Combined effects of homogeneous and heterogeneous reactions on peristalsis of Ree-Eyring liquid: Application in hemodynamic flow

This research examines the influence of homogeneous and heterogeneous chemical reactions on the peristaltic flow via an inclined permeable channel. The current investigation emphasizes on modeling the flow of blood in narrow arteries by taking convective and wall properties into account. The Ree-Eyring non-Newtonian model is used to govern the fluid flow due to its significance in understanding the behavior of dilatant, pseudoplastic, and viscous liquids. The variation in variable viscosity and thermal conductivity is considered for analyzing the complex rheological behavior of blood. The similarity transformations are used in the process of nondimensionalization. The series solution procedure is adopted to solve the governing nonlinear differential equations. The expressions for velocity, temperature, concentration, and trapped bolus are obtained. The computational results are analyzed with the help of graphs for shear thickening, shear thinning, and Newtonian fluid models. One of the significant findings of the current model is that an introduction of variable liquid properties improves the temperature and velocity profiles for Newtonian and pseudoplastic fluid models. Compared with the other theoretical models developed, the rheological and flow properties of various biological fluids can be derived from the model used in the present investigation.     

Laminar Flow and Heat Transfer to a Non-Newtonian Fluid in an Entrance Region of a Square Duct with Prescribed Constant Axial Wall Heat Flux

Abstract

Forced-convection heat transfer information as a function of the pertinent nondimensional numbers is obtained numerically for laminar incompressible non-Newtonian fluid flow in the entrance region of a square duct with simultaneously developing temperature and velocity profiles for constant axial wall heat flux with uniform peripheral wall temperature. The power-law model characterizes the non-Newtonian behavior.

Finite-difference representations are developed for the equations of the mathematical model, and numerical solutions are obtained assuming uniform inlet velocity and temperature distributions. Results are presented for local and mean Nusselt numbers as functions of the Graetz number and the Prandtl number in the entrance region. Comparisons are made with previous analytical work for Newtonian fluids. The results show a strong effect of the Prandtl number on the Nusselt numbers with fully developed and uniform velocity profiles representing the lower and upper limits, respectively. The results provide a new insight into the true three-dimensional character of the pseudoplastlc fluid flow in the entrance region of a square duct and are accurate.     

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.     

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.     

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.     

Peristaltic Transport of a Herschel–Bulkley Fluid in an Elastic Tube

In this paper, we investigate the peristaltic transport of a non‐Newtonian viscous fluid in an elastic tube. The governing equations are solved using the assumptions of long wavelength and low Reynolds number approximations. The constitution of blood has a non‐Newtonian fluid model and it demands the yield stress fluid model: The blood transport in small blood vessels is done under peristalsis. Among the available yield stress fluid models for blood flow, the non‐Newtonian Herschel–Bulkley fluid is preferred (because Bingham, power‐law and Newtonian models can be obtained as its special cases). The Herschel–Bulkley model has two parameters namely the yield stress and the power‐law index. The expressions for velocity, plug flow velocity, wall shear stress, and the flow rate are derived. The flux is determined as a function of inlet, outlet, external pressures, yield stress, amplitude ratio, and the elastic property of the tube. Further when the power‐law index n = 1 and the yield stress and in the absence of peristalsis, our results agree with Rubinow and Keller [J. Theor. Biol. 35 , 299 (1972)]. Furthermore, it is observed that, the yield stress, peristaltic wave, and the elastic parameters have strong effects on the flux of the non‐Newtonian fluid flow. Effects of various wave forms (namely, sinusoidal, trapezoidal and square) on the flow are discussed. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study on the non‐Newtonian fluid phenomena, especially the shear‐thinning phenomena. Shear thinning reduces the wall shear stress.     

