Thermal effects of two immiscible fluids through a permeable stenosed artery having nanofluid in the core region

A theoretical investigation of two-layered fluid flow in a stenosed tube having permeable walls is studied. The fluid (blood with nanoparticles) within the core region behaves as a non-Newtonian fluid (nanofluid) and the fluid within the peripheral layer behaves as a Newtonian fluid. Flow equations are linearized considering mild stenoses. The closed form mathematical expressions for flow resistance and wall shear stress are computed. The problem is solved using HPM (homotopy perturbation method). The numerical calculations of flow parameters (like flow resistance, wall shear stress) are performed and are discussed graphically. A novel result is found that with increased permeability and viscosity, the resistance of the fluid flow and shear at the wall is found to decrease. Moreover, the velocity profiles are increasing in the radial direction with the enhancement of viscosity of the fluid in the peripheral layer but decrease with permeability. Streamlines are drawn to examine the flow pattern.     

Heat transfer of a non-Newtonian fluid (Carbopol aqueous solution) in transitional pipe flow

An experimental study of the forced convection heat transfer for non-Newtonian fluid flow in a pipe is presented. We focus particularly on the transitional regime. A wall boundary heating condition of heat flux is imposed. The non-Newtonian fluid used is Carbopol (polyacrylic acid) aqueous solutions. Detailed rheology as well as the variation of the rheological parameters with temperature are reported. Newtonian and shear thinning fluids are also tested for comparative purposes. The characterization of the flow and the thermal convection is made via the pressure drop and the wall temperature measurements over a range of Reynolds number from laminar to turbulent regime. Our measurements show that the non-Newtonian character stabilizes the flow, i.e., the critical Reynolds number to transitional flow increases with shear thinning and yield stress. The heat transfer coefficients are given and compared with heat transfer laws for different regime flows. Details when the heat transfer coefficient loses rapidly its local dependence on the Reynolds number are analyzed.     

Finite element analysis of non‐Newtonian magnetohemodynamic flow conveying nanoparticles through a stenosed coronary artery

The present study considers two‐dimensional mathematical modeling of non‐Newtonian nanofluid hemodynamics with heat and mass transfer in a stenosed coronary artery in the presence of a radial magnetic field. The second‐grade differential viscoelastic constitutive model is adopted for blood to mimic non‐Newtonian characteristics, and blood is considered to contain a homogenous suspension of nanoparticles. The Vogel model is employed to simulate the variation of blood viscosity as a function of temperature. The governing equations are an extension of the Navier‐Stokes equations with linear Boussinesq's approximation and Buongiorno's nanoscale model (which simulates both heat and mass transfer). The conservation equations are normalized by employing appropriate nondimensional variables. It is assumed that the maximum height of the stenosis is small in comparison with the radius of the artery, and, furthermore, that the radius of the artery and length of the stenotic region are of comparable magnitude. To study the influence of vessel geometry on blood flow and nanoparticle transport, variation in the design and size of the stenosis is considered in the domain. The transformed equations are solved numerically by means of the finite element method based on the variational approach and simulated using the FreeFEM++ code. A detailed grid‐independence study is included. Blood flow, heat, and mass transfer characteristics are examined for the effects of selected geometric, nanoscale, rheological, viscosity, and magnetic parameters, that is, stenotic diameter (d), viscoelastic parameter (), thermophoresis parameter (), Brownian motion parameter (), and magnetic body force parameter (M) at the throat of the stenosis and throughout the arterial domain. The velocity, temperature, and nanoparticle concentration fields are also visualized through instantaneous patterns of contours. An increase in magnetic and thermophoresis parameters is found to enhance the temperature, nanoparticle concentration, and skin‐friction coefficient. Increasing Brownian motion parameter is observed to accelerate the blood flow. Narrower stenosis significantly alters the temperature and nanoparticle distributions and magnitudes. The novelty of the study relates to the combination of geometric complexity, multiphysical nanoscale, and thermomagnetic behavior, and also the simultaneous presence of biorheological behavior (all of which arise in actual cardiovascular heat transfer phenomena) in a single work with extensive visualization of the flow, heat, and mass transfer characteristics. The simulations are relevant to the diffusion of nano‐drugs in magnet‐targeted treatment of stenosed arterial disease.     

