Computational modeling of MHD flow of blood and heat transfer enhancement in a slowly varying arterial segment (original) (raw)
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This paper deals with a mathematical model describing the heat transfer and fluid flow characteristic of blood flow in multi-stenosis arteries in the presence of magnetic field. Here introducing a mathematical model of the multi-stenosis inside the arteries through a finite difference scheme in terms of vorticity-stream function along with their boundary conditions. An observation is made about the degree of stenosis and the effect of magnetic field on Nusselt number and wall shear stress, and observed that magnetic field modifies the flow pattern's and increase heat transfer rate. The hardness of the stenosis affects the wall shear stress characteristic significantly and hence local Nusselt number is going to increases because magnetic field torque will be increasing the thermal boundary layer thickness and temperature gradient. It is here assumed that the surface roughness is exponentially and the maximum height of the roughness is very small compared with the radius of the unconstricted tube.
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An investigation of an oscillatory blood flow in an indented artery with heat source in the presence of magnetic field was carried out. The formulated governing models are solved using Frobenius method where the solutions are transformed into Bessel functions 0 () I r β and 0 () K r β of order zero of the first and second kind. The computational results are presented graphically for the velocity profile (,) w r t , the temperature profile () r θ. The study reveals that the blood flow is appreciably influenced by the presence of a magnetic field and also by the value of the Grashof Gr number. It is observed that the presence of the magnetic field M retards the velocity profile as well as the flow rate; the Grasof number Gr causes an increment in the velocity profile which is consistent with the existing laws of physics. Furthermore, the radiation parameter Rd does affect the velocity profile which means, it
Frontiers in Heat and Mass Transfer, 2018
Present work aims to investigate the blood stream in a permeable vessel in the presence of an external magnetic field with heat and mass transfer. The instability in the coupled flow and temperature fields is considered to be produced due to the time-dependent extending velocity and the surface temperature of the vessel. The non-uniform heat source/sink effects on a chemically responded blood stream and heat viscous. This study is of potential value in the clinical healing of cardiovascular disorders accompanied by accelerated circulation. The problem is treated mathematically by reducing it to a system of joined non-linear differential equations, which have been solved by utilizing similarity transformation and boundary layer approximation. The resultant non-linear coupled ordinary differential equations are solved numerically by utilizing the fourth order Runge-Kutta method with shooting technique. Computational results are gotten for the velocity, temperature, the skin-friction coefficient, the rate of heat transfer and rate of mass transfer in the vessel. The evaluated results are compared with another analytical study reported earlier in scientific literatures. The present investigation exposes that the heat transfer rate is upgraded as the value of the unsteadiness parameter increases, but it decreases for the increment of the space reliance parameter for heat source/sink.
We present a numerical investigation of tapered arteries that addresses the transient simulation of non-Newtonian bio-magnetic fluid dynamics (BFD) of blood through a stenosis artery in the presence of a transverse magnetic field. The current model is consistent with ferro-hydrodynamic (FHD) and magneto-hydrodynamic (MHD) principles. In the present work, blood in small arteries is analyzed using the Carreau-Yasuda model. The arterial wall is assumed to be fixed with cosine geometry for the stenosis. A parametric study was conducted to reveal the effects of the stenosis intensity and the Hartman number on a wide range of flow parameters, such as the flow velocity, temperature, and wall shear stress. Current findings are in a good agreement with recent findings in previous research studies. The results show that wall temperature control can keep the blood in its ideal blood temperature range (below 40˚C) and that a severe pressure drop occurs for blockages of more than 60 percent. Additionally, with an increase in the Ha number, a velocity drop in the blood vessel is experienced.
