Pulsatile unsteady flow of blood through porous medium in a stenotic artery under the influence of transverse magnetic field

Mukesh Kumar Sharma; Kuldip Bansal; Seema Bansal

Korea-Australia Rheology Journal, Vol.24, No.3, 181-189, September, 2012

DOI10.1007/s13367-012-0022-1 Export Citation

Pulsatile unsteady flow of blood through porous medium in a stenotic artery under the influence of transverse magnetic field

Mukesh Kumar Sharma^†, Kuldip Bansal, and Seema Bansal

Department of Mathematics, Guru Jambheshwar University of Science & Technology, Hisar-125001 (Haryana) INDIA, India

E-mail:

The periodic nature of the cardiac cycle induces a pulsatile, unsteady flow within the circulatory system. The pulsatile model of blood flow provides data to analyse the physiological situation in close proximity. The distribution of fatty cholesterol and artery-clogging blood clots in the lumen of the coronary artery is assumed as a porous medium. A mathematical model for pulsatile flow through an stenosed artery filled with porous medium in the presence of transverse static magnetic field has been formulated under the consideration of hematocrit dependent viscosity of blood that governed by Einstein equation. The velocity profile, volume flux, pressure gradient and wall shear stress are obtained and the effects of magnetic number, Darcy number, Womersely number are computed and represented through graphs.

Keywords:pulsatile flow;stenosis;MHD;wall shear stress

[References]

Barnothy MF, 1964-1969, Biological Effects of Magnetic Fields, Vols. 1& 2, Plenum Press, New York.
Bird RB, Stewart WE, Light Foot EN, Transport Phenomena, John Wiley and Sons, Inc. New York, U.S.A. (1960)
Burton AC, Introductory text, Physiology and Biophysics of Circulation, Year Book Medical Publisher, Chicago, IL. (1966)
Chakravarty S, Sen S, Korea-Aust. Rheol. J., 17(2), 47 (2005)
Constantinides P, Am. J. Cardiol., 66(16), G37 (1990)
Cowling TG, Magnetohydrodynamics, Interscience Publishers, New York. (1957)
Dash RK, Mehta KN, Jayarman G, Int.J. Eng. Sci., 34, 1145 (1996)
David MW, Christos PM, Stephen RH, David NK, Annals of Biomedical Engineering., 29(4), 321 (2001)
Davies MJ, Thomas A, N. Engl.J. Med., 310(18), 1137 (1984)
Davies MJ, Thomas AC, Br. Heart J., 53(4), 363 (1985)
Davies MJ, Circulation., (Suppl.3), 82, 1138 (1990)
Deplano V, Siouffi M, J. of Biomechanics., 32, 1081 (1999)
EL-Shahed M, Appl. Math.Comput., 138(2,3), 479 (2003)
EL Shehawey EF, EL Sebaei W, International Journal of Mathematics and Mathematical Sciences., 24, 217 (2000)
Fung YC, Biodynamics circulation, Springer-Verlag, New York. 29. (1984)
Gupta AS, Applied Scientific Research., 9(1), 319 (1960)
Halder K, Ghosh SN, Ind. Jr. Pure and Appl. Math., 25(3), 345 (1994)
Javadzadegan A, Esmaeili M, Majidi S, Fakhimghanbarzadeh B, Journal of Mechanical Science and Technology., 23, 2456 (2009)
Kolin A, Exp.Biol. Med., 35(1), 53 (1936)
Korchevskii EM, Marochnik LS, Biophysics., 10, 411 (1965)
Keltner JR, Roos MS, Brakeman PR, Budinger TF, Mag. Reson.Med. J., 16(1), 139 (1990)
Kumar S, Sharma MK, Singh K, Garg NR, International J. of Math. Sci. & Engg. Appls. (IJMSEA)., 5(11), 63 (2011)
Layek GC, Mukhopadhyay S, Int. J. of Applications and Applied Mathematics., 3, 308 (2008)
Lee KW, Xu XY, Med Eng. Phys., 24(9), 575 (2002)
Mazumdar JN, Bio-fluid Mechanics., Word Scientific Press. (1992)
Mazumdar HP, Ganguly UN, Ghorai S, Dalal DC, Ind.J.of pure and Appl.Maths., 27, 1137 (1996)
McDonald DA, 1960, 1974, Blood Flow in Arteries, Arnold, London.
McKay JC, Prato FS, Thomas AW, Bioelectromagnetics., 28, 81 (2007)
Mekheimer KS, El Kot MA, Appl. Math. Mech. -Engl. Ed., 29(8), 1093 (2008)
Prakash J, Makinde OD, Ogulu A, Botswana Journal of Technology., 13(1), 45 (2004)
Rathod VP, Tanveer S, Bull. Malays. Math. Sci. Soc., 32(2), 245 (2009)
Sanyal DC, Maiti AK, Ind. J. Maths., 40(2), 199 (1998)
Sud VK, Sekhon GS, Biophys. J., 84, 2638 (2003)
Tashtoush B, Magableh A, Heat and Mass Transfer., 44(3), 297 (2008)
Tzirtzilakis EE, Physics of Fluids., 17, 1 (2005)
Xu Z, Lioi J, Mu J, Kamocka MM, Liu X, Chen DZ, Rosen ED, Alber MA, Biophysical Journal., 98, 1723 (2010)
Xu Z, Chen N, Shadden S, Marsden JE, Kamocka MM, Rosen ED, Alber MS, Soft Matter., 5, 769 (2009)
Xu Z, Chen LN, Kamocka MM, Rosen ED, Alber MS, Journal of the Royal Society Interface., 4(24), 705 (2008)
Young DF, ASME Journal of Biomechanics., 6, 547 (1968)
Zamir M, The Physics of Coronary Blood Flow., Springer. (2005)

[Referenced By]

[1] Barnothy MF, 1964-1969, Biological Effects of Magnetic Fields, Vols. 1& 2, Plenum Press, New York.