An Investigation of Stokes' Second Problem for Non-Newtonian Fluids

ABSTRACT

Stokes flow produced by an oscillatory motion of a wall is analyzed in the presence of a non-Newtonian fluid. A total of eight non-Newtonian models are considered. A mass balance approach is introduced to solve the governing Equations. The velocity and temperature profiles for these models are obtained and compared to those of Newtonian fluids. For the power law model, correlations for the velocity distribution and the time required to reach the steady periodic flow are developed and discussed. Furthermore, the effects of the dimensionless parameters on the flow are studied. For the temperature distribution, an analytical solution for Newtonian fluid is developed as a comparative source. To simulate the rheological behavior of blood at unsteady state, three non-Newtonian constitutive relationships are used to study the wall shear stress. It is found that in the case of unsteady stokes flow, although the patterns of velocity and wall shear stress is consistent across all models, the magnitude is affected by the model utilized.     

Unsteady,three-dimensional fluid mechanic analysis of blood flow in plaque-narrowed and plaque-freed arteries

Fluid mechanic analysis is used to create and implement a metric to quantify the effectiveness of plaque removal (i.e., debulking) modalities in small arteries. The quantification is based on a three-dimensional, unsteady model of blood flow in complex tubular geometries which characterizes plaque-narrowed arteries. Blood flow unsteadiness is due to the heart-imposed temporal variations which occur during the cardiac cycle. The arterial geometries used for the analysis were determined by the reconstruction of ultrasonic images which were captured before and after debulking. Numerical simulation was used to implement the fluid mechanic model, and separate consideration is given to Newtonian and non-Newtonian constitutive equations. The results of the analysis indicates that the removal of the plaque led to an increase in the rate of blood flow of approximately 2.5, both during the systole and diastole portions of the cardiac cycle. This increase corresponds to the application of the same time-varying, end-to-end pressure difference across the artery segments. The shear stress on the artery wall, a major determinant of the buildup of plaque, is found to be higher for a debulked artery than for a plaque-narrowed artery. This outcome is favorable in that the higher the wall shear, the lower the rate of plaque formation.     

Simulation of heat transfer on an oscillatory blood flow in an indented porous artery

The effect of heat transfer on the motion of blood in a diseased artery has been modeled under the optically thin fluid assumption. Closed-form analytical solutions are obtained for the volume flow rate, rate of heat transfer and shear stress at the vessel wall. The study shows that, in addition to the constriction of the blood vessel and the effect of a magnetic field, the heat transfer also affects the blood flow in the cardiovascular system. This effect is noticeable in the velocity and temperature distributions. The model clearly shows the situation of a patient with a stenosed artery under feverish condition.     

Natural convection in a cavity with undulated walls filled with water-based non-Newtonian power-law CuO–water nanofluid under the influence of the external magnetic field

Natural convection heat transfer in a square cavity (with wavy or plane wall) filled with non-Newtonian power-law nanofluid has been elucidated for several input parameters like Ra spanning from 10⁵ to 10⁶, power-law index (n) from 0.6 to 1.4, and volume fraction of CuO nanoparticles (?) from to 0 to 0.12. Effect of external magnetic field on heat transfer has been illustrated by varying the Ha from 0 to 90. In the present study, our main objective is to explore the effect of nanoparticles on heat transfer enhancement in non-Newtonian power-law fluid. It is found that the addition of nanoparticles (?) to shear thinning fluid enhances the heat transfer approximately 15% when ? increases from 0 to 0.12 for Ha less than 60 at all Ra. For a shear thickening fluid, the same thing happens for all Ha at any Ra. The average surface Nusselt number for a cavity with wavy wall is less than that of a plane wall for all cases which is not true for the case of local Nusselt number.     