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In the present study, a two-dimensional pulsatile blood flow model is created and the related heat transfer characteristics through a stenosed artery are investigated in the presence of a defined magnetic field with the body acceleration. The blood domain is assumed as a nonlinear, time-dependent, incompressible and laminar flow. The blood flow is considered with the unsteady characteristics because the pulsatile pressure gradient is arising due to the systematic reactions between the heart and the body acceleration. The non-linear momentum and continuity equations are solved with suitable initial and boundary conditions using the Crank-Nicolson scheme. In this study, the blood flow characteristics (velocity profiles, temperature, volumetric flow rate and flow resistance) are evaluated, also effects of the defined stenosis severity, the heat transfer factors and the considered magnetic field on the effective flow properties are discussed. Besides, the blood flow characteristics have been analyzed in a comparison form for two rigid and elastic arteries. Finally, it should be said that the present outputs are in good agreement with some available and validated results.
A mathematical model for blood flow in magnetic field
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The unsteady oscillatory magneto-hydrodynamic flow of blood in small diameter arteries with mild constriction is analyzed, blood being modelled as a Herschel-Bulkley fluid. Finite difference method is employed for solving the associated initial boundary value problem. Explicit finite difference schemes for velocity distribution, flow rate, skin friction and longitudinal impedance to the flow are obtained. The effects of pressure gradient, yield stress, magnetic field, power law index and maximum depth of the stenosis on the aforesaid flow quantities are discussed through appropriate graphs. It is found that the velocity and flow rate decrease and the skin friction and longitudinal impedance to flow increase with the increase of the magnetic field parameter. It was recorded that the flow rate increases and the skin friction decreases with the increase of the phase angle. It was also noted the skin friction and longitudinal impedance to flow that increase almost linearly with the increase of maximum depth of the stenosis. The estimates of the increase in the longitudinal impedance to flow and skin friction are increased considerably by the presence of the magnetic field.
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International Journal of Multidisciplinary Research and Analysis, 2023
In this study, we investigated the effect of a heat source on blood flow through a gradient-tapered vessel under the influence of a gradient magnetic field by reformulating the problem using a mathematical model representing the blood momentum and energy equations. The partial differential equations were dimensionlessly scaled using a scaling parameter and further reduced to a system of ordinary differential equations. A coupled system of regular equations was solved using the series method to obtain analytical solutions for temperature and blood velocity profiles. Numerical simulations were performed using Wolfram Mathematica version 12 and varied parameters relevant to the investigation. The results showed that the relevant parameters—magnetic field, radiation parameter, Grashof number, and tilt angle contributed to liquid temperature and blood flow velocity, respectively. The novelty of this study is the fact that heat can be introduced from a heat source for the purpose of helpi...
Blood Flow Behaviour in a Straight Vein under the Influence of a Magnetic Field
International Journal of Computational Fluid Dynamics, 2020
A mathematical model is developed to study on the influence of magnetic field on the flow of biofluids. This paper describes the laminar, viscous incompressible flow, which is a fully developed flow of a conducting biomagnetic fluid in a rectangular duct with square cross-section, is numerically studied under the influence of magnetic field. Therefore, numerical simulation was carried out by using the Spectral method as a main numerical technique and Newton-Raphson method, Collocation Method and Chebyshev polynomial are considered as secondary tools. The results revealed that the magnetic field separates red blood cells from the whole blood with collapsing in the central line. This results will be applicable in the potential applications of medical science such as the development of magnetic devices for cell separation, targeted transport of drugs using magnetic particles as drug carriers, magnetic wound or cancer tumour treatment causing magnetic hyperthermia, reduction of bleeding during some surgeries.
2021
Received: 25 October 2019 Accepted: 2 December 2020 In this study, the heat and mass transfer of the blood flow, particularly in a capillary tube having a porous lumen and permeable wall in the presence of external magnetic field are considered. The velocity, temperature and concentration of blood flow become unsteady due to the time dependence of the stretching velocity, surface temperature and surface concentration. The thermal and mass buoyancy effect on blood flow, heat transfer and mass transfer are taken into account in the presence of thermal radiation. This analysis is very much useful in the treatment of cardiovascular disorders. The equations governing the flow under some assumptions are complex in nature, but capable of presenting the realistic model of blood flow using the theory of boundary layer approximation and similarity transformation. First, the system of coupled partial differential equations (PDEs) is converted into a system of coupled ordinary differential equa...