Numerical simulation of laminar flow of water-based magneto-rheological fluids in microtubes with wall roughness effect

Fully developed laminar flows of water-based magneto-rheological (MR) fluids in microtubes at various Reynolds and Hedsrom numbers have been numerically simulated using finite difference method. The Bingham plastic constitutive model has been used to represent the flow behavior of MR fluids. The combined effects of wall roughness and shear yield stress on the flow characteristics of MR fluids, which are considered to be homogeneous by assuming the small particles with low concentration in the water, through microtubes have been numerically investigated. The effect of wall roughness on the flow behavior has been taken into account by incorporating a roughness–viscosity model based on the variation of the MR fluid apparent viscosity across the tube. Significant departures from the conventional laminar flow theory have been acquired for the microtube flows considered.     

Exact solution of two phase stratified flow through the pipes for non-Newtonian Herschel–Bulkley fluids

Steady state, laminar and fully developed stratified two phase flow including two immiscible fluids through the pipe has been studied analytically. One of the phases is Newtonian and the other one is non-Newtonian which obeys the Herschel–Bulkley fluid model. The dimensionless velocity distribution, Martinelli correction factor and non-Newtonian liquid holdup have been reported. The effect of interface curvature and wide range of viscosity ratio of two phases on flow behavior has been investigated. The results illustrate that the non-Newtonian rheological properties have significant effects on dimensionless velocity and consequently on two phase flow pressure drop specially for larger viscosity ratio.     

Binary chemical reaction with activation energy in radiative rotating disk flow of Bingham plastic fluid

This article presents flow, heat and mass transfer phenomena in Bingham plastic fluid. The flow channel is considered to be a rotating disk with a slip which is different in span and streamwise directions, and heat transfer is investigated using dissipation term of the fluid. Arrhenius activation energy and binary chemical reaction are the imperative features of the study of mass transfer. Bingham plastic fluid and anisotropic slip are the key factors of the study due to their numerous applications in manufacturing industries. On the other hand, the radiative heat transfer phenomenon is considered which is widely used in nuclear and power generating systems. The partial differential equations that govern the flow, and heat and mass transfer are converted into ordinary differential equations by utilizing von Kármán's similarity transformation for rotating disk flows. The velocity, temperature, and concentration profiles and some important physical quantities are examined against important flow parameters. It is observed that the thermal radiation showed an increasing effect on temperature profile and the activation energy enhanced the mass transfer rate. The radial slip increased the volumetric flow rate and reduced the boundary layer thickness. The tangential slip reduced the volumetric flow rate and increased the boundary layer thickness.     

Thermorheological effect on Rayleigh–Bénard magnetoconvection in a biviscous Bingham fluid with rough boundary condition on velocity and Robin boundary condition on temperature

The thermorheological effect on the onset of Rayleigh–Bénard convection in a biviscous Bingham fluid in the presence of a horizontal magnetic field is investigated considering rough boundary conditions on velocity and Robin boundary conditions on temperature. The viscosity of the electrically conducting fluid is assumed to be sensitive to temperature variation. Linear and global nonlinear stability analyses are performed using the Chebyshev pseudospectral method to determine the existence of instability or otherwise. A general interpretation is made from the results to show the effects of the magnetic field and the variable viscosity on the system's stability. The biviscous Bingham parameter and the Chandrasekhar number are shown to have a delay in the onset of convection, while the effect of temperature sensitivity is to advance the onset. It is found that the results of linear and global nonlinear stability are not in agreement, so the region of subcritical instability exists. Also, the results obtained for Rayleigh–Bénard convection agree pretty well with those of Platten and Legros and Siddheshwar et al. for the limiting cases.     

Rheological effects on peristaltic transport of Bingham fluid through an elastic tube with variable fluid properties and porous walls

The peristaltic pumping of non‐Newtonian material configured by a tube is quite interesting phenomenon to examine the behavior of physiological fluids. The present paper investigates the role of variable viscosity and thermal conductivity on the peristaltic mechanism of Bingham fluid in an elastic tube with porous and convective boundary conditions. The long wavelength and small Reynolds number approximation is used to obtain the analytical solutions for velocity, plug flow velocity, streamlines, flow rate, and temperature. The theoretical determination of flux is calculated using the equilibrium condition, and an application to flow through an artery is highlighted by using the tension relation in an elastic tube. It is observed that the rate of flow within the elastic tube declined with variation of variable viscosity. An enhanced temperature distribution near the tube axis has been observed with increment of variable viscosity. An increasing influence of the porous parameter in the bolus size can also be seen from the streamlines plotted.     