Unsteady blood flow and mass transfer of a human left coronary artery bifurcation: FSI vs. CFD

In this study, a Fluid Solid Interaction analysis (FSI) of a computerized tomography (CT) scan reconstructed left coronary artery was performed. The arterial wall was modeled as an isotropic hyperelastic material. The arterial wall shear stress (WSS) was computed in order to investigate a correlation between flow-induced wall shear stress and geometry of the artery. An unsteady state FSI analysis with a commercial finite element software was performed in order to evaluate the maximum and the minimum wall shear stress as a function of the flow regime and the arterial wall compliance in the left coronary. As boundary conditions, physiological pressure waveforms were applied. Comparison of the computational results between the FSI and rigid-wall models showed that the wall shear stress (WSS) distributions were substantially affected by the arterial wall compliance. In particular, the minimum and maximum WSS values significantly vary.     

Numerical Investigation of Nanofluid Laminar Convective Heat Transfer through a Circular Tube

Laminar-flow convective heat transfer of nanofluid in a circular tube with constant wall temperature boundary condition is investigated numerically. A dispersion model is used to account for the presence of nanoparticles. Numerical predictions are in agreement with experimental results obtained in our laboratory for different particles in different sizes. Results clearly show that addition of nanoparticles to base liquid produces considerable enhancement of heat transfer. Heat transfer coefficients increase with nanoparticle concentration. Decreasing nanoparticles size at a specific concentration increases heat transfer coefficients.     

纳米流体动态湿润的格子-Boltzmann模拟

纳米流体动态湿润特性与纳米颗粒的微观运动密切相关。由于缺乏纳米尺度的实验观测技术及相关理论描述,纳米流体动态湿润的研究极具挑战,相关机理仍未明晰。采用格子-Boltzmann方法研究纳米颗粒在纳米尺度下(10-9 m)的微观运动及颗粒沉积所导致的基液流体表面张力、流变性改变及结构分离压力对宏观动态湿润(10-3 m)的影响机制。结果表明,纳米颗粒对基液的表面张力的改性影响纳米流体平衡湿润特性,决定纳米流体是完全浸润还是部分浸润。而纳米颗粒对基液流体流变性的改变影响纳米流体动态湿润过程的铺展指数。纳米颗粒在液滴底部的沉积对动态湿润过程影响较小,而在接触线区域的沉积显著改变纳米流体的动态湿润行为。研究尝试从跨尺度的角度阐释纳米颗粒微观运动对宏观动态湿润行为的影响,探索从微观层面调控纳米流体动态湿润的新方法。     

Numerical simulation of fluid–structure interaction in stenotic arteries considering two layer nonlinear anisotropic structural model

The unsteady non-Newtonian blood flow in symmetric stenotic arteries is numerically simulated considering fluid–structure interaction (FSI) using the code ADINA. A two layer hyperelastic anisotropic structural model is used for the compliant arterial wall. The pressure used as outlet boundary condition was obtained running a CFD simulation for each stenosis with a physiologically-realistic time variation of pressure at inlet for different velocities. The obtained pressure drop increases in potential form with the inlet velocity for a fixed stenosis severity. The FSI results show that the maxima velocity and WSS at throat increase in exponential form with stenosis severity. The minimum and maximum effective stress at throat for stenosis severity of S = 70% ranged between 47 kPa and 96 kPa at diastole and systole, respectively.     