LAMINAR IMPINGING JET HEAT TRANSFER WITH A PURELY VISCOUS INELASTIC FLUID

Laminar impinging flow heat transfer is considered with a purely viscous inelastic fluid. The rheology of the fluid is modeled using a strain rate dependent viscosity coupled with asymptotic Newtonian behavior in the zero shear limit. The velocity and temperature fields are computed numerically for a confined laminar axisymmetric impinging flow. Important features of the non-Newtonian developing flow field are described and contrasted with the Newtonian situation. It is demonstrated that very small departures from Newtonian rheology lead to qualitative changes in the Nusselt number distribution along the impinging surface. In particular, a mildly shear thinning fluid displays a pronounced off-stagnation point heat transfer maxima, a feature that is not observed with a Newtonian fluid. Hence, Newtonian fluid approximations cannot adequately describe experimental heat transfer measurements in such situations even though they may be deemed acceptable in terms of describing the velocity field in the incoming nozzle. Numerical results are presented to analyze the effect of the dimensionless nozzle-to-plate distance, the rheological parameters, and the Reynolds and Prandtl numbers on the magnitude of the off-stagnation point peak heat transfer rate. The influence of the rheology of the fluid is particularly significant at low nozzle-to-plate distances since the mean strain rate in the flow field increases as the nozzle-to-plate distance is reduced. The numerical heat transfer results are interpreted in the context of the developing flow field.     

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.     

Forced convection of non-Newtonian fluids on a heated flat plate

Forced convective heat transfer due to a non-Newtonian fluid flowing past a flat plate has been investigated using a modified power-law viscosity model. This model does not contain physically unrealistic limits; consequently, no irremovable singularities are introduced into boundary-layer formulations for such fluids. Therefore, the boundary-layer equations can be solved by (numerically) marching downstream from the leading edge as is common for boundary layers involving Newtonian fluids. For shear-thinning and shear-thickening fluids, non-Newtonian effects are illustrated via velocity and temperature distributions, shear stresses, and heat transfer rates. The most significant effects occur near the leading edge, gradually tailing off far downstream where the variation of shear stresses becomes smaller.     

Analytical solution for Newtonian–Bingham plastic two-phase pressure driven stratified flow through the circular ducts

For steady state, stratified, laminar, fully developed two-phase flow which one of them is Newtonian and the other one is Bingham plastic, the motion equations in horizontal pipe with appropriate boundary conditions have been solved analytically. Pressure drop, velocity distribution and location of plug region related to Bingham plastic fluid have been reported. The results show that the non-Newtonian rheological properties have negligible effects on two-phase velocity profile and consequently on pressure gradient in small viscosity ratio of two fluids. With promotion of viscosity ratio, the influence of yield stress on two-phase velocity profile is more considerable.     

Analysis of dissipative non-Newtonian magnetic polymer flow from a curved stretching surface with slip and radiative effects

The convective–radiative magnetohydrodynamic non-Newtonian second-grade fluid boundary layer flow from a curved stretching surface has been scrutinized in the present study. The Reiner–Rivlin second-grade viscoelastic model is deployed which provides a good approximation for certain magnetic polymers. High temperature invokes the presence of radiative heat transfer, which is simulated with the Rosseland diffusion approximation. Viscous dissipation and Joule heating are also featured in the model and hydrodynamic (velocity) slip at the wall is also incorporated in the boundary conditions. The emerging nonlinear coupled dimensionless transport equations are solved with a Runge–Kutta method and a shooting numerical scheme. The influence of emerging multiphysical flow parameters on the dimensionless profiles is examined with the help of plots for comparative analysis of both non-Newtonian fluid and Newtonian fluid. The numerical solutions are validated for special cases with existing works. The velocity declines for a higher magnetic field, whereas the reverse trend is noted for the temperature function. The augmentation in the thermal field is noted with increments in radiation parameters. Furthermore, the fluid temperature of the second-grade fluid is higher with increasing Brinkmann number. The wall slip induces deceleration. Contour plots for streamlines and isotherms are also visualized and analyzed.     