Natural convection flow along the vertical wavy cone in case of uniform surface heat flux where viscosity is an exponential function of temperature

The effect of temperature dependent viscosity μ(T), on steady two dimensional natural convection flow along a vertical wavy cone with uniform surface heat flux has been investigated. Viscosity is taken to be an exponential function of temperature. Using the appropriate variables the basic equations are transformed to non-dimensional boundary layer equations and then solved numerically employing implicit finite difference method. The effects of viscosity variation parameter on the velocity profile, temperature profile, velocity vector field, skin friction, average Nusselt number, streamlines and isotherm have been discussed. The results have been shown graphically by utilizing the visualizing software Techplot.     

Effect of Void Fraction and Two-Phase Dynamic Viscosity Models on Prediction of Hydrostatic and Frictional Pressure Drop in Vertical Upward Gas–Liquid Two-Phase Flow

In gas–liquid two-phase flow, the prediction of two-phase density and hence the hydrostatic pressure drop relies on the void fraction and is sensitive to the error in prediction of void fraction. The objectives of this study are to analyze dependence of two-phase density on void fraction and to examine slip ratio and drift flux model-based correlations for their performance in prediction of void fraction and two-phase densities for the two extremes of two-phase flow conditions, that is, bubbly and annular flow or, alternatively, the low and high region of the void fraction. It is shown that the drift flux model-based correlations perform better than the slip ratio model-based correlations in prediction of void fraction and hence the two-phase mixture density. Another objective of this study is to verify performance of different two-phase dynamic viscosity models in prediction of two-phase frictional pressure drop. Fourteen two-phase dynamic viscosity models are assessed for their performance against 616 data points consisting of 10 different pipe diameters in annular flow regime. It is found that none of these two-phase dynamic viscosity models are able to predict the frictional pressure drop in annular flow regime for a range of pipe diameters. The correlations that are successful for small pipe diameters fail for large pipe diameters and vice versa.     

Direct contact heat transfer with phase change: Theoretical expression for instantaneous velocity of a two-phase bubble

An analytical expression for instantaneous velocity of two-phase bubble evaporating through immiscible liquid, has been developed. This expression, predicts very well, the experimental data for n-pentane and furan drops evaporating through high viscosity aqueous glycerol.     

Heat Transfer of Bingham Fluids in an Annular Duct with Viscous Dissipation

ABSTRACT

Analytical expressions for the velocity and temperature profiles in a fully-developed laminar Poiseuille flow through a concentric annular duct of a Bingham fluid with constant wall heat flux at the inner and outer wall, in the presence of viscous dissipation are deduced and presented. It is found that the proportion of the heat generated by viscous dissipation near the outer wall increases with an increase of the dimensionless flow parameter, and a decrease of the duct radius ratio. The Nusselt numbers are first calculated based on a single bulk temperature for the entire duct cross section. The possibility of performing calculations of the relevant parameters discussed in this work is available via the Supplementary Material as an Excel file. Also in this work a new approach is employed, where two different bulk temperatures are used, one for each side of the radial location in the temperature profile whose derivative is zero. With this new approach the Nusselt number behavior is free of either unphysical discontinuities or negative values. As a consequence, the Nusselt number values better reflect the actual heat transfer coefficient at the walls and are more comparable with the heat transfer inside ducts when the temperature profile is symmetric.     

Effect of Fluid Yield Stress on Natural Convection From Horizontal Cylinders in a Square Enclosure

In this study, laminar natural convection heat transfer to Bingham plastic fluids from two differentially heated isothermal cylinders confined in a square enclosure (with isothermal walls) has been investigated numerically. The governing partial differential equations have been solved over the ranges of the dimensionless parameters, namely, Rayleigh number, 10² to 10⁶, Prandtl number, 10 to 100, and Bingham number, 0.01 to 100, for seven locations of inner cylinders as ±0.25, ±0.2, ±0.1 and 0. These values correspond to the range of Grashof number varying from 10 to 10⁵. The detailed flow and temperature fields are visualized in terms of the streamlines and isotherm contours. Further insights are developed by examining the iso-shear rate contours and the yield surfaces delineating the fluid-like and solid-like regions. The corresponding heat transfer results are analyzed in terms of the distribution of the local Nusselt number along the cylinder surface together with its surface averaged value as functions of the Rayleigh number, Prandtl number, Bingham number, and positions of the cylinders. It is found that the average Nusselt number increases with the increasing values of the Rayleigh number and decreases with the increasing Bingham number. For sufficiently large values of the Bingham number, the average Nusselt number reaches its asymptotic value wherein heat transfer takes place solely by conduction. Based on the present numerical results, simple correlations for the prediction of the average Nusselt number and the limiting Bingham number have been developed. Also, a dimensionless criterion denoting the cessation of convection regime is outlined for this configuration.     

