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Atherosclerotic Study of non-Isothermal non-Newtonian Steady Flow of Blood in a Plane by Adomian Decomposition Method

Author Affiliations

  • 1Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, 44000, Islamabad, Pakistan
  • 2Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, 44000, Islamabad, Pakistan
  • 3Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, 44000, Islamabad, Pakistan

Int. Res. J. Biological Sci., Volume 5, Issue (4), Pages 54-63, April,10 (2016)

Abstract

In the present study, the analytical solutions of blood flow for two dimensional non-isothermal, non-Newtonian fluids flowing through the channel having symmetric stenosis of cosine shape are discussed. The governing Navier-Stokes equations are reduced to compatibility equation along with energy equation and solved analytically by Adomian decomposition method (ADM) and regular perturbation method (RPM). The results are presented analytically and graphically in terms of streamlines, wall shear stress, separation and reattachment points and temperature distribution on blood flow through a stenoised channel. It has been observed that the non-Newtonian nature of blood reduces the magnitude of the peak of flow over the stenoised region. Further, increase in second grade parameter increases the temperature and wall shear stress while the critical Re decreases. It is observed from comparison that the ADM is efficient, reliable, easily computable and provides a fast convergent series. It worthy noting that the results obtained in this paper are compared with published results and found good agreement.

References

  1. Adomian G. (1984)., Convergent series solution of nonlinear equations., J. Comput. Appl. Math., 11(2).
  2. Adomian G. (1984)., On the convergence region for decomposition solutions., J. Comput. Appl. Math. 11.
  3. Adomian G. (1986)., Nonlinear Stochastic Operator Equations., Academic Press, San Diego.
  4. Adomian G. (1988)., A review of the decomposition method in applied mathematics., J. Math. Anal. Appl. 135, 501-544.
  5. Bellomo N. and Monaco R.A. (1985)., Comparison between Adomian, J. Math. Anal. Appl. 110, 495-502.
  6. Young D.F. (1968)., Effect of a time-dependent stenosis on flow through a tube., J. Engng Ind., Trans. Am. Soc. Mech. Engrs., 90, 248-254.
  7. Forrester J.H. and Young D.F. (1970)., Flow through a converging-diverging tube and its implications in occlusive vascular disease., J. Biomech., 3, 297-316.
  8. Lee J.S. and Fung Y.C. (1970)., Flow in locally constricted tubes at low Reynolds number., J. Appl. Mech., 37, 9-16.
  9. Morgan B.E. and Young D.F. (1974)., An integral method for the analysis of flow in arterial stenoses., J. Math. Bio. 36, 39-53.
  10. Haldar K. (1991)., Analysis of separation of blood flow in constricted arteries., Archives of Mechanics, 43(1), 107-113.
  11. Chow J.C.F., Soda K. and Dean C. (2013)., On laminar flow in wavy channel, Developments in Mechanics., 6, proceedings of the 12th Midwestern Mechanics Conference.
  12. Shukla J.B., Parihar R.S. and Rao B.R.P. (1980)., Effects of stenosis on Non-Newtonian flow of the blood in an artery., Bull. of Math. Bio. 42, 283-294.
  13. Vahdati S., Tavassoli Kajani M. and Ghasemi M. (2013)., Application to Homotopy Analysis Method to SIR Epidemic Model., Res. J. Recent Sci., 2(1), 91-96.
  14. Thundil Karuppa, Raj R. and Ramsai R. (2012)., Numerical study of fluid flow and effect of inlet pipe angle in catalytic converter using CFD., Res. J. Recent Sci., 1(7), 39-44.
  15. Chauhan Rajsinh B. and Thundil Karuppa Raj R. (2012)., Numerical investigation of external flow around the Ahmed reference body using computational fluid dynamics., Res. J. Recent Sci., 1(9), 1-5.
  16. Siddiqui A.M. and Kaloni P.N. (1986)., Certain inverse solutions of a non-Newtonian fluid., Int. J. Non-Linear Mech., 21(6), 459-473.