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.     

Estimating Heat Transfer Coefficients and Friction Factors in Non-Newtonian Flows between Parallel Plates

A simplified method, successfully tested previously for flow in circular pipes, is used in this work to estimate the friction factor and Nusselt number in fully-developed laminar flow between parallel plates of non-Newtonian fluids. Both constant wall temperature and constant wall heat flux cases are considered. The methodology was tested using several constitutive equations, including generalized Newtonian fluids, such as the Herschel–Bulkley, Bingham, Casson, and Carreau–Yasuda models, and also the simplified Phan-Thien–Tanner viscoelastic model. The error of the approximate methodology was found to be small, below 3.4%, except for the fluids with yield stress for which the maximum error increased to 8.4% for the cases analyzed, which cover a wide range of shear viscosity curves.     

Second-order slip and Newtonian cooling impact on unsteady mixed convective radiative chemically reacting fluid with Hall current and cross-diffusion over a stretching sheet

The aim of the current study is to develop a mathematical model for unsteady mixed convective radiative chemically reactive fluid flow with Hall current, cross-diffusion, Newtonian cooling impacts and boundary conditions are influenced by second-order slip velocity. Effectively a viscous formulation combining different novel effects model is deployed. The basic Navier–Stokes derived flow equations are transformed into dimensionless form via particular similarity transformations for which numerical simulations utilize the finite element method. The numerical results for velocity components, temperature, and concentration on various flow parameters are sketched. For validation of the present results a comparison with previously published studies are conducted for some limiting conditions and reveals an excellent accuracy. Engineering items of interest like shear stresses, Nusselt number, and Sherwood number are computed and discussed extensively with the foremost parameters. Our analysis explores the fact that the physical parameters have a substantial influence upon boundary layer profiles.     

Computational Study of Convective Transport in a Coating Applicator for a Non-Newtonian Fluid

Convective transport in an optical fiber coating applicator and die system has been simulated for a non-Newtonian fluid. Low-density polyethylene (LDPE) is employed for the numerical analysis, though ultraviolet (UV) curable acrylates are more commonly used, because of a lack of property information for acrylates and similar behavior of these two materials. The equations governing fluid flow and heat transfer are transformed to obtain flow in a cylindrical domain. A numerical scheme similar to the SIMPLE algorithm is developed and employed with a nonuniform grid. Variable fluid properties are employed because of the strong dependence of these on the temperature. In contrast to the isothermal case, streamlines for the non-Newtonian fluid are found to be quite different for various fiber speeds. The temperature level in the applicator is much higher for the Newtonian case, due to the larger fluid viscosity and associated viscous dissipation. The shear near the fiber is found to be lower for the Newtonian fluid. As expected, the effects become larger with increasing fiber speed. A fairly high temperature rise is observed in the die, regardless of fiber speed. This study focuses on the computational modeling of non-Newtonian effects during the coating process, and several interesting and important features, as compared to the Newtonian case, are observed.     

Viscous dissipation effects on the asymptotic behaviour of laminar forced convection for Bingham plastics in circular ducts

The present study concentrates on the effects of viscous dissipation and the yield shear stress on the asymptotic behaviour of the laminar forced convection in a circular duct for a Bingham fluid. It is supposed that the physical properties are constant and the axial conduction is negligible. The asymptotic temperature profile and the asymptotic Nusselt number are determined for various axial distributions of wall heat flux which yield a thermally developed region. It is shown that if the asymptotic value of wall heat flux distribution is vanishes, the asymptotic value of the Nusselt number is zero. The case of the asymptotic wall heat flux distribution non-vanishing giving a value of the Nusselt number dependent on the Brinkman number and on the dimensionless radius of the plug flow region was also analysed. For an infinite asymptotic value of wall heat flux distributions, the asymptotic value of the Nusselt number depends on the dimensionless radius of the plug flow region and on the dimensionless parameter which depends on the asymptotic behaviour of the wall heat flux. The condition of uniform wall temperature and convection with an external isothermal fluid were also considered. The comparison with other existing solutions in the literature in the Newtonian case is analysed.     