[2] Bird RB, Stewart WE, Light Foot EN, Transport Phenomena, John Wiley and Sons, Inc. New York, U.S.A. (1960)

[3] Burton AC, Introductory text, Physiology and Biophysics of Circulation, Year Book Medical Publisher, Chicago, IL. (1966)

[4] Chakravarty S, Sen S, Korea-Aust. Rheol. J., 17(2), 47 (2005)

[5] Constantinides P, Am. J. Cardiol., 66(16), G37 (1990)

[6] Cowling TG, Magnetohydrodynamics, Interscience Publishers, New York. (1957)

[7] Dash RK, Mehta KN, Jayarman G, Int.J. Eng. Sci., 34, 1145 (1996)

[8] David MW, Christos PM, Stephen RH, David NK, Annals of Biomedical Engineering., 29(4), 321 (2001)

[9] Davies MJ, Thomas A, N. Engl.J. Med., 310(18), 1137 (1984)

[10] Davies MJ, Thomas AC, Br. Heart J., 53(4), 363 (1985)

[11] Davies MJ, Circulation., (Suppl.3), 82, 1138 (1990)

[12] Deplano V, Siouffi M, J. of Biomechanics., 32, 1081 (1999)

[13] EL-Shahed M, Appl. Math.Comput., 138(2,3), 479 (2003)

[14] EL Shehawey EF, EL Sebaei W, International Journal of Mathematics and Mathematical Sciences., 24, 217 (2000)

[15] Fung YC, Biodynamics circulation, Springer-Verlag, New York. 29. (1984)

[16] Gupta AS, Applied Scientific Research., 9(1), 319 (1960)

[17] Halder K, Ghosh SN, Ind. Jr. Pure and Appl. Math., 25(3), 345 (1994)

[18] Javadzadegan A, Esmaeili M, Majidi S, Fakhimghanbarzadeh B, Journal of Mechanical Science and Technology., 23, 2456 (2009)

[19] Kolin A, Exp.Biol. Med., 35(1), 53 (1936)

[20] Korchevskii EM, Marochnik LS, Biophysics., 10, 411 (1965)

[21] Keltner JR, Roos MS, Brakeman PR, Budinger TF, Mag. Reson.Med. J., 16(1), 139 (1990)

[22] Kumar S, Sharma MK, Singh K, Garg NR, International J. of Math. Sci. & Engg. Appls. (IJMSEA)., 5(11), 63 (2011)

[23] Layek GC, Mukhopadhyay S, Int. J. of Applications and Applied Mathematics., 3, 308 (2008)

[24] Lee KW, Xu XY, Med Eng. Phys., 24(9), 575 (2002)

[25] Mazumdar JN, Bio-fluid Mechanics., Word Scientific Press. (1992)

[26] Mazumdar HP, Ganguly UN, Ghorai S, Dalal DC, Ind.J.of pure and Appl.Maths., 27, 1137 (1996)

[27] McDonald DA, 1960, 1974, Blood Flow in Arteries, Arnold, London.

[28] McKay JC, Prato FS, Thomas AW, Bioelectromagnetics., 28, 81 (2007)

[29] Mekheimer KS, El Kot MA, Appl. Math. Mech. -Engl. Ed., 29(8), 1093 (2008)

[30] Prakash J, Makinde OD, Ogulu A, Botswana Journal of Technology., 13(1), 45 (2004)

[31] Rathod VP, Tanveer S, Bull. Malays. Math. Sci. Soc., 32(2), 245 (2009)

[32] Sanyal DC, Maiti AK, Ind. J. Maths., 40(2), 199 (1998)

[33] Sud VK, Sekhon GS, Biophys. J., 84, 2638 (2003)

[34] Tashtoush B, Magableh A, Heat and Mass Transfer., 44(3), 297 (2008)

[35] Tzirtzilakis EE, Physics of Fluids., 17, 1 (2005)

[36] Xu Z, Lioi J, Mu J, Kamocka MM, Liu X, Chen DZ, Rosen ED, Alber MA, Biophysical Journal., 98, 1723 (2010)

[37] Xu Z, Chen N, Shadden S, Marsden JE, Kamocka MM, Rosen ED, Alber MS, Soft Matter., 5, 769 (2009)

[38] Xu Z, Chen LN, Kamocka MM, Rosen ED, Alber MS, Journal of the Royal Society Interface., 4(24), 705 (2008)

[39] Young DF, ASME Journal of Biomechanics., 6, 547 (1968)

[40] Zamir M, The Physics of Coronary Blood Flow., Springer. (2005)