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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.
Key wordsbiomagnetic fluid-blood-stretching walls-porous medium-electromagnetic hyperthermia
Chinese Library ClassificationO361.3-O373
2000 Mathematics Subject Classification76A10-74L15
Applied Mathematics and Mechanics 04/2012; 31(11):1405-1420. · 0.56 Impact Factor
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ABSTRACT: Fluid mechanical peristaltic transport through esophagus has been of concern
in the paper. A mathematical model has been developed with an aim to study the
peristaltic transport of a rheological fluid for arbitrary wave shapes and tube
lengths. The Ostwald-de Waele power law of viscous fluid is considered here to
depict the non-Newtonian behaviour of the fluid. The model is formulated and
analyzed with the specific aim of exploring some important information
concerning the movement of food bolus through the esophagus. The analysis has
been carried out by using lubrication theory. The study is particularly
suitable for cases where the Reynolds number is small. The esophagus is treated
as a circular tube through which the transport of food bolus takes places by
periodic contraction of the esophageal wall. Variation of different variables
concerned with the transport phenomena such as pressure, flow velocity,
particle trajectory and reflux are investigated for a single wave as well as
for a train of periodic peristaltic waves. Locally variable pressure is seen to
be highly sensitive to the flow index `n'. The study clearly shows that
continuous fluid transport for Newtonian/rheological fluids by wave train
propagation is much more effective than widely spaced single wave propagation
in the case of peristaltic movement of food bolus in the esophagus.
12/2011;
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ABSTRACT: Of concern in the paper is a generalized theoretical study of the
non-Newtonian characteristics of peristaltic flow of blood through
micro-vessels, e.g. arterioles. The vessel is considered to be of variable
cross-section and blood to be a Herschel-Bulkley type of fluid. The progressive
wave front of the peristaltic flow is supposed sinusoidal/straight section
dominated (SSD) (expansion/contraction type); Reynolds number is considered to
be small with reference to blood flow in the micro-circulatory system. The
equations that govern the non-Newtonian peristaltic flow of blood are
considered to be non-linear. The objective of the study has been to examine the
effect of amplitude ratio, mean pressure gradient, yield stress and the power
law index on the velocity distribution, wall shear stress, streamline pattern
and trapping. It is observed that the numerical estimates for the aforesaid
quantities in the case of peristaltic transport of the blood in a channel are
much different from those for flow in an axisymmetric vessel of circular
cross-section. The study further shows that peristaltic pumping, flow velocity
and wall shear stress are significantly altered due to the non-uniformity of
the cross-sectional radius of blood vessels of the micro-circulatory system.
Moreover, the magnitude of the amplitude ratio and the value of the fluid index
are important parameters that affect the flow behaviour. Novel features of SSD
wave propagation that affect the flow behaviour of blood have also been
discussed.
08/2011;
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ABSTRACT: The paper deals with a theoretical study of the transport of a fluid in a
channel, which takes place by the phenomenon of peristalsis. A mathematical
analysis of the said problem has been presented. The analysis involves the
application of a suitable perturbation technique. The velocity profile and the
critical pressure for the occurrence of reflux are investigated with particular
emphasis by using appropriate numerical methods. The effects of various
parameters, such as Reynolds number, pressure gradient, porosity parameter,
Darcy number, slip parameter, amplitude ratio and wave number on velocity and
critical pressure for reflux are investigated in detail. The computed results
are compared with a previous analytical work and an experimental investigation
reported earlier in existing scientific literatures. The results of the present
study are in conformity to both of them. The study has got some relevance to
the physiological flow of bile in the common bile duct in a pathological state.
It reveals that in the presence of gallstones, bile velocity increases as the
value of the porosity parameter increases, while the critical pressure for
reflux decreases as porosity increases.
07/2011;
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Journal of Mechanics in Medicine and Biology (World Scientific). 01/2011;
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Applied Mathematics and Computation (Elsevier). 01/2011; 217(20):7932-7939.
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International Journal of Biomathematics (World Scientific). 01/2011;
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Journal of Fluid Mechanics (Cambridge Univ. Press). 01/2011;
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[show abstract]
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ABSTRACT: The characteristics of flow and heat transfer of a fluid in a channel with oscillatory stretching walls in
the presence of an externally applied magnetic field are investigated. The fluid considered is a second-grade viscoelastic
electrically conducting fluid. The partial differential equations that govern the flow are solved by developing
a suitable numerical technique. The computational results for the velocity, temperature and the wall shear stress
are presented graphically. The study reveals that flow reversal takes place near the central line of the channel. This
flow reversal can be reduced to a considerable extent by applying a strong external magnetic field. The results are
found to be in good agreement with those of earlier investigations.
