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Flow of a biomagnetic viscoelastic fluid: application to estimation of blood flow in arteries during electromagnetic hyperthermia, a therapeutic procedure for cancer treatment

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Abstract

The paper deals with the theoretical investigation of a fundamental problem of biomagnetic fluid flow through a porous medium subject to a magnetic field by using the principles of biomagnetic fluid dynamics (BFD). The study pertains to a situation where magnetization of the fluid varies with temperature. The fluid is considered to be non-Newtonian, whose flow is governed by the equation of a second-grade viscoelastic fluid. The walls of the channel are assumed to be stretchable, where the surface velocity is proportional to the longitudinal distance from the origin of coordinates. The problem is first reduced to solving a system of coupled nonlinear differential equations involving seven parameters. Considering blood as a biomagnetic fluid and using the present analysis, an attempt is made to compute some parameters of the blood flow by developing a suitable numerical method and by devising an appropriate finite difference scheme. The computational results are presented in graphical form, and thereby some theoretical predictions are made with respect to the hemodynamical flow of the blood in a hyperthermal state under the action of a magnetic field. The results clearly indicate that the presence of a magnetic dipole bears the potential so as to affect the characteristics of the blood flow in arteries to a significant extent during the therapeutic procedure of electromagnetic hyperthermia. The study will attract the attention of clinicians, to whom the results would be useful in the treatment of cancer patients by the method of electromagnetic hyperthermia.

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Abbreviations

ξ, η:

non-dimensional coordinates

α :

dimensionless distance

H :

magnetic field strength

T :

temperature

\( \bar k \) :

permeability constant

K 1 :

pyromagnetic coefficient

M :

magnetization (magnetic moment per unit volume)

B :

ferromagnetic interaction parameter

K :

viscoelastic parameter

Re :

Reynolds number

Pr :

Prandtl number

K 2 :

permeability parameter

k 0 :

coefficient of visco-elasticity

ρ :

density of the fluid

p :

pressure

λ :

viscous dissipation parameter

μ :

dynamic viscosity

μ 0 :

magnetic permeability

c p :

specific heat at constant pressure

k :

thermal conductivity

u :

velocity along the horizontal direction

v :

velocity along the vertical direction.

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Authors and Affiliations

  1. Department of Information Technology, Siksha O Anusandhan University, Bhubaneswar, 751030, Orissa, India

    J. C. Misra

  2. School of Medical Science and Technology, Indian Institute of Technology, Kharagpur, 721302, India

    A. Sinha

  3. Department of Mathematics, Jadavpur University, Kolkata, 700032, India

    G.C. Shit

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  2. A. Sinha
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  3. G.C. Shit
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Correspondence to J. C. Misra.

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Communicated by Zhe-wei ZHOU

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Misra, J.C., Sinha, A. & Shit, G. Flow of a biomagnetic viscoelastic fluid: application to estimation of blood flow in arteries during electromagnetic hyperthermia, a therapeutic procedure for cancer treatment. Appl. Math. Mech.-Engl. Ed. 31, 1405–1420 (2010). https://doi.org/10.1007/s10483-010-1371-6

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  • DOI: https://doi.org/10.1007/s10483-010-1371-6

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