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Role of Slip Velocity on the Oscillatory Flow of Blood Through a Porous Vessel in the Presence of Heat Source and Chemical Reaction

Published online by Cambridge University Press:  13 March 2014

A. Sinha  and
G. C. Shit
A. Sinha
Affiliation:
Department of Mathematics, Jadavpur University, Kolkata-700032, India
G. C. Shit*
Affiliation:
Department of Mathematics, Jadavpur University, Kolkata-700032, India
*
gopal_iitkgp@yahoo.co.in
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Abstract

Of concern in this paper is a problem motivated towards studying the influence of slip velocity on heat and mass transfer in the unsteady flow of blood through a porous vessel, when the lumen of the vessel has turned into a porous structure with internal heat generation or absorption in the presence of chemical reaction. It is assumed that the influence of a uniform magnetic field acts normal to the flow and the permeability of the porous medium fluctuates with time. The suction velocity is also taken to be oscillates periodically. The problem is solved numerically by using Crank-Nicolson scheme. The computational results are presented graphically for the velocity, temperature and concentration distribution as well as the variation of skin-friction co-efficient, Nusselt number and Sherwood number for various values of the parameters involved in this analysis. The study reveals that the flow is appreciably influenced by the presence of a magnetic field and slip velocity.

Keywords

Slip velocityMagnetohydrodynamicsSuction velocityChemical reactionSkin-friction
Type
Research Article
Information
Journal of Mechanics , Volume 30 , Issue 2 , April 2014 , pp. 209 - 218
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

