The entrance region
flow of a Herschel-Bulkley fluid in an annular cylinder has been investigated
numerically without making prior assumptions on the form of velocity profile
within the boundary layer region. This velocity distribution is determined as
part of the procedure by cross sectional integration of the momentum
differential equation for a given distance z from the channel entrance. Using
the macroscopic mass and momentum balance equation, the entrance length at each
cross section of the entrance region of the annuli and pressure distribution
have been calculated for specific values of Herschel-Bulkley number and various
values of aspect ratio and flow behavior index. The effects of non-Newtonian
characteristics and channel width on the velocity profile, pressure
distribution and the entrance length have been discussed.
Cite this paper
Pai, R. and Kandasamy, A. (2014) Entrance Region Flow of Herschel-Bulkley Fluid in an Annular Cylinder. Applied Mathematics
, 1964-1976. doi: 10.4236/am.2014.513189
 Batra, R.L. and Jena, B. (1990) Entrance Region Flow of Blood in Concentric Annulus. International Journal of Engineering Science, 28, 407-419. http://dx.doi.org/10.1016/0020-7225(90)90006-5
 Tandon, P.N., Srivastava, L.M. and Kushwaha, K. (1994) Developing Bloodflow in the Entrance Region of an Artery. International Journal of Bio-Medical Computing, 36, 257-265. http://dx.doi.org/10.1016/0020-7101(94)90079-5
 Dash, R.K., Jayaraman, G. and Mehta, K.N. (1996) Estimation of Increased Flow Resistance in a Narrow Catheterized Artery—A theoretical model. Journal of Biomechanics, 29, 917-930. http://dx.doi.org/10.1016/0021-9290(95)00153-0
 Gupta, R.C. (2001) On Developing Laminar Non-Newtonian Flow in Pipes and Channels. Nonlinear Analysis: Real World Applications, 2, 171-193. http://dx.doi.org/10.1016/S0362-546X(00)00109-7
 Maia, M.C.A. and Gasparetto, C.A. (2003) A Numerical Solution for the Entrance Region of Non-Newtonian Flow in Annuli. Brazilian Journal of Chemical Engineering, 20, 1-18. http://dx.doi.org/10.1590/S0104-66322003000200014
 Sankar, D.S. and Hemalatha, K. (2007) Pulsatile Flow of Herschel-Bulklely Fluid through Catherized Arteries—A Mathematical Model. Applied Mathematical Modeling, 31, 1497-1517. http://dx.doi.org/10.1016/j.apm.2006.04.012
 Poole, R.J. and Chhabra, R.P. (2010) Development Length Requirements for Fully Developed Laminar Pipe Flow of Yield Stress fluids. Journal of Fluids Engineering, 132, 034501-034504. http://dx.doi.org/10.1115/1.4001079
 Kandasamy, A. and Pai, R.G. (2013) Core Variation in the Entrance Region Flow of Casson Fluid in an Annuli. Applied Mechanics and Materials, 391, 376-381.
 Kandasamy, A. and Pai, R.G. (2014) Core Variation in the Entrance Region Flow of Herschel-Bulkley Fluid in an Annuli. Accepted for International Conference of Mechanical Engineering to Be Held at Imperial College London, July 2014.