Mathematical modeling of biomagnetic flow in a micropolar fluid-saturated darcian porous medium

International Journal of Fluid Mechanics Research

Volumn 34, Issue 5, 2007, Pages 403-424

  Beg, Osman Anwar ^a,b,c   Takhar, Harmindar S ^d   Bhargava, R ^e   Sharma, S ^e   Hung, T K ^f  

^a LEEDS METROPOLITAN UNIVERSITY   (United Kingdom)

^b BAE Systems Saudi Arabia   (Saudi Arabia)

^c Engovation Engineering Sciences Research   (United Kingdom)

^d MANCHESTER METROPOLITAN UNIVERSITY   (United Kingdom)

^e INDIAN INSTITUTE OF TECHNOLOGY ROORKEE   (India)

^f UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANGULAR MOMENTUM; FINITE ELEMENT METHOD; FLOW MEASUREMENT; HYDRODYNAMICS; MAGNETIC FLUIDS; MATHEMATICAL MODELS; POROUS MATERIALS; PRESSURE GRADIENT; TUMORS; VISCOUS FLOW;

BIOMEDICAL DEVICE; DARCIAN LINEAR DRAG; DARCY NUMBER; MICROPOLAR FLUID; MICROPOLAR VISCOSITY; MOMENTUM CONSERVATION;

BIOMAGNETISM;

EID: 34548424936     PISSN: 21525102     EISSN: 21525110     Source Type: Journal    
DOI: 10.1615/InterJFluidMechRes.v34.i5.20     Document Type: Article

References (43)

