.
    H.K. Moffatt, Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18 (1964) 1–18.Google Scholar
  17. 17.
    P. Henriksen and O. Hassager, Corner flow of power law fluids. J. Rheology 33 (1989) 865–879.Google Scholar
  18. 18.
    NAG Ltd., FASTFLO User Manual. Oxford, England: Numerical Algorithms Group (1999).Google Scholar
  19. 19.
    X. Nicolas, P. Traore, A. Mojtabi and J.P. Caltagirone, Augmented Lagrangian method and open boundary conditions in 2D simulation of Poiseuille-Bernard channel flow. Int. J. Num. Meth. Fluid Mech. 25 (1997) 265–283.Google Scholar
  20. 20.
    M.E. Brewster, S.J. Chapman, A.D. Fitt and C.P. Please, Asymptotics of very small exponent power-law shear-thinning fluids in a wedge. Euro. J. Appl. Math. 6 (1995) 559–571.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • A.D. Fitt
    • 1
  • C.P. Please
    • 2
  1. 1.Faculty of Mathematical StudiesUniversity of SouthamptonSouthamptonUK
  2. 2.Faculty of Mathematical StudiesUniversity of SouthamptonSouthamptonUK

Personalised recommendations