Non-Newtonian blood flow with magnetic nanoparticles in a W-shaped stenosed arterial segment: A numerical study

Flow of blood, infused with magnetic nanoparticles, in a W-shaped stenosed human arterial segment is studied numerically using a realistic non-Newtonian blood rheology model. It is observed that the Newtonian model predicts less time to reach a steady state than the non-Newtonian blood rheology model. An increased drug retention time at the target site with an increase in nanoparticle concentration is predicted. Detailed simulations further reveal that the skin friction coefficient does not increase significantly with the increase in nanoparticle concentration. Hence, it is anticipated from our study that the infusion of drug-carrying nanoparticles in blood flow does not excessively enhance wall shear stress that may lead to arterial wall damage. An overall increase in heat transfer rates and wall shear stress at the stenosed section is seen with an increase in Reynolds number. The present study provides valuable information for designing computer-assisted drug delivery systems.     

Heat and mass transfer in MHD boundary layer flow of a second-grade fluid past an infinite vertical permeable surface

Heat and mass transfer of non-Newtonian fluids is increasingly being studied by researchers due to its applications in many branches of science and engineering, such as metallurgical processes, polymer extrusion, glass blowing, crystal growing, and so forth. The present work is mainly concerned with the unsteady laminar magnetohydrodynamic flow of a heat-generating or absorbing second-grade fluid past an infinite vertical porous plate. The nondimensional governing equations are solved for the best analytical solution. Results for various flow characteristics are presented through graphs and tables delineating the effect of various parameters characterizing the flow. For engineering interest, the shear stresses, Nusselt number, and Sherwood number are computed and exchanged of views with reference to the important parameters. Our analysis explored that the influences of a chemical reaction and fluid oscillations reduced the concentration distribution in the entire liquid region. The rotation effect decreases the shear stress, whereas it is augmented through an increase in the permeability of porous medium and second-grade fluid parameters' impact.     

Entropy Generation Due to the Flow of a Non-Newtonian Fluid with Variable Viscosity in a Circular Pipe

The non-Newtonian fluid can be considered as a third-grade fluid with variable viscosity. In this case, the rate of fluid strain can be formulated using the third-grade fluid analogy. In the present study, entropy generation due to non-Newtonian fluid flow in a pipe is investigated. A third-grade fluid with variable viscosity is accommodated in the analysis. Analytical solutions for velocity and temperature distributions are presented, and an entropy generation number is computed for different non-Newtonian parameters, viscosity parameters, and Brinkman numbers. It is found that increasing the non-Newtonian parameter lowers the entropy generation number. This is more pronounced in the region close to the pipe wall. Increasing the viscosity parameter and Brinkman number enhances the entropy generation number, particularly in the vicinity of the pipe wall.     

MHD Eyring–Powell nanofluid past over an unsteady exponentially stretching surface with entropy generation and thermal radiation

This study's primary objective is to analyze the entropy generation in an unsteady magnetohydrodynamics (MHD) Eyring–Powell nanofluid flow. A surface that stretched out exponentially induced flow. The influences of thermal radiation, thermophoresis, and Brownian motion are also taken into consideration. The mathematical formulation for the transport of mass, momentum, and heat described by a set of partial differential equation is used, which is then interpreted by embracing the homotopy analysis method and with a fourth-order precision program (bvp4c). Graphical results display the consequences of numerous parameters on velocity, temperature, concentration, and entropy generation. Moreover, escalating amounts of the magnetic parameter, thermal radiation parameter, Reynolds number, and Brinkman number improve the entropy profile of the nanofluid. The rate of heat flux and the mass flux conspicuously improves for non-Newtonian fluid as compared to Newtonian fluid.