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The paper deals with a theoretical study on blood flow in a stenosed segment of an artery, when blood is mixed with nano-particles. Blood is treated here as a couple stress fluid. Stenosis is known to impede blood flow and to be the cause... more
The paper deals with a theoretical study on blood flow in a stenosed segment of an artery, when blood is mixed with nano-particles. Blood is treated here as a couple stress fluid. Stenosis is known to impede blood flow and to be the cause of different cardiac diseases. Since the arterial wall is weakened due to arterial stenosis, it may lead to dilatation /aneurysm. The homotopy perturbation technique is employed to determine the solution to the problem for the case of mild stenosis. Analytical expressions for velocity, shear stress at the wall, pressure drop, and flow resistance are derived. The impact of different physical constants on the wall shear stress and impedance of the fluid is examined by numerical simulation. Streamline patterns of the nanofluid are investigated for different situations.
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A mathematical model has been developed in this paper with an aim to study arterial blood flow in a vibration environment. Blood is treated as a couple stress fluid. Oscillatory flow in a porous channel is considered in the study, when... more
A mathematical model has been developed in this paper with an aim to study arterial blood flow in a vibration environment. Blood is treated as a couple stress fluid. Oscillatory flow in a porous channel is considered in the study, when the flow takes place under the action of an external pressure gradient. The fluid flows between two porous plates lying parallel to each other. The fluid is considered to be injected on one plate with a constant velocity. The plates are considered to be oscillating with the same frequency in their own planes. However, the plate velocity of single-harmonic oscillation is not constant. The effects of various parameters representing couple stress, suction and magnitude of the oscillating pressure gradient on the velocity profile and wall shear stress are discussed. It is found that the presence of couple stress in the fluid enhances the velocity of the fluid in both axial and transverse directions, while a reverse phenomenon is observed for the wall shea...
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Abstract.In the case of steady flow of a fluid under the combined influence of external electric and magnetic fields, the fluid moves forward by forming an axial momentum boundary layer. With this end in view a study has been performed... more
Abstract.In the case of steady flow of a fluid under the combined influence of external electric and magnetic fields, the fluid moves forward by forming an axial momentum boundary layer. With this end in view a study has been performed here to investigate the problem of entropy generation during electroosmotically modulated flow of a third-order electrically conducting fluid flowing on a microchannel bounded by silicon-made parallel plates under the influence of a magnetic field, by paying due consideration to the steric effect. The associated mechanism of heat transfer has also been duly taken care of, by considering Cattaneo-Christov heat flux. A suitable finite difference scheme has been developed for the numerical procedure. A detailed study of the velocity and temperature distributions has been made by considering their variations with respect to different physical parameters involved in the problem. The results of numerical computation have been displayed graphically. The computational work has been carried out by considering blood as the working fluid, with the motivation of exploring some interesting phenomena in the context of hemodynamical flow in micro-vessels. Among other variables, parametric variations of the important physical variables, viz. i) skin friction and ii) Nusselt number have been investigated. The study confirms that the random motion of the fluid particles can be controlled by a suitable adjustment of the intensity of an externally applied magnetic field in the transverse direction. It is further revealed that the Nusselt number diminishes, as the Prandtl number gradually increases; however, a steady increase in the Nusselt number occurs with increase in thermal relaxation. Entropy generation is also found to be enhanced with increase in Joule heating. The results of the present study have also been validated in a proper manner.
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The paper is devoted to a study of steady hydromagnetic fluid flow with heat and mass transfer over an inclined nonlinear shrinking porous sheet in the presence of thermophoresis and heat generation. The problem is formulated as a... more
The paper is devoted to a study of steady hydromagnetic fluid flow with heat and mass transfer over an inclined nonlinear shrinking porous sheet in the presence of thermophoresis and heat generation. The problem is formulated as a non-linear boundary value problem. A numerical method is developed to solve the problem. The surface velocity of the shrinking sheet and the applied transverse magnetic field are considered as power functions of the distance from the origin. The viscosity and thermal conductivity of the fluid are considered temperature-dependent. The viscosity is taken to be an inverse function of temperature, while the thermal conductivity is supposed to vary linearly with temperature. By using suitable transformation, the equations governing the flow, temperature and concentration fields are reduced to a system of coupled non-linear ordinary differential equations, which are solved numerically by developing an appropriate numerical method. Velocity, temperature and conce...
