Micropolar Fluid Model for Blood Flow through a Small Tapered Tube
Keywords:
Reynold’s Number, Rotational Viscosity, Rotational Gradient Coefficient, Micro rotational VelocityAbstract
The steady flow of blood through a small rigid circular tube with small tapering angles of 10 and 20 is analysed by a micro-continuum approach using the boundary conditions proposed by Ariman et al. [J Appl. Mech. (March 1974),1]. Analytical expression for flow velocity, micro-rotational velocity, volume flow rate and shear stress at blood vessel wall are obtained. The influence of hematocrit, Reynolds number and tapered angles on the flow characteristics are discussed. As the tapered angle increases the wall shearing stress increases resulting in a decrease in the velocity.
References
[1] Allen SJ, Desilva CN & Kline K A, Digest 7th Int Conf Med Biol Eng, Stockholm, Sweden, edited by B Jacbson 1967, 375.
[2] Bluestein J L, Green A E, Int J Eng Scl, 5 (1967) 323.
[3] Ariman T, J Biomech, 4 (1971) 185.https://doi.org/10.1016/0021-9290(71)90003-0
[4] Bulliarello G & Sevilla A, J Biorheology, 7 (1970) 85. https://doi.org/10.3233/BIR-1970-7202
[5] McDonald D A, (William and Wilkins Co, Blatimore) 1960.
[6] Attinger E O. (McGraw Hill Book Co, New York) 1964.
[7] Thompson D W. (Cambridge Univ Press, Cambridge) 2nd edn 1942, 954.
[8] Weibel E R, (Academic press Inc, New York) 1963.
[9] Womersley J R, Wright Air Dev Centre Tech Rep, TR-56-614, [Wright Patterson AFN Ohio] 1957.,
[10] Streeter V L, Ford W F & Bohr D F, Cire Res, 13 (1965) 3. https://doi.org/10.1161/01.RES.13.1.3
[11] Wirz HJ & Smolderen J J, (McGraw Hill Book Co New York). 1978, 140.
[12] Allyn G M, Jame A D & Charles G R, Surgery, 53(4) (1963) 513.
[13] Eringen A C, J Math Mech, 16(1) (1966) 1. https://doi.org/10.1512/iumj.1966.16.16001
[14] Ariman T, Turk M A & Sylvester N D, J Appl Mech (March 1974) 1.
[15] Tanner R 1, Br J Appl Phys, 17 (1966) 663. https://doi.org/10.1088/0508-3443/17/5/313
[16] Skalak R & Stathis T, Biomechanics, edited by Y C Fung, 1966,68.
[17] Narasimhan M N L & Okada K, Int J Eng Sci, 16 (1978) 1045. https://doi.org/10.1016/0020-7225(78)90060-5
[18] Chaturani P & Upadhyay V S, Biorheology, 16 (1979) 419. https://doi.org/10.3233/BIR-1979-16606