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Nonlinear Forced Convective Hydromagnetic Flow of Unsteady Biomagnetic Fluid Over a Wedge with Convective Surface Condition

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Chaos, Complexity and Leadership 2012

Part of the book series: Springer Proceedings in Complexity ((SPCOM))

Abstract

Nonlinear forced convective hydromagnetic flow of an unsteady biomagnetic fluid over a wedge with convective surface has been analyzed numerically. The highly nonlinear coupled governing equations for the momentum, energy, angular momentum for the blood corpuscles and the magnetic induction are reduced to ordinary differential similarity equations by the introduction of a new similarity transformation. These equations are solved using very robust computer algebra software Maple 13. The effects of the various material parameters on the flow, temperature and microrotation fields are investigated. The results show that unsteadiness significantly controls the flow and heat transfer characteristics of the biomagnetic fluid. Strong unsteadiness may trigger back flow even for an accelerated flow. Due to the strong magnetic effect blood corpuscles may oscillate along the surface of the wedge. Induced magnetic field reduces fluid velocity and gives rise to its temperature significantly, which suggests that in the modeling of biomagnetic fluid the effect of induced magnetic field should be taken into account.

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Abbreviations

Bi :

Biot number

C f :

Skin friction coefficient

c p :

Specific heat at constant pressure

Ec :

Eckert number

f :

Dimensionless stream function

h :

Induced magnetic field parameter

h f :

Heat transfer coefficient

H*:

Induced magnetic field intensity

H :

Dimensionless H*

H 0 :

Applied magnetic field intensity

H w :

Induced magnetic field

j :

Micro-inertia per unit mass

K :

Unsteadiness parameter

M :

Magnetic field parameter

m :

Velocity exponent

N :

Dimensionless microrotation

Nu :

Local Nusselt number

n :

Microrotation parameter

P :

Pressure

Pm :

Magnetic Prandtl parameter

Pr :

Prandtl number

q w :

Surface heat flux

Re :

Local Reynolds number

S :

Coefficient of vortex viscosity

t :

Time

T :

Temperature within boundary layer

T f :

Temperature at the bottom

T w :

Temperature at the surface

T ∞ :

Temperature of the ambient fluid

u :

Velocity along x-axis

U :

Free stream velocity

U 0 :

Characteristic velocity

U * :

Nondim. free stream velocity

v :

Velocity along y-axis

X :

Characteristic length

x :

Coordinate along the surface

y :

Coordinate normal to surface

ρ :

Density of the fluid

β :

Wedge angle parameter

δ :

Length scale

μ :

Dynamic viscosity

μ e :

Magnetic permeability

υ :

Kinematic viscosity

υ s :

Spin-gradient viscosity

Δ:

Vortex viscosity parameter

ξ :

Micro-inertia parameter

ω :

Microrotation

σ :

Fluid electric conductivity

ψ :

Stream function

κ :

Thermal conductivity

η :

Similarity parameter

τ w :

Shear stress

λ :

Nondim boundary layer thickness

λ 1 :

Dimensionless displacement thickness

λ 2 :

Dimensionless momentum thickness

θ :

Dimensionless temperature

Δη :

Step size

w :

Surface condition

∞ :

Boundary layer edge

References

  • Ahmadi G (1976) Self-similar solution of incompressible micropolar boundary layer flow over a semi- infinite plate. Int J Eng Sci 14(7):639–646

    Article  MATH  Google Scholar 

  • Anad M, Rajagopal KR (2004) A shear-thinning viscoelastic fluid model for describing the flow of blood. Int J Cardiol Med Sci 4(2):59–68

    Google Scholar 

  • Anjali Devi SP, Kandasamy R (2001) Thermal stratification effects on laminar boundary-layer flow over a wedge with suction or injection. Mech Res Commun 28(3):349–354

    Article  MATH  Google Scholar 

  • Ariman T, Turk NA, Sylvester ND (1974) On steady pulsatile flow of blood. ASME J Appl Mech 41(1):1–7

    Article  Google Scholar 

  • Atefi and Moosaie MA (2005) Analysis of blood flow through arteries using the theory of micropolar fluids. In: Proceedings of the 12th Iranian biomedical engineering conference, Tabriz

    Google Scholar 

  • Aziz A (2009) A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition. Commun Nonlinear Sci Numer Simul 14(4):1064–1068

    Article  ADS  Google Scholar 

  • Bataller RC (2008) Radiation effects for the Blassius and Sakiadis flows with a convective surface boundary condition. Appl Math Comput 206(2):832–840