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... 624 JC MISRA et al. APPENDIX B Expressions for D and D' Involved in Equations (25) D = (ztan a, )" k2kl (z tan a,) (c,3 k, + c23)L(z tan a2 )k, ' (z tan a, )" + 1] (k, + I)LJI ' and o, I kz (czzc,3k,) 1 ID (z... more
... 624 JC MISRA et al. APPENDIX B Expressions for D and D' Involved in Equations (25) D = (ztan a, )" k2kl (z tan a,) (c,3 k, + c23)L(z tan a2 )k, ' (z tan a, )" + 1] (k, + I)LJI ' and o, I kz (czzc,3k,) 1 ID (z tan al)ki (1 kl)z tan a, (1 k,)L3 [(z tan a2)"' (z tan a,)k''' Expressions for B, BE and E ...
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ABSTRACT The paper is devoted to a study of the electro-osmotic flow of a micropolar fluid, when the flow takes place between two plates that are in a state of periodic vibrations and the the system is subjected to the action of an AC... more
ABSTRACT The paper is devoted to a study of the electro-osmotic flow of a micropolar fluid, when the flow takes place between two plates that are in a state of periodic vibrations and the the system is subjected to the action of an AC electric field. The effects of rotation of the micro-particles of the fluid and the Debye-Huckel parameter have been taken into account. Variation in velocity and microrotation with time are computed. The variation in the distribution of velocity and microrotation parameter is also estimated numerically for a fixed set of values of the involved parameters at a particular time-instant. The results presented graphically should serve as a source of novel insight into the process of designing electro-osmotically actuated bio-sensing and micro-fluidic devices.
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Finite deformations and stresses in vascular walls are studied analytically in the paper. Nonlinear viscoelastic constitutive relations suitably modified for the consideration of the anisotropic behavior of the vessel walls are used in... more
Finite deformations and stresses in vascular walls are studied analytically in the paper. Nonlinear viscoelastic constitutive relations suitably modified for the consideration of the anisotropic behavior of the vessel walls are used in the analysis. The time dependence of the inner surface and the force exerted by the surrounding connective tissues are also taken into account. Using approximations for short time ranges, a quantitative analysis is made in order to illustrate the applicability of the analytical study.
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Abstract The paper deals with a 2-dimensional problem of an anisotropic elastic strip having an infinite row of Griffith cracks. By using integral equation approach, the problem is treated analytically. The stress intensity factor, the... more
Abstract The paper deals with a 2-dimensional problem of an anisotropic elastic strip having an infinite row of Griffith cracks. By using integral equation approach, the problem is treated analytically. The stress intensity factor, the critical pressure and the energy required to open the crack are studied for two cases—(a) when the edges of the strip are in contact with smooth and rigid planes and (b) when the edges of the strip are free of tractions. Numerical results for the aforementioned quantities are obtained for both the cases for a specific anisotropic material and a comparison is made with the corresponding results for a strip made of an isotropic material.
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... Editor JC Misra Professor, Department of Mathematics Indian Institute of Technology, Kharagpur, India Copyright© 2003 Narosa Publishing House NAROSA PUBLISHING ... 006 306 Shiv Centre, DBC Sector 17, KU Bazar PO, Navi Mumbai 400 705... more
... Editor JC Misra Professor, Department of Mathematics Indian Institute of Technology, Kharagpur, India Copyright© 2003 Narosa Publishing House NAROSA PUBLISHING ... 006 306 Shiv Centre, DBC Sector 17, KU Bazar PO, Navi Mumbai 400 705 2F-2G Shivam Chambers, 53 ...
