Mathematical modelling of couple stresses on fluid flow in constricted tapered artery in presence of slip velocity-effects of catheter

This paper explores the mathematical model for couple stress fluid flow through an annular region. The above model is used for studying the blood flow be-tween the clogged （stenotic） artery and the catheter. The asymmetric nature of the stenosis is considered. The closed form expressions for the physiological parameters such as impedance and shear stress at the wall are obtained. The effects of various geomet-ric parameters and the parameters arising out of the fluid considered are discussed by considering the slip velocity and tapering angle. The study of the above model is very significant as it has direct applications in the treatment of cardiovascular diseases.

Couple stress and Darcy Forchheimer hybrid nanofluid flow on a vertical plate by means of double diffusion Cattaneo-Christov analysis

A three-dimensional Darcy Forchheimer mixed convective flow of a couple stress hybrid nanofluid flow through a vertical plate by means of the double diffusion Cattaneo-Christov model is presented in this study.The influence of highorder velocity slip flow,as well as a passive and active control,is also considered.The motive of the research is to develop a computational model,using cobalt ferrite(Co Fe_(2)O_(4))and copper(Cu)nanoparticles(NPs)in the carrier fluid water,to magnify the energy and mass communication rate and boost the efficiency and performance of thermal energy conduction for a variety of commercial and biological purposes.The proposed model becomes more significant,with an additional effect of non-Fick's mass flux and Fourier's heat model to report the energy and mass passage rate.The results are obtained through the computational strategy parametric continuation method.The figures are plotted to reveal the physical sketch of the obtained solution,while the statistical assessment has been evaluated through tables.It has been observed that the dispersion of Cu and Co Fe_(2)O_(4)NPs to the base fluid significantly enhances the velocity and thermal conductivity of water,which is the most remarkable property of these NPs from the industrial point of view.

Numerical Solution for Thermal Elastohydrodynamic Lubrication of Line Contact with Couple Stress Fluid as Lubricant

In this paper,the detailed analysis of the influence of thermal and non-Newtonian aspects of lubricant(couple stress fluid)on EHL line contact as a function of slide-roll ratio is presented.The novel low complexity FAS(full approximation scheme),of the multigrid scheme,with Jacobi dipole and Gauss Seidel relaxation is used for the solution of coupled equations viz.modified Reynolds equation,film thickness equation and energy equation satisfying appropriate boundary conditions.The analysis reveals the combined influence of non-Newtonian,thermal and slide-roll ratio(of bearing moving with different speeds)on pressure,film thickness and pressure spike covering a wide range of physical parameters of interest.Results show that pressure spike is strongly influenced by thermal,slide-roll ratio and non-Newtonian character of lubricant with negligible effect on the overall pressure distribution.Also,the minimum film thickness is slightly altered and it increases with the increase in the couple stress parameter.These findings confirm the importance of non-Newtonian and thermal effects in the study of EHL.

Mathematical Model and Experiment Validation of Fluid Torque by Shear Stress under Influence of Fluid Temperature in Hydro-viscous Clutch

The current design of hydro-viscous clutch（HVC） in tracked vehicle fan transmission mainly focuses on high-speed and high power. However, the fluid torque under the influence of fluid temperature can not be predicted accurately by conventional mathematical model or experimental research. In order to validate the fluid torque of HVC by taking the viscosity-temperature characteristic of fluid into account, the test rig is designed. The outlet oil temperature is measured and fitted with different rotation speed, oil film thickness, oil flow rate, and inlet oil temperature. Meanwhile, the film torque can be obtained. Based on Navier-Stokes equations and the continuity equation, the mathematical model of fluid torque is proposed in cylindrical coordinate. Iterative method is employed to solve the equations. The radial and tangential speed distribution, radial pressure distribution and theoretical flow rate are determined and analyzed. The models of equivalent radius and fluid torque of friction pairs are introduced. The experimental and theoretical results indicate that tangential speed distribution is mainly determined by the relative rotating speed between the friction plate and the separator disc. However, the radial speed distribution and pressure distribution are dominated by pressure difference at the lower rotating speed. The oil film fills the clearance and the film torque increases with increasing rotating speed. However, when the speed reaches a certain value, the centrifugal force will play an important role on the fluid distribution. The pressure is negative at the outer radius when inlet flow rate is less than theoretical flow, so the film starts to shrink which decreases the film torque sharply. The theoretical fluid torque has good agreement with the experimental data. This research proposes a new fluid torque mathematical model which may predict the film torque under the influence of temperature more accurately.