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References

REFERENCES

1.Korchevskii, M. and Marochnik, L. S., “Magnetohydrodynamic Version of Movement of Blood,” Biophysics, 10, pp. 411–413 (1965).Google Scholar
2.Kolin, A., “An Electromagnetic Flow Meter: Principle of the Method and its Application to Blood Flow Measurements,” Proceedings of the Society Experimental Biology, New York, 35, pp. 53–56 (1936).Google Scholar
3.Vardanyan, V. A., “Effect of Magnetic Field on Blood Flow,” Biofizika, 18, pp. 491–496 (1973).Google Scholar
4.Haik, Y., Pai, V. and Chen, C. J., “Apparent Viscosity of Human Blood in a High Static Magnetic Field,” Journal of Magnetism and Magnetic Materials, 225, pp. 180–186 (2001).CrossRefGoogle Scholar
5.Haik, Y., Pai, V. and Chen, C. J., “Development of Magnetic Device for Cell Separation,” Journal of Magnetism and Magnetic Materials, 194, pp. 254–261 (1999).CrossRefGoogle Scholar
6.Halder, K., “Effect of a Magnetic Field on Blood Flow Through an Indented Tube in the Presence of Erythrocytes,” Indian Journal of Pure and Applied Mathematics, 25, pp. 345–352 (1994).Google Scholar
7.Tzirtzilakis, E. E., “A Mathematical Model for Blood flow in Magnetic field,” Physics of Fluids, 17, p. 077103 (2005).CrossRefGoogle Scholar
8.Nadeem, S. and Akbar, N. S., “Influence of Heat Transfer on a Peristaltic Flow of Johnson Segalman Fluid in a Non-Uniform Tube,” International Communications of Heat and Mass Transfer, 36, pp. 1050–1059 (2009).CrossRefGoogle Scholar
9.Srinivas, S. and Gayathri, R., “Peristaltic Transport of a Newtonian Fluid in a Vertical Asymmetric Channel with Heat Transfer and Porous Medium,” Applied Mathematical and Computer, 215, pp. 185–196 (2009).Google Scholar
10.Srinivas, S. and Kothandapani, M., “Peristaltic Transport in an Asymmetric Channel with Heat Transfer-A Note,” International Communications of Heat and Mass Transfer, 35, pp. 514–522 (2008).CrossRefGoogle Scholar
11.Chakravarty, S. and Sen, S., “Dynamic Response of Heat and Mass Transfer in Blood Flow through Stenosed Bifurcated Arteries,” Korea-Australia Rheology Journal, 17, pp. 47–62 (2005).Google Scholar
12.Eldabe, N. T. M., El-Sayed, M. F., Ghaly, A. Y. and Sayed, H. M., “Mixed Convective Heat and Mass Transfer in a Non-Newtonian Fluid at a Peristaltic Surface with Temperature-Dependent Viscosity,” Archives of Applied Mechanics, 78, pp. 599–624 (2007).CrossRefGoogle Scholar
13.Khanafer, K., Bull, J. L., Pop, I. and Berguer, R., “Influence of Pulsatile Blood Flow and Heating Scheme on the Temperature Distribution during Hyperthermia Treatment,” International Journal Heat and Mass Transfer, 50, pp. 4883–4890 (2007).CrossRefGoogle Scholar
14.Ogulu, A. and Abbey, T. M., “Simulation of Heat Transfer on an Oscillatory Blood Flow in an Indented Porous Artery,” International Communications of Heat and Mass Transfer, 32, pp. 983–989 (2005).CrossRefGoogle Scholar
15.Kawase, Y. and Ulbrecht, J. J., “Heat and Mass Transfer in Non-Newtonian Fluid Flow with Power Function Velocity Profiles,” Canadian Journal Chemical Engineers, 61, pp. 791–800 (1983).CrossRefGoogle Scholar
16.Valencia, A. and Villanueva, M., “Unsteady Flow and Mass Transfer in Models of Stenotic Arteries Considering Fluid-Structure Interaction,” International Communications of Heat and Mass Transfer, 33, pp. 966–975 (2006).CrossRefGoogle Scholar
17.Friedman, M. H. and Ehrlich, L. W., “Effects of Spatial Variations in Shear on Diffusion at the Wall of an Arterial Branch,” Circulation Research, 37, pp. 446–454 (1975).CrossRefGoogle ScholarPubMed
18.Allwood, M. J. and Burry, H. S., “The Effect of Local Temperature on Blood Flow in the Human Foot,” Journal of Physiol, 124, pp. 345–357 (1954).CrossRefGoogle ScholarPubMed
19.Charm, S., Paltiel, B. and Kurland, G. S., “Heat Transfer Coefficients in Blood flow,” Biorheology, 5, pp. 133–145 (1968).CrossRefGoogle ScholarPubMed
20.Victor, S. A. and Shah, V. L., “Heat Transfer to Blood flowing in a Tube,” Biorheology, 12, pp. 361–368 (1975).CrossRefGoogle ScholarPubMed