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Summary This paper is concerned with a mathematical analysis of the flow of blood in the lungs. The smallest microscopic blood vessels in human lungs are organized into sheet like networks. Each sheet may be idealized into a channel... more
Summary This paper is concerned with a mathematical analysis of the flow of blood in the lungs. The smallest microscopic blood vessels in human lungs are organized into sheet like networks. Each sheet may be idealized into a channel bounded by two thin layers of porous media. A microcontinuum approach is used to determine the velocity and pressure distributions in the channel which is taken to diverge exponentially. Analytical expressions for the velocity and pressure distributions in the thin layer (interstitial space) as well as the corresponding computational results are presented. The flow velocity in the channel and the cell rotational velocity have also been determined.
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The paper deals with a problem related to the flow of blood in vessels. It is known that physiological pumps produce flow by alternate contraction and expansion of the vessel. When muscles start squeezing the vessel wall, the valve at the... more
The paper deals with a problem related to the flow of blood in vessels. It is known that physiological pumps produce flow by alternate contraction and expansion of the vessel. When muscles start squeezing the vessel wall, the valve at the upstream end gets closed and that at the downstream end becomes open. As a result of this, blood is pumped out in the downstream direction. During systole, when the blood in the left ventricle is forced into the aorta, the mitral valve becomes closed, while the atrioventricular valve becomes open. In a situation such as this, the left ventricle takes the form of a vessel with one end closed. In order to study such a situation, a model has been developed here that consists of a fluid-filled long cylindrical pipe with one end closed by a compliant membrane (that prevents the axial motion of the fluid, leaving radial motion completely unrestricted). An approximate solution of the Navier–Stokes equation for the flow of a second-order fluid is presented...
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... highly prestigious Raja Ram Mohan Roy Prize for outstanding contributions in the field of Mathematics and the Rashtriya Gaurav Award (National ... Contents xxiii 16 Modelling in Bone Biomechanics 451 JC Misra and S. Samanta 1... more
... highly prestigious Raja Ram Mohan Roy Prize for outstanding contributions in the field of Mathematics and the Rashtriya Gaurav Award (National ... Contents xxiii 16 Modelling in Bone Biomechanics 451 JC Misra and S. Samanta 1 Introduction 451 2 Bone Biomechanics and Its ...
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An asymptotic series solution for steady flow of an incompressible, second-grade electrically conducting fluid in a channel permeated by a uniform transverse magnetic field is presented. The depth of the channel is assumed to vary slowly... more
An asymptotic series solution for steady flow of an incompressible, second-grade electrically conducting fluid in a channel permeated by a uniform transverse magnetic field is presented. The depth of the channel is assumed to vary slowly in the axial direction. Analytical expressions are derived for the vorticity and pressure drop along the channel as well as the wall shear stress. It is found that for fixed values of the Reynolds number R and the non-Newtonian parameter K1, the wall shear stress increases with increasing value of magnetic parameter M. Numerical computations carried out for a specific slowly varying channel show that flow separation occurs for both second-grade (K1<0) and second-order (K1>0) fluids when |K1|<0.15. The analysis also reveals the interesting result that while flow separation takes place for a second-order fluid for K1≥0.15, no separation occurs at all for |K1|≥0.15 for a second-grade fluid.
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The present paper is concerned with the study of a mathematical model for the flow of blood through a multi-stenosed artery. Blood is considered here to consist of a peripheral plasma layer which is free from red cells, and a core region... more
The present paper is concerned with the study of a mathematical model for the flow of blood through a multi-stenosed artery. Blood is considered here to consist of a peripheral plasma layer which is free from red cells, and a core region which is represented by a Casson fluid. A suitable generalized geometry of multiple stenoses existing in the arterial segment under consideration is taken for the study. A thorough quantitative analysis has been made through numerical computations of the variables involved in the analysis that are of special interest in the study. The computational results are presented graphically.
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Research Interests: Mechanical Engineering, Mathematics, Materials Science, Mechanics, Biomedical Engineering, and 15 moreStructural Engineering, Viscoelasticity, Biomechanics, Medicine, Elasticity, Humans, Models, Damping, Deformation, Biomaterial, Constraint, Bone remodeling, Bone Nails, Bone and Bones, and Axial Symmetry
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