    Article  MathSciNet  MATH  Google Scholar 

  • Charm S, Paltiel B, Kurland GS (1968) Heat transfer coefficient in blood flow. Biorheology 5:133–145

    Google Scholar 

  • Charny CK (1992) Mathematical models of bioheat transfer. Bioengineering heat transfer, special issue. Adv Heat Transf 22:19–155

    Article  ADS  Google Scholar 

  • Chato JC (1980) Heat transfer to blood vessels. J Biomech Eng 102(2):110–118

    Article  Google Scholar 

  • Chaudhary RC, Sharma BK (2006) Combined heat and mass transfer by laminar mixed convection flow from a vertical surface with induced magnetic field. J Appl Phys 99:034901–034910

    Article  ADS  Google Scholar 

  • Choi HW, Barakat AI (2005) Numerical study of the impact of non-Newtonian blood behavior on flow over a two-dimensional backward facing step. Biorheology 42(6):493–509

    Google Scholar 

  • Eringen AC (1966) Theory of micropolar fluids. J Math Mech 16:909–923

    Google Scholar 

  • Eringen AC, Kang CK (1976) The effect of microstructure on the rheological properties of blood. Bull Math Biol 38(2):135–159

    MATH  Google Scholar 

  • Falkner VM, Skan SW (1931) Some approximate solutions of the boundary layer equations. Philos Mag 12:865–896

    Google Scholar 

  • Haik Y, Pai V, Chen CJ (1999) Development of magnetic device for cell separation. J Magn Magn Mater 194(1–3):254–261

    Article  ADS  Google Scholar 

  • Hartee DR (1937) On an equation occurring in Falkner and Skan’s approximate treatment of the equations of the boundary layer. Math Proc Cambridge Philo Soci 33(Part II)(2):223–239

    Article  ADS  Google Scholar 

  • Himenz K (1911) Die Grenzscchicht an einen in gleichformign Flussigkeitsstrom eingetanchten geraden Kreiszylider. Dinglers Polytechnol J 326(321):1911

    Google Scholar 

  • Hogan HA, Henriksen M (1989) An evaluation of a micropolar model for blood flow through an idealized stenosis. J Biomech 22(3):211–218

    Article  Google Scholar 

  • Ishak A (2010) Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition. Appl Math Comput 217(2):837–842

    Article  MathSciNet  MATH  Google Scholar 

  • Kafoussias NG, Nanousis ND (1997) Magnetohydrodynamic laminar boundary-layer flow over a wedge with suction or injection. Can J Phys 75(11):733–745

    Article  ADS  Google Scholar 

  • Kandasamy R, Periasamy K, Prabhu KKS (2005) Effects of chemical reaction, heat and mass transfer along a wedge with heat source and concentration in the presence of suction or injection. Int J Heat Mass Tran 48(7):1388–1394

    Article  MATH  Google Scholar 

  • Kays WM, Crawford ME (1987) Convective heat and mass transfer, 2nd edn. McGraw-Hill, New York

    Google Scholar 

  • Kuo BL (2005) Heat transfer analysis for the Falkner-Skan wedge flow by the differential transformation method. Int J Heat Mass Tran 48(23–24):5036–5046

    Article  MATH  Google Scholar 

  • Lin HT, Lin LK (1987) Similarity solutions for laminar forced convection heat transfer from wedges to fluids of any Prandtl number. Int J Heat Mass Tran 30(6):1111–1118

    Article  ADS  Google Scholar 

  • Na TY (1979) Computational methods in engineering boundary value problems. Academic, New York

    MATH  Google Scholar 

  • Pennes HH (1948) Analysis of tissue and arterial blood temperatures in the resting human forearm. J Appl Physiol 1(2):93–122

    ADS  Google Scholar 

  • Plavins J, Lauva M (1993) Study of colloidal magnetite binding erythrocytes: prospects for cell separation. J Magn Magn Mater 122(1–3):349–353

    Article  ADS  Google Scholar 

  • Rahman MM (2011a) Heat transfer in biomagnetic fluid over a wedge with convective surface boundary condition in the presence of induced magnetic field. Int J Energy Technol 3(17):1–8

    Google Scholar 

  • Rahman MM (2011b) Locally similar solutions for hydromagnetic and thermal slip flow boundary layers over a flat plate with variable fluid properties and convective surface boundary condition. Meccanica 46:1127–1143

    Article  MathSciNet  MATH  Google Scholar 

  • Rahman MM, Eltayeb IA (2011) Convective slip flow of rarefied fluids over a wedge with thermal jump and variable transport properties. Int J Therm Sci 50(4):468–479