An investigation of two-phase flow pressure drop in helical rectangular channel

Numerical simulations have been carried out to evaluate the two-phase frictional pressure drop for air-water two-phase flow in horizontal helical rectangular channels by varying configurations, inlet velocity and inlet sectional liquid holdup. The investigations performed using eight coils, five different inlet velocity and four different inlet sectional liquid holdups. The effects of curvature, torsion, fluid velocity and inlet sectional liquid holdup on two-phase frictional pressure drop have been illustrated. It is found that the two-phase frictional pressure drop relates strongly to the superficial velocities of air or water, and that the curvature and torsion have some effect on the pressure drop for higher Reynolds number flows in large-scale helical rectangular channel; the inlet sectional liquid holdup only increases the magnitude of pressure drop in helical channel and has no effect on the development of pressure drop. The correlation developed predicts the two-phase frictional pressure drop in helical rectangular channel with acceptable statistical accuracy.     

One-dimensional drift-flux model for two-phase flow in a large diameter pipe

In view of the practical importance of the drift-flux model for two-phase-flow analysis in general and in the analysis of nuclear-reactor transients and accidents in particular, the distribution parameter and the drift velocity have been studied for vertical upward two-phase flow in a large diameter pipe. One of the important flow characteristics in a large diameter pipe is a liquid recirculation induced at low mixture volumetric flux. Since the liquid recirculation may affect the liquid velocity profile and promote the formation of cap or slug bubbles, the distribution parameter and the drift velocity in a large diameter pipe can be quite different from those in a small diameter pipe where the liquid recirculation may not be significant. A flow regime at a test section inlet may also affect the liquid recirculation pattern, resulting in the inlet-flow-regime dependent distribution parameter and drift velocity. Based on the above detailed discussions, two types of inlet-flow-regime dependent drift-flux correlations have been developed for two-phase flow in a large diameter pipe at low mixture volumetric flux. A comparison of the newly developed correlations with various data at low mixture volumetric flux shows a satisfactory agreement. As the drift-flux correlations in a large diameter pipe at high mixture volumetric flux, the drift-flux correlations developed by Kataoka-Ishii, and Ishii have been recommended for cap bubbly flow, and churn and annular flows, respectively, based on the comparisons of the correlations with existing experimental data.     

Analytical investigation of polar fluid flow with induced magnetic field in concentric annular region

The influence of microrotational velocity on a fully developed laminar, natural convection flow in vertical concentric annuli in the presence of radial magnetic field between two nonconducting vertical concentric annuli is investigated in the present study. The induced magnetic field is generated due to the motion of an electrically conducting fluid in the annulus; the polar fluid has been considered in the present analysis. Transport equations such as momentum, energy, polar fluid, and induced magnetic field are solved analytically for the isothermal case. The effects of the different pertinent parameters of the present model are obtained and analyzed after verification of present methodology. The effects of the Hartmann number, the gap between two cylinders, and vertex viscosity parameters on velocity profiles, induced magnetic field, induced current density, and microrotational velocity profiles are studied. It is observed that the velocity profile and induced magnetic field decrease due to the vertex viscosity parameter; the Hartmann number accelerates the velocity of the microrotation; the induced current density profile decreases for both the Hartmann number and vertex viscosity parameter. The Hartmann number reduces the magnitude of mass flux and skin frictions at the inner and outer cylinder.     

A numerical study of turbulent flow and conjugate heat transfer in concentric annuli with moving inner rod

A numerical study is conducted to investigate turbulent flow and conjugate heat transfer in a concentric annulus with a heated inner cylinder moving in the streamwise direction. A modified two-equation k-ε model with low Reynolds number treatment near wall is employed to model the Reynolds stress and turbulent thermal field which are based on Boussinesq’s approximation. The governing equations are numerically resolved by means of a hybrid finite analysis method. A uniform inlet flow and thermal conditions are specified to consider the effects of entrance of both solid and fluid regions. For a constant Prandtl number of 6.99 of water flow, calculating results of the time-averaged streamwise velocity, turbulent viscosity and temperature field are obtained for the Reynolds numbers from 1.0 × 10⁴ to 5.0 × 10⁵, rod velocity ratio between 0 and 1.0, and the radius ratio ranging from 0.286 to 0.750. The parametric studies show that the bigger rod speed ratio or the radius ratio is, the temperature is higher within solid rod. For a certain absolute rod speed, temperature profile diminishes at both sides of solid rod and fluid as Reynolds number grows. Numerical results also show that compared with the case of β=0 where solid rod is stationary, for large rod speed ratio the averaged axial velocity and turbulent viscosity profiles have substantial deformations, that is, the gradient of averaged axial velocity and turbulent viscosity near rod surface greatly reduced by the axial movement of solid rod.     