Journal of Engineering Mathematics (Springer). 01/2011; 69(1):91-100.
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ABSTRACT: Of concern in the paper is a study of steady incompressible viscoelastic and electrically conducting fluid flow and heat transfer in a parallel plate channel with stretching walls in the presence of a magnetic field applied externally. The flow is considered to be governed by Walter's liquid B fluid. The problem is solved by developing a suitable numerical method. The results are found to be in good agrement with those of earlier investigations reported in existing scientific literatures. The study reveals that a back flow occurs near the central line of the channel due to the stretching walls and further that this flow reversal can be stopped by applying a strong external magnetic field. The study also shows that with the increase in the strength of the magnetic field, the fluid velocity decreases but the temperature increases. Thus the study bears potential applications in the study of the haemodynamic flow of blood in the cardiovascular system when subjected to an external magnetic field. Comment: 26 pages, 12 Figures
07/2010;
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[show abstract]
[hide abstract]
ABSTRACT: The paper is devoted to a study of the peristaltic motion of blood in the
micro-circulatory system. The vessel is considered to be of varying
cross-section. The progressive peristaltic waves are taken to be of sinusoidal
nature. Blood is considered to be a Herschel-Bulkley fluid. Of particular
concern here is to investigate the effects of amplitude ratio, mean pressure
gradient, yield stress and the power law index on the velocity distribution,
streamline pattern and wall shear stress. On the basis of the derived
analytical expression, extensive numerical calculations have been made. The
study reveals that velocity of blood and wall shear stress are appreciably
affected due to the non-uniform geometry of blood vessels. They are also highly
sensitive to the magnitude of the amplitude ratio and the value of the fluid
index.
06/2010;
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[show abstract]
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ABSTRACT: The present paper deals with a theoretical investigation of the peristaltic
transport of a couple stress fluid in a porous channel. The study is motivated
towards the physiological flow of blood in the micro-circulatory system, by
taking account of the particle size effect. The velocity, pressure gradient,
stream function and frictional force of blood are investigated, when the
Reynolds number is small and the wavelength is large, by using appropriate
analytical and numerical methods. Effects of different physical parameters
reflecting porosity, Darcy number, couple stress parameter as well as amplitude
ratio on velocity profiles, pumping action and frictional force, streamlines
pattern and trapping of blood are studied with particular emphasis. The
computational results are presented in graphical form. The results are found to
be in good agreement with those of Shapiro et. al \cite{r25} that was carried
out for a non-porous channel in the absence of couple stress effect. The
present study puts forward an important observation that for peristaltic
transport of a couple stress fluid during free pumping when the couple stress
effect of the fluid/Darcy permeability of the medium, flow reversal can be
controlled to a considerable extent. Also by reducing the permeability it is
possible to avoid the occurrence of trapping phenomenon.
06/2010;
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[show abstract]
[hide abstract]
ABSTRACT: 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.
Applied Mathematics and Mechanics (Springer). 01/2010; 31:1405-1420.
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Journal of Applied Mechanics. 07/2009; 76:061006.
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Ninth International Conference of Vibration Problems (ICoVP), Indian Institute of Technology, kharagpur; 06/2009
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Applied Mathematics and Computation. 02/2009; 210:350-361.
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Journal of Mechanics in Medicine and Biology (JMMB) World Scientific. 12/2008; 8:507-525.
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Mathematical Modelling and Analysis. 12/2008; 13:401-412.
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Journal of Mechanics in Medicine and Biology (JMMB) World Scientific. 06/2008; 8:265-279.
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[show abstract]
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ABSTRACT: A mathematical model is developed here with an aim to study the pul-
satile flow of blood through an arterial segment having a time-dependent stenosis.
Blood is considered to consist of a core layer where erythrocytes are concentrated
and a peripheral plasma layer that is free from erythrocytes. The plasma layer is
taken to behave as a Newtonian fluid,while the core layer is represented by as a Cas-
son fluid (non-Newtonian) model. The pulsatile flow is analyzed by considering a
periodic pressure gradient, which is a function of time. A perturbation analysis is
employed to solve the governing differential equations by taking the Womersley frequency parameter to be small (� < 1). This is a realistic assumption for physiological
fluid flows, particularly for flow of blood in small vessels. Using appropriate boundary conditions, analytical expressions for the velocity profile, the volumetric flow rate,
the wall shear stress and the flow resistance have been derived. These expressions
are computed numerically and the computational results are presented graphically, in
order to illustrate the variation of different quantities that are of particular interest
in the study.
Mathematical Modelling and Analysis (MMA). 03/2008; 13:401-412.
