Entrance Region Flow of Herschel-Bulkley Fluid in an Annular Cylinder
- 1 Department of Mathematics, Manipal Institute of Technology, Manipal, India
- 2 Department of M.A.C.S., N.I.T.K., Mangalore, India
Abstract
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.
- 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. http://dx.doi.org/10.4028/www.scientific.net/AMM.391.376
- 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.