21.Chato, J. C., “Heat Transfer to Blood Vessels,” Journal of Biomechanical Engineering, ASME, 102, pp. 110–118 (1980).CrossRefGoogle ScholarPubMed
22.Lagendijk, J. W., “The Influence of Blood Flow in Large Vessels on the Temperature Distribution in Hyperthermia,” Physics Medical and Biological, 27, pp. 17–82 (1982).CrossRefGoogle Scholar
23.Barozzi, G. S. and Dumas, A., “Convective Heat Transfer Coefficients in the Circulation,” Journal of Biomedical Engineering, 113, pp. 308–313 (1991).Google ScholarPubMed
24.A.fy, A. A., “MHD Free-Convective Flow and Mass Transfer over a Stretching Sheet with Chemical Reaction,” Heat and Mass Transfer, 40, pp. 495–500 (2004).Google Scholar
25.Misra, J. C., Patra, M. K. and Misra, S. C., “A Non-Newtonian Fluid Model for Blood Flow Through Arteries Under the Stenotic Conditions,” Journal of Biomechanics, 26, pp. 1129–1141 (1993).CrossRefGoogle ScholarPubMed
26.Misra, J. C. and Shit, G. C., “Blood Flow Through Arteries in a Pathological State: A Theoretical Study,” International Journal of Engineering Science, 44, 662–671 (2006).CrossRefGoogle Scholar
27.Beavers, G. S. and Joseph, D. D., “Boundary Conditions at a Natural Permeable Wall,” Journal of Fluid Mechanics, 30, pp. 197–207 (1967).CrossRefGoogle Scholar
28.Maiti, S. and Misra, J. C., “Peristaltic Flow of a Fluid in a Porous Channel: A Study Having Relevance to Flow of Bile Within Ducts in a Pathological State,” International Journal of Engineering Science, 49, pp. 950–966 (2011).CrossRefGoogle Scholar
29.Misra, J. C. and Shit, G. C., “Role of Slip Velocity in Blood flow Through Stenosed Arteries: A Non-Newtonian Model,” Journal of Mechanical Medical and Biological, 7, pp. 337–353 (2007).CrossRefGoogle Scholar
30.Brunn, P., “The Velocity Slip of Polar fluids,” Rheology Acta, 14, pp. 1039–1054 (1975).CrossRefGoogle Scholar
31.Nubar, Y., “Blood flow, Slip and Viscometry,” Biophysical Journal, 11, pp. 252–264 (1971).CrossRefGoogle ScholarPubMed
32.Ritman, E. L. and Lerman, A., “Role of Vasa Vasorum in Arterial Disease: A Re-emerging Factor,” Current Cardiology Reviews, 3, pp. 43–55 (2007).CrossRefGoogle Scholar
33.Khaled, A. R. A. and Vafai, K., “The Role of Porous Media in Modeling flow and Heat Transfer in Biological Tissues,” International Journal Heat and Mass Transfer, 46, pp. 4989–5003 (2003).CrossRefGoogle Scholar
34.Jha, B. K. and Prasad, R., “Effects of Applied Magnetic Field on Transient Free Convective Flow in a Vertical Channel,” Journal of Mathematical Physics Science, 26, pp. 1–8 (1992).Google Scholar
35.Lai, F. C., “Coupled Heat and Mass Transfer by Mixed Convection from a Vertical Plate in a Saturated Porous Medium,” International Communications of Heat and Mass Transfer, 18, pp. 93–106 (1991)CrossRefGoogle Scholar
36.Acharya, M., Dash, G. C. and Singh, L. P., “Magnetic Field Effects on the Free Convection and Mass Transfer Flow Through Porous Medium with Constant Suction and Constant Heat flux,” Indian Journal of Pure Applied Mathematics, 31, pp. 1–18 (2000).Google Scholar
37.Kumar, A., Chand, B. and Kaushik, A., “On Unsteady Oscillatory Laminar Free Convection flow of an Electrically Conducting fluid Through Porous Medium Along a Porous Hot Plate with Time Dependent Suction in the Presence of Heat Source/Sink,” Journal of Academy Mathematik, 24, pp. 339–354 (2002).Google Scholar
38.Yin, F. and Fung, Y. C., “Peristaltic Waves in Circular Cylindrical Tubes,” Journal of Applied Mechanics, 36, pp. 679–687 (1969).CrossRefGoogle Scholar
39.Shapiro, A. H., Jaffrin, M. Y. and Weinberg, S. L., “Peristaltic Pumping with Long Wavelengths at Low Reynolds Number,” Journal of Fluid Mechanics, 37, pp. 799–825 (1969)CrossRefGoogle Scholar
40.Singh, A. K., Singh, A. K. and Singh, N. P., “Heat and Mass Transfer in MHD flow of a Viscous fluid Past a Vertical Plate Under Oscillatory Suction Velocity,” Indian Journal of Pure Applied Mathematics, 34, 429–442 (2003).Google Scholar
41.Chaudhary, R. C. and Jha, A. K., “Effect of Chemical Reactions on MHD Micropolar Fluid Flow Past a Vertical Plate in Slip-Flow Regime,” Applied Mathematics and Mechanics (English edition), 29, pp. 1179–1194 (2008).CrossRefGoogle Scholar