Numerical simulation on convection-diffusion in an overlapping stenosed artery
Keywords:Newtonian fluid flow, Mass transport, Overlapping stenosis, Finite difference method,
AbstractConsider an unsteady Newtonian blood flow coupled with mass transport in which flowing through an artery with the presence of an overlapping stenosis. The flowing blood is governed by nonlinear partial differential equations while the convection-diffusion equation to blood is employed to couple with the Newtonian equation in order to characterize the mass transport of blood-borne components such as low-density lipoprotein (LDL). This mass transport refers to the movement of blood-borne molecules from flowing blood into the artery wall, or vice versa. These coupled equations are solved numerically using finite-difference method with an appropriate prescribed initial and boundary conditions. The graphical results of velocity profiles and mass concentration of the solute are presented along the distributions over the entire considered arterial segment. These results show the important role of mass transport in stenosed artery.
A. Valencia and M. Villanueva, Int. Comm. Heat and Mass Transfer, 33 (2006) 966-975.
S. Fazli, E. Shirani and M.R. Sadeghi, J. of Biomechanics, 44 (2011) 68-76.
L. Xiao, F. Yubo, D. Xiaoyan and Z. Fan, J. of Biomechanics, 44 (2011) 1123-1131.
C.G. Caro, J.M. Fitz-Gerald and R.C. Schroter, Proc. Of Royal Soc. London, Ser. B Biological Science, 177 (1970) 109-159.
L.H. Back, J.R. Radbill and D.W. Crawford, J. of Biomechanics, 10 (1977) 763-774.
M.R. Kaazempur-Mofrad, S. Wada, J.G. Myers and C.R. Ethier, Int. J. of Heat and Mass Transfer, 48 (2005) 4510-4517.
Sarifuddin, S. Chakravarty, P.K. Mandal and H.I. Andersson, Z. angew. Math. Phys., 60 (2009) 299-323.
N. Sun, N.B. Wood, A.D. Hughes, S.A.M Thom and X.Y. Xu, Am. J. of Physiology Heart and Circulatory Physiology, 292 (2007) H31148-H33157.  N. Yang and K. Vafai, Int. J. of Heat and Mass Transfer, 51 (2008) 497-505.
S. Chung and K. Vafai, J. of Biomechanics, 45 (2012) 371-381.
S. Chakravarty and P.K. Mandal, Math. Comp. Modelling, 24 (1996) 43-58.
S. Chakravarty and P.K. Mandal, Int. J. Non-linear Mechanics, 35 (2000) 779-793.
S. Chakravarty and A.K. Sannigrahi, Math. Comp. Modelling, 29 (1999) 9-25.
S.C. Ling and H.B. Atabek, J. of Fluid Mechanics, 55 (1972) 493-511.  E. Belardinelli and S. Cavalcanti, J. of Biomechanics, 25(11) (1992) 1337-1349.
S. Cavalcanti, J. of Biomechanics, 28 (1995) 387-399.
M.D. Deshpande, D.P. Giddens and R.F. Mabon, J. of Biomechanics, 9 (1976) 165-174.
I. Abdullah and N. Amin, Math. Meth. Appl. Sci., 33 (2010) 1910-1923.
C.E Niehaus, A. Nicoll, R. Wootton, B. Williams, J. Lewis, D.J. Coltart and B. Lewis, Lancet, 2 (1977) 469-471.
B.G. Nordestgaard, H.A. Tybjaerg and B. Lewis, Arterios. Thrombosis, 12 (1992) 6-18.
D.C. Schwenke and R.W. St. Clair, Arterios. Thrombosis, 13 (1993) 1368-1381.
L.B. Nielsen, Atherosclerosis, 123 (1996) 1-15.