Thermosolutal Marangoni convection of Bingham non-Newtonian fluids within inclined lid-driven enclosures full of porous media

Multiconvection modes together with the entropy generation due to Marangoni effects, movement of the side walls, and double-diffusive convection within lid-driven enclosures filled by a porous medium are examined. The current flow domain is an inclined non-Darcy porous geometry having a top free surface where linear expressions in terms of the temperature and concentration are presented for the surface tension. The dynamic viscosity of the suspension has an exponential profile and the convective boundary conditions are taken into account. The finite volume method in which values of the pressure are computed using the SIMPLE algorithm is applied to solve the governing system. The non-Newtonian Bingham fluids are applied for different governing parameters, such as Grashof number, Reynolds number, Marangoni number, Darcy number, inclination angle of the cavity, Biot number, Bingham number, and geometrical parameters. It is observed that a rise in the Bingham number from 0 to 0.5 causes a decrease in the average Bejan number up to 4.77%. Also, the averaged and mixing temperatures are augmented as the inclination angle is altered, regardless values of the Biot number.     

变倾角管道气力输送阻力特性研究

在变倾角管道气力输送试验装置中,对平均粒径相同（d=2 mm）、密度不同的空心玻璃珠和小米进行了气力输送试验,研究了气固两相流动在不同倾角管路中的阻力特性,着重分析了表观气速变化、管道倾斜角度和输送固气质量比的变化对气固两相管道流动压力损失的影响。结果表明,固气质量比、输送管道的倾斜角度及空气表观气速的变化对输送管道单位长度上的压差都有较大影响;而固相颗粒物性的变化对其结果也有一定的影响。     

内循环多级喷动脱硫塔内的气固两相流动

在试验台上,应用粒子动态分析仪(PDA)对内循环多级喷动脱硫塔内流场进行了试验研究,获得了脱硫塔内颗粒浓度和气固两相速度分布特性.结果表明:多级喷动塔体结构可增加脱硫塔内颗粒内循环,提高塔内颗粒浓度;边壁与中心颗粒数比可达125;并通过定义无因次速度比,说明连续变化的截面提高了气固滑移速度和气液传质系数.研究结论对工程应用有很好的参考价值.     

Refrigerant flow in capillary tube: An assessment of the two-phase viscosity correlations on model prediction

The homogeneous flow model has been widely used to analyse the two-phase flow of refrigerant in a capillary tube of a vapour compression refrigeration system. However, to effectively apply the model, it is necessary to use an appropriate two-phase friction factor with a suitable two-phase viscosity correlation. In this paper, the effects of the various two-phase viscosity correlations on the homogeneous flow model prediction are assessed by comparing with the predicted pressure drops along the capillary tube with measured data.     

Laminar Natural Convection of Bingham Fluids in Square Cross-Sectioned Cylindrical Annular Cavity with Differentially Heated Vertical Walls Subjected to Constant Heat Fluxes

Steady-state numerical simulations have been conducted to investigate natural convection of yield stress fluids obeying Bingham model in square cross-sectioned axisymmetric cylindrical annular enclosure with vertical walls subjected to constant heat fluxes for nominal Rayleigh number range of 10³ to 10⁶, nominal Prandtl number of 10 to 10³ for different values of internal cylinder radius. It is found that the mean Nusselt number on the inner periphery increases (decreases) with increasing nominal Rayleigh (Bingham) number due to strengthening (weakening) of thermal advection. However, the values of the mean Nusselt number on the inner periphery obtained for Bingham fluids are smaller than that obtained for Newtonian fluids for the same set of nominal Rayleigh and Prandtl numbers. The mean Nusselt number normalized by the corresponding value obtained for pure conductive transport increases with increasing internal radius before asymptotically approaching the mean Nusselt number for a square enclosure. This suggests that the ratio of the convective to the conductive transport strengthens with increasing cylinder radius in the cylindrical annular cavity. Detailed physical explanations have been provided for the effects of the aforementioned parameters on the mean Nusselt number on the inner periphery and correlations have been proposed for the mean Nusselt number on the inner periphery for both Newtonian and Bingham fluids.     

Effect of heat transfer on stability and transition characteristics of boundary-layers

Stability and transition problems of two dimensional boundary-layers with heated walls have been studied numerically using the linear stability theory. Incompressible stability equations have been modified to account for the variation of temperature dependent fluid properties across the layer. The equations obtained have been solved with an efficient shoot-search technique. Low speed flows of air and water have been analyzed with a wide range of heat transfer rates. In addition to the mean velocity profile characteristics, variable viscosity and density terms in the stability equations also have considerable influence on the results of the stability and transition analysis.