Analysis of thermal radiation,Joule heating,and viscous dissipation effects on blood-gold couple stress nanofluid flow driven by electroosmosis

Gold nanoparticles associated with DNA, RNA, proteins, oligonucleotides, and peptides are useful in therapies and drug delivery. The present article mainatins that gold nanoparticles play a tremendous role in remedying cancer and fatal diseases. A mathematical model is proposed for the two-dimensional motion of the couple stress nanofluid consisting of gold nanoparticles under the application of peristaltic propulsion and electroosmosis mechanisms in an asymmetric microchannel. The effects of radiation with slip boundary have been employed. The governing equations are simplified under the assumptions of low Reynolds number and long wavelength and the Poisson-Boltzmann equation is solved under Debye–Hückel linearization. Analytical solutions for the velocity of fluid motion, nanoparticle temperature, stream function, pressure gradient, are evaluated and analyzed graphically under the effects of various physical parameters. It is notable from the analysis that raising the Brinkman number boosts the nanoparticle temperature and heat transfer coefficient which validate the physical model and analysis. Moreover, it is noticed that sphere-shaped gold nanoparticles enhance the temperature as compared to other geometries of nanoparticles. The present study results may assist in developing the technology, smart micropumps, drugs, and device for hemodialysis and other health care applications.     

Stagnation point flow of Maxwell nanofluid containing gyrotactic micro‐organism impinging obliquely on a convective surface

A numerical study is performed to discuss the nonaligned stagnation of a rate type fluid over a convective surface. The rheology of the fluid is presented by the constitutive equation of the Maxwell fluid model. Buongiorno's model is used to elaborate on the effects of Brownian motion and thermophoresis and motile microorganisms are introduced for the stability of the nanoparticles. The governing equations were solved by the implicit finite difference method. Graphical illustrations for velocity, temperature, nanoparticle concentration and motile microorganism profiles for various involved parameters are presented for both convective and nonconvective surfaces. It is depicted that the temperature, nanoparticle, and microorganism concentration profiles decease while both axial and tangential velocities increase with the velocity ratio parameter for both Newtonian and Maxwellian fluids. The magnitude of temperature, nanoparticle, and microorganism concentration profiles is large for the nonconvective surface as compared to the convective surface. The Nusselt number, Sherwood number, and motile organism number decrease as we move from Newtonian fluid to non‐Newtonian fluid. Furthermore, the increase in the Brownian motion parameter and thermophoresis parameter decreases the density of the motile organism over the convective as well as nonconvective surface.     

高浓度水煤浆直管内流动的数值模拟

通过管流法试验得出质量浓度为65.3%的兖州煤水煤浆为剪切增稠的幂流体。将试验得出的流变模型和参数作为计算的依据,运用FLUENT软件提供的非牛顿流体模块,对水煤浆在直管中的流动进行了数值模拟。计算得出水煤浆在管道中流动产生滑移的临界速度,并得到临界速度与管径的变化关系。提出滑移速度新的定义方法,计算得出三个管径中不同平均流速下的滑移速度均为0.02 m/s,表明水煤浆的滑移速度与平均流速和管径呈弱相关。通过对滑移速度进行修正,得出滑移修正后的单位长度压差与实测值相吻合,表明计算模型是正确的。计算得到管道截面水煤浆的表观粘度变化曲线,从管壁到管道中心先缓慢减少再急剧降低。     

A numerical investigation on the heat and fluid flow of various nanofluids on a stretching sheet

Following the necessity of investigating fluid flow and heat transfer in the stretching sheet problem and effect of nanofluids on them, performance of various nanofluids were investigated in the present study. Three base fluids (deionized water, ethylene glycol, and engine oil) in combination with 18 nanoparticles (metals and their oxides) were investigated. While experimental methods are preferable, a mathematical model was developed and solved by applying differential quadrature method due to lack of such experimental data. With the results obtained in the real dimensions, the error caused by the cancellation of the viscosity effect due to the dimensionless variables was omitted. Effects of magnetic field and volume fraction of nanoparticle on the fluid flow and heat transfer characteristics were investigated. Highest heat transfer rate as well as small amounts of shear stress was obtained for deionized water–Al and deionized water–Mg nanofluids. Increasing volume fraction of nanoparticle was observed to increase both heat transfer and shear stress rates, while presence of a magnetic field caused an increase in shear stress and decrease in heat transfer rate.     

