Numerical simulation of pulsatile flow of blood in a porous-saturated overlapping stenosed artery

Pulsatile flow of blood through a porous-saturated stenotic artery has been studied under the influence of periodic body acceleration. The constitutive equation of Cross model is considered to characterize the blood and also modified form of Darcy's law applicable to Cross model is used in this study. The shape of the stenosis in the arterial lumen is chosen to be overlapping w -shape. The present analysis models the pathological situation in which blood flows through an artery filled with blood clots and fatty cholesterol. In order to obtain the numerical solution, the modeled partial differential equation are normalized and then solved by using finite difference method. Numerical results are calculated for thorough investigation of the effects of porous medium on velocity, impedance, wall shear stress and flow rate. Calculations reveal that velocity, flow rate and shear stress increase while resistance to flow decreases with greater permeability parameter. Furthermore, the size of trapped bolus of fluid is also found to be reduced for large values of the permeability parameter indicating that progressively more porous media avoid bolus growth.

[1]  D. F. Young,et al.  Flow through a converging-diverging tube and its implications in occlusive vascular disease. I. Theoretical development. , 1970, Journal of biomechanics.

[2]  N. Ali,et al.  UNSTEADY TWO-LAYERED BLOOD FLOW THROUGH A $w$ -SHAPED STENOSED ARTERY USING THE GENERALIZED OLDROYD-B FLUID MODEL , 2016, The ANZIAM Journal.

[3]  J. Doffin,et al.  Oscillating flow between a clot model and a stenosis. , 1981, Journal of biomechanics.

[4]  R. Usha,et al.  Pulsatile flow of particle-fluid suspension model of blood under periodic body acceleration , 1999 .

[5]  Prashanta Kumar Mandal,et al.  An unsteady analysis of non-Newtonian blood flow through tapered arteries with a stenosis , 2005 .

[6]  Davood Domiri Ganji,et al.  Electrohydrodynamic flow analysis in a circular cylindrical conduit using Least Square Method , 2014 .

[7]  Prashanta Kumar Mandal,et al.  Effect of heat and mass transfer on non-Newtonian flow – Links to atherosclerosis , 2009 .

[8]  Danny Bluestein,et al.  Fluid mechanics of arterial stenosis: Relationship to the development of mural thrombus , 1997, Annals of Biomedical Engineering.

[9]  Rama Bhargava,et al.  Finite element study of nonlinear two-dimensional deoxygenated biomagnetic micropolar flow , 2010 .

[10]  Davood Domiri Ganji,et al.  A comprehensive analysis of the flow and heat transfer for a nanofluid over an unsteady stretching flat plate , 2014 .

[11]  D. F. Young.  Effect of a Time-Dependent Stenosis on Flow Through a Tube , 1968 .

[12]  Rajandrea Sethi,et al.  Extension of the Darcy–Forchheimer Law for Shear-Thinning Fluids and Validation via Pore-Scale Flow Simulations , 2012, Transport in Porous Media.

[13]  Dalin Tang,et al.  A numerical simulation of viscous flows in collapsible tubes with stenoses , 2000 .

[14]  Kh. S. Mekheimer,et al.  The micropolar fluid model for blood flow through a tapered artery with a stenosis , 2008 .

[15]  Alan Chadburn Burton,et al.  Physiology and biophysics of the circulation : an introductory text , 1965 .

[16]  Prashanta Kumar Mandal,et al.  Unsteady response of non-Newtonian blood flow through a stenosed artery in magnetic field , 2009 .

[17]  Mehrdad Massoudi,et al.  Pulsatile flow of blood using a modified second-grade fluid model , 2008, Comput. Math. Appl..

[18]  Ranjan K. Dash,et al.  Casson fluid flow in a pipe filled with a homogeneous porous medium , 1996 .

[19]  G. Domairry,et al.  Squeezing Cu–water nanofluid flow analysis between parallel plates by DTM-Padé Method , 2014 .

[20]  Mehmet Yasar Gundogdu,et al.  A critical review on blood flow in large arteries; relevance to blood rheology, viscosity models, and physiologic conditions , 2008 .

[21]  Rama Bhargava,et al.  Finite element simulation of unsteady magneto-hydrodynamic transport phenomena on a stretching sheet in a rotating nanofluid , 2013 .

[22]  H. Barnes,et al.  An introduction to rheology , 1989 .

[23]  Y. Fung,et al.  Flow in Locally Constricted Tubes at Low Reynolds Numbers , 1970 .

[24]  D. F. Young,et al.  Flow characteristics in models of arterial stenoses. I. Steady flow. , 1973, Journal of biomechanics.

[25]  Prashanta Kumar Mandal,et al.  Effect of body acceleration on unsteady pulsatile flow of non-newtonian fluid through a stenosed artery , 2007, Appl. Math. Comput..

[26]  Davood Domiri Ganji,et al.  Computer simulation of MHD blood conveying gold nanoparticles as a third grade non-Newtonian nanofluid in a hollow porous vessel , 2014, Comput. Methods Programs Biomed..

[27]  Dharmendra Tripathi,et al.  FINITE ELEMENT STUDY OF TRANSIENT PULSATILE MAGNETO-HEMODYNAMIC NON-NEWTONIAN FLOW AND DRUG DIFFUSION IN A POROUS MEDIUM CHANNEL , 2012 .

[28]  J. Eckenhoff,et al.  Physiology and Biophysics of the Circulation , 1965 .

[29]  Davood Domiri Ganji,et al.  Natural convection of sodium alginate (SA) non-Newtonian nanofluid flow between two vertical flat plates by analytical and numerical methods , 2014 .

[30]  Mukesh Kumar Sharma,et al.  Pulsatile unsteady flow of blood through porous medium in a stenotic artery under the influence of transverse magnetic field , 2012, Korea-Australia Rheology Journal.

[31]  Moustafa El-Shahed,et al.  Pulsatile flow of blood through a stenosed porous medium under periodic body acceleration , 2003, Appl. Math. Comput..

[32]  Davood Domiri Ganji,et al.  Study on blood flow containing nanoparticles through porous arteries in presence of magnetic field using analytical methods , 2015 .

[33]  J. C. Misra,et al.  Flow in arteries in the presence of stenosis. , 1986, Journal of biomechanics.

[34]  Nasir Ali,et al.  Numerical simulation of unsteady micropolar hemodynamics in a tapered catheterized artery with a combination of stenosis and aneurysm , 2015, Medical & Biological Engineering & Computing.

[35]  Sharidan Shafie,et al.  Unsteady Two-Dimensional Blood Flow in Porous Artery with Multi-Irregular Stenoses , 2012, Transport in Porous Media.

[36]  D. Piotrowski,et al.  [Introduction to rheology]. , 1982, Acta haematologica Polonica.

[37]  J. C. Misra,et al.  Flow through blood vessels under the action of a periodic acceleration field:A mathematical analysis , 1988 .

[38]  M E Clark,et al.  Three-dimensional simulation of steady flow past a partial stenosis. , 1981, Journal of biomechanics.