1. Eringen, A. C., Theory of Micropolar Fluids, USSR J. Math. Mech., 1966, 16, No. 1, pp. 909-923.
2. Ariman, T., Turk, N. A. and Sylvester, N. D., On Steady Pulsatile Flow of Blood, ASME J. Appl. Mech., 1974, 41, pp. 1-7.
3. Bugliarello, G. and Sevilla, J., Velocity Distribution and Other Characteristics of Steady and Pulsatile Blood Flow in Fine Glass Tubes, Biorheology 1, 1970, 7, pp. 85-95.
4. Renuka Ravindran and R.Girija Devi, Wave Propagation in a Micropolar Fluid Contained in a Viscoelastic Membrane, Proc. Ind. Acad. Sci., 1970, LXXII, pp. 108-120.
5. Eringen, A. C. and Kang, C. K., The Effect of Microstructure on the Rheological Properties of Blood, Bull. Math. Biol., 1976, 38, No. 2, pp. 135-159.
6. Laskowski, L. K. and Wronski, S., On Pulsatile Flow of Micropolar Fluid, Arch. Mech., 1976, 28, pp. 615-624.
7. Chaturani, P. and Mahajan, S. P., Poiseuille Flow of Micropolar Fluid with Non-Zero Couple Stress at Boundary with Applications to Blood Flow, Biorheology J., 1982, 19, No. 4, pp. 507-518.
8. Devanathan, R. and Parvathamma, S., Flow of Micropolar Fluid Through a Tube with Stenosis, Med. Biol. Engng Comput., 1983, 21, pp. 438-445.
9. Hogan, H. A and Henriksen, M., An Evaluation of a Micropolar Model for Blood Flow Through an Idealized Stenosis, J Biomech., 1989, 22, No. 3, pp. 211-218.
10. Vlachakis, N. W. and Kioussis, E. K., Two Dimensional, Two Phase Micropolar Blood Flow, In: 2-nd Conf. Hellenic Soc. for Theor. Applied Mech. (IUTAM-adhering org.), Athens, Greece, 1989.
11. Atefi, Gh. and Moosaie, A., Analysis of Blood Flow Through Arteries Using the Theory of Micropolar Fluids, Proc. 12-th Iran. Biomed. Engng Conf., Tabriz, Iran, November, 2005.
12. Hogan, H. A. and Henriksen, M., A Finite Element Formulation for Laminar Flow of a Fluid with Microstructure, Int. J. Numer. Meth. Fluids, 2005, 13, No. 10, pp. 1267-1287.
13. Bég, O. A. and Sajid, A., Cerebro-Spinal Poroelastic Fluid Dynamics: Modeling Blood Flow Through "Porous" Brain Tissue, Technical Report, Universidyne Consultancy, Bradford Univ. Sci. Park, UK, November, 2002.
14. Sorek, S. and Sideman, S., A Porous Medium Approach for Modelling Heart Mechanics. A. Theory, Math. Biol. Sci., 1986, 81, pp. 1-14.
15. Sorek, S. and Sideman, S., A Porous Medium Approach for Modelling Heart Mechanics. B. 1-D Case, Math. Biol. Sci., 1986, 81, pp. 14-32.
16. Lei, X. X., Wu, W. Y., Wen, G. B., and Chen, J. G., Mass Transport in Solid Tumors I: Fluid Dynamics, Appl. Math. Mech. - Engng Ed., 1998, 19, pp. 1025-1032.
17. Preziosi, L. and Farina, A. On Darcy's Law for Growing Porous Media Int. J. Non-Lin. Mech.200237485-491
18. Vankan, W. J., Huyghe, J. M., Janssen, J. D., Huson, A., Hacking, W. J. G., and Schrenner, W., Finite Element Analysis of Blood Flow Through Biological Tissue, Int. J. Engng Sci., 1997, 35, pp. 375-385.
19. Renuka Ravindran and R. Girija Devi, Wave Propagation in a Micropolar Fluid Contained in a Porous Tube, Biomech. Resch Proc., 1974, 1, pp. 10-19.
20. Axtell, N. K., Park, M., and Cushman, J. H., Micromorphic Fluid in an Elastic Porous Body: Blood Flow in Tissues with Microcirculation, Int. J. Multiscale Comput. Engng, 3, No. 1, 2005, pp. 71-84.
21. Takeuchi, T., Mizuno, T., Higashi, T., Yamagishi, A., and Date, M., Orientation of Red Blood Cells in High Magnetic Field, J. Magn. Magnet. Mater., 1995, 140-144, pp. 1462-1463.
22. Pauling, L. and Coryell, C. D., The Magnetic Properties and Structure of Haemoglobin, Oxyhaemoglobin and Carbon-Monoxy Haemoglobin, Proc. Nat Acad. Sci., 1936, 22, pp. 210-216.
23. Keltner, J. R., Roos, M. S., Brakeman, P. R., and Budinger, T. F., Magnetohydrodynamics of Blood Flow, Magn. Reson. Med. J., 1990, 16, No. 1, pp. 139-149.
24. Sud, V. K. and Sekhon, G. S., Blood Flow Through the Human Arterial System in the Presence of a Steady Magnetic Field, Biophys. J., 2003, 84, pp. 2638-2645.
25. Ruuge, E. K. and Rusetski, A. N., Magnetic Fluids As Drug Carriers: Targeted Transport of Drugs by a Magnetic Field, J. Magn. Magnet. Mater., 1993, 122, pp. 335-339.
26. Haik, Y., Chen, J. C., and Pai, V. M., Development of Biomagnetic Fluid Dynamics, In: Proc IX Int. Symp. Transport Phenomena in Thermal Fluids Engng, Pacific Centre Thermal Fluids Engng, June, 1996, pp. 25-28.
27. Sanyal, D. C. and Maiti, A. K., On Steady and Pulsatile Motion of Blood, Czechosl. J. Phys., 1998, 48, No. 3, pp. 347-354.
28. Tzirtzilakis, E. E. and Tanoudis, G. B., Numerical Study of Biomagnetic Fluid Flow Over a Stretching Sheet with Heat Transfer, Int. J. Numer. Meth. Heat Fluid Flow, 2003, 13, No. 7, pp. 830-848.
29. Stokes, V. K., Theories of Fluids with Microstructure, Springer Verlag, New York, 1984.
30. Louckopoulos, V. C. and Tzirtzilakis, E. E., Biomagnetic Channel Flow in Spatially Varying Magnetic Field, Int. J. Engng Sci., 2004, 42, pp. 571-590.
31. Bég, O. A., Takhar, H. S., and Singh, A. K., Multi-Parameter Perturbation Analysis of Unsteady Oscillatory Magneto-Convection Through Porous Media with Heat Source Effects, Int. J. Fluid Mech. Resch, 2005, 32, pp. 635-661.
32. Rosensweig, R. E., Ferrohydrodynamics, Dover, New York, 1985.
33. Gorla, R. S. R., Page, C. L., and Takhar, H. S., A Non-Similar Micropolar Boundary Layer on a Moving Wall, J. Theor. Appl. Fluid Mech., 1997, 3, No. 4, pp. 264-278.
34. Reddy, J. N., An Introduction to the Finite Element Method, Macgraw-Hill, New York, 1985.
35. Takhar, H. S., Agarwal, R. S., Bhargava, R., and Jain, S., Mixed Convective Non-Steady 3-Dimensional Micropolar Fluid Flow at a Stagnation Point, Heat Mass Transfer J., 1998, 33, pp. 443-448.
36. Takhar, H. S., Bhargava, R., and Agarwal, R. S., Finite Element Solution of a Micropolar Fluid from an Enclosed Rotating Disk with Suction and Injection, Int. J.Engng Sci., 2001, 39, pp. 913-927.
37. Bhargava, R., Kumar, L., and Takhar, H. S., Finite Element Solution of Mixed Convection Micropolar Flow Driven by a Porous Stretching Sheet, Int. J. Engng Sci., 2003, 41, pp. 2161-2178.
38. Naroua, H., Takhar, H. S., Ram, P. C., Tasveer A. Beg, and O. Anwar Beg, Hydromagnetic Transient Free Convection in a Partially-Ionized Rotating Heat-Generating Gas with Hall/Ion-Slip Current Effects: Finite Element Solutions, Int. J. Fluid Mech. Resch, 2007, 35 [in press].
39. Kirwan, A. D. and Newman, N., Simple Flow of a Fluid Containing Deformable Structures, Int. J. Engng Sci., 1969, 7, pp. 1067-1078.
40. Dahler, J. S. and Scriven, E., Theory of Structured Continua. I. General Consideration of Angular Momentum and Polarization, Proc. Roy. Soc. Lond., 1963, A275, pp. 504-527.
41. Kirwan, A. D., Boundary Conditions for Micropolar Fluids, Int. J. Engng Sci., 1986, 24, pp. 1237-1242.
42. Neuringer, J. L., Some Viscous Flows of a Saturated Ferrofluid Under the Combined Influence of Thermal and Magnetic Field Gradients, Int. J. Non-Lin. Mech., 1966, 1, pp. 123-137.
43. Andersson, H. I. and Vaines, O. A., Flow of a Heated Ferrofluid Over a Stretching Sheet in the Presence of a Magnetic Dipole, Acta Mechanica, 1998, 128, pp. 39-47.