Influence of undulating wall heat and mass flux on MHD natural convection boundary layer flow from a vertical wall

Current study expounds an unsteady magnetohydrodynamic natural convective flow along a vertical wall in presence of variable transverse magnetic field. Small amplitude undulation in wall heat flux and wall mass flux are imposed at the vertical wall to generate the boundary layer flow. The flow governing equations are divided into sets of steady and unsteady equations and then transformed into the similarity and nonsimilarity equations, respectively, by introducing stream function formulations. The sets of nonsimilarity equations are solved numerically by using three different techniques, namely, perturbation solution technique, asymptotic solution technique and implicit finite difference technique applied, respectively, for lower, higher, and all frequencies (ξ). Results are illustrated in connection with the amplitude and phase angles of shear stress, wall temperature, and concentration against the frequency (ξ) for wide ranges of physically significant parameters. Likening of the results obtained by above mentioned numerical methods are presented in every figure and table. Results reveal that the amplitude of undulating shear stress and wall temperature dwindle and the amplitude of wall concentration increases due to increment in Prandtl number (Pr). Besides, on incrementing Schmidt number (Sc) the amplitude of undulating shear stress and wall concentration dwindle and the amplitude of wall temperature increases. Results also reveal that on incrementing magnetic parameter (M) the amplitude of transient shear stress dwindles while the amplitude of transient wall temperature and concentration increase.     

A coupling model for macromolecule transport in a stenosed arterial wall

A mathematical model is developed for the coupled analysis of the transport of macromolecules, such as low-density lipoproteins (LDL), in the blood stream and in the arterial walls. The advection–diffusion equations in porous media are used to model the species field in the arterial wall layers. The physical parameters needed are computed based on the available data from in vivo and in vitro measurements. The computed parameters are compared to those provided by other models and the differences are discussed. The advantage of the current model is that its set up is based on in vivo/vitro measurements and the calculated exact solutions of concentration field, leading to more reliable results. The model is used to simulate the LDL transport in a stenosed artery with various area reductions and stenosis numbers. The effects of hypertension and geometrical variation on the LDL accumulation within the wall are studied and discussed. This work provides essential information for studying atherogenesis.     

Three-dimensional numerical simulation of a failed coronary stent implant at different degrees of residual stenosis. Part I: Fluid dynamics and shear stress on the vascular wall

The influence of the degree of residual stenosis on the hemodynamics inside coronary arteries is investigated through three-dimensional (3D) numerical simulations. The present paper, which is the first of a series of two, focuses on the influence that the degree of residual stenosis (DOR) has on the fluid dynamics and the shear stresses acting on the stent and the artery wall. The pulsatile nature of the blood flow and its non-Newtonian features are taken into account. Four models of artery are investigated. The results show that the wall shear stress (WSS) increases monotonically, but not linearly, with the DOR.     

Modeling pulsatile blood flow within a homogeneous porous bed in the presence of a uniform magnetic field and time-dependent suction

The study models pulsatile blood flow in the cardiovascular system employing the Navier–Stokes equation. Resulting partial differential equations are solved approximately for the flow field. Solutions obtained which compare favourably with previously reported studies, show an increase in the wall shear stress when the porosity of the medium is increased.     

Mixed convection of non-Newtonian fluids along a heated vertical flat plate

Mixed convective heat transfer of non-Newtonian fluids on a flat plate has been investigated using a modified power-law viscosity model. This model does not contain physically unrealistic limits of zero or infinite viscosity as are encountered in the boundary-layer formulation with traditional models of viscosity for power-law fluids. These unrealistic limits can introduce an irremovable singularity at the leading edge; consequently, the model is physically incorrect. The present modified model matches well with the measurement of viscosity, and does not introduce irremovable singularities. Therefore, the boundary-layer equations can be solved by marching from the leading edge downstream as for Newtonian fluids. The numerical results are presented for a shear-thinning fluid in terms of the velocity and temperature distribution, and for important physical properties, namely the wall shear stress and heat transfer rates.