    Article  Google Scholar 

  • Rahman MM, Sattar MA (2006) Magnetohydrodynamic convective flow of a micropolar fluid past a continuously moving vertical porous plate in the presence of heat generation/absorption. ASME J Heat Tran 128(2):142–152

    Article  Google Scholar 

  • Rajagopal KR, Gupta AS, Na TY (1983) A note on the Falkner-Skan flows of a non-Newtonian fluid. Int J Nonlinear Mech 18(4):313–320

    Article  MathSciNet  MATH  Google Scholar 

  • Rashad AM, Bakier AY (2009) MHD effects on non-Darcy forced convection boundary layer flow past a permeable wedge in a porous medium with uniform heat flux. Nonlinear Anal Model Contr 14(2):249–261

    MathSciNet  MATH  Google Scholar 

  • Rubinsky B (1999) Heat transfer in biomedical engineering and biotechnology. In: Proceedings of the 5th ASME/JSME joint thermal engineering conference, San Diego, CA, March 15--19, AJTE-6528

    Google Scholar 

  • Ruuge EK, Rusetski AN (1993) Magnetic fluid as drug carriers: targeted transport of drugs by a magnetic field. J Magn Magn Mater 122(1–3):335–339

    Article  ADS  Google Scholar 

  • Sattar MA (2011) A local similarity transformation for the unsteady two-dimensional hydrodynamic boundary layer equations of a flow past a wedge. Int J Appl Math Mech 7(1):15–28

    MathSciNet  ADS  MATH  Google Scholar 

  • Schlichting H (1968) Boundary layer theory. McGraw Hill, New York

    Google Scholar 

  • Skalak R, Chien S (1982) Rheology of blood cells as soft tissues. Biorheology 19:453–461

    Google Scholar 

  • Srivastava VP (2003) Flow of a couple stress fluid representing blood through stenotic vessels with a peripheral layer. Indian J Pure Appl Math 34:1727–1740

    MATH  Google Scholar 

  • Stewartson K (1954) Further solutions of Falkner-Skan equation. Math Proc Cambridge Philo Soci 50(3):454–465

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Tzirtzilakis EE, Tanoudis GB (2003) Numerical study of biomagnetic fluid flow over a stretching sheet with heat transfer. Int J Numer Method Fluid Flow 13(7):830–848

    Article  MathSciNet  MATH  Google Scholar 

  • Valvano JW, Nho S, Anderson GT (1994) Analysis of the Weibaum-Jiji model of blood flow in the canine kidney cortex for self-heated thermistors. J Biomech Eng 116(2):201–207

    Article  Google Scholar 

  • Watanabe T (1990) Thermal boundary layers over a wedge with uniform suction or injection in forced flow. Acta Mech 83(3–4):119–126

    Article  Google Scholar 

  • Yao S, Fang T, Zhong Y (2011) Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions. Commun Nonlinear Sci Numer Simul 16(2):752–760

    Article  ADS  MATH  Google Scholar 

  • Yih KA (1998) Uniform suction/blowing effect on the forced convection about a wedge: uniform heat flux. Acta Mech 128(3–4):173–181

    Article  MATH  Google Scholar 

Download references

Acknowledgment

M.M. Rahman would like to thank the Sultan Qaboos University for financial support through the research grant IG/SCI/DOMAS/10/02. M.A. Sattar expresses his sincere gratitude to Sultan Qaboos University for proving local hospitality during his visit.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.C. 123 Al-Khod, 36, Muscat, Sultanate of Oman

    M. M. Rahman

  2. Department of Electrical Engineering and Computer Science, North South University, Dhaka, 1229, Bangladesh

    M. A. Sattar

Authors
  1. M. M. Rahman
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  2. M. A. Sattar
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Corresponding author

Correspondence to M. M. Rahman .

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Editors and Affiliations

  1. International Science Association, Ankara, Turkey

    Santo Banerjee

  2. International Science Association, Ankara, Turkey

    Şefika Şule Erçetin

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Rahman, M.M., Sattar, M.A. (2014). Nonlinear Forced Convective Hydromagnetic Flow of Unsteady Biomagnetic Fluid Over a Wedge with Convective Surface Condition. In: Banerjee, S., Erçetin, Ş. (eds) Chaos, Complexity and Leadership 2012. Springer Proceedings in Complexity. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7362-2_49

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  • DOI: https://doi.org/10.1007/978-94-007-7362-2_49

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-7361-5

  • Online ISBN: 978-94-007-7362-2

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