Stagnation-point flow of couple stress fluid with melting heat transfer

Melting heat transfer in the boundary layer flow of a couple stress fluid over a stretching surface is investigated. The developed differential equations are solved for homotopic solutions. It is observed that the velocity and the boundary layer thickness are decreasing functions of the couple stress fluid parameter. However, the temperature and surface heat transfer increase when the values of the couple stress fluid parameter increase. The velocity and temperature fields increase with an increase in the melting process of the stretching sheet.

Peristaltic flow of couple stress fluid through uniform porous medium

Investigation concerning peristaltic motion of couple stress fluid is made. An incompressible couple stress fluid occupies the porous medium. Mathematical anal- ysis is presented through large wavelength and low Reynolds number. Exact analytical expressions of axial velocity, volume flow rate, pressure gradient, and stream function are calculated as a function of couple stress parameter. The essential feature of the analysis is a full description of influence of couple stress parameter and permeability parameter on the pressure, frictional force, mechanical efficiency, and trapping.

Transient analysis of diffusive chemical reactive species for couple stress fluid flow over vertical cylinder

The unsteady natural convective couple stress fluid flow over a semi-infinite vertical cylinder is analyzed for the homogeneous first-order chemical reaction effect. The couple stress fluid flow model introduces the length dependent effect based on the material constant and dynamic viscosity. Also, it introduces the biharmonic operator in the Navier-Stokes equations, which is absent in the case of Newtonian fluids. The solution to the time-dependent non-linear and coupled governing equations is carried out with an unconditionally stable Crank-Nicolson type of numerical schemes. Numerical results for the transient flow variables, the average wall shear stress, the Nusselt number, and the Sherwood number are shown graphically for both generative and destructive reactions. The time to reach the temporal maximum increases as the reaction constant K increases. The average values of the wall shear stress and the heat transfer rate decrease as K increases, while increase with the increase in the Sherwood number.

A fluid flow model in the lacunar-canalicular system under the pressure gradient and electrical field driven loads

The lacunar-canalicular system(LCS)is acknowledged to directly participate in bone tissue remodeling.The fluid flow in the LCS is synergic driven by the pressure gradient and electric field loads due to the electro-mechanical properties of bone.In this paper,an idealized annulus Maxwell fluid flow model in bone canaliculus is established,and the analytical solutions of the fluid velocity,the fluid shear stress,and the fluid flow rate are obtained.The results of the fluid flow under pressure gradient driven(PGD),electric field driven(EFD),and pressure-electricity synergic driven(P-ESD)patterns are compared and discussed.The effects of the diameter of canaliculi and osteocyte processes are evaluated.The results show that the P-ESD pattern can combine the regulatory advantages of single PGD and EFD patterns,and the osteocyte process surface can feel a relatively uniform shear stress distribution.As the bone canalicular inner radius increases,the produced shear stress under the PGD or P-ESD pattern increases slightly but changes little under the EFD pattern.The increase in the viscosity makes the flow slow down but does not affect the fluid shear stress(FSS)on the canalicular inner wall and osteocyte process surface.The increase in the high-valent ions does not affect the flow velocity and the flow rate,but the FSS on the canalicular inner wall and osteocyte process surface increases linearly.In this study,the results show that the shear stress sensed by the osteocyte process under the P-ESD pattern can be regulated by changing the pressure gradient and the intensity of electric field,as well as the parameters of the annulus fluid and the canaliculus size,which is helpful for the osteocyte mechanical responses.The established model provides a basis for the study of the mechanisms of electro-mechanical signals stimulating bone tissue(cells)growth.

Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders

The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0＋ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles.

Natural convection flow of a couple stress fluid between two vertical parallel plates with Hall and ion-slip effects

The Hall and ion-slip effects on fully developed electrically conducting couple stress fluid flow between vertical parallel plates in the presence of a temperature dependent heat source are investigated. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. The resulting equations are then solved using the homotopy analysis method （HAM）. The effects of the magnetic parameter, Hall parameter, ion-slip parameter and couple stress fluid parameter on velocity and temperature are discussed and shown graphically

Interstitial fluid flow:simulation of mechanical environment of cells in the interosseous membrane

In vitro experiments have shown that subtle fluid flow environment plays a significant role in living biological tissues, while there is no in vivo practical dynamical measurement of the interstitial fluid flow velocity. On the basis of a new finding that capillaries and collagen fibrils in the interosseous membrane form a parallel array, we set up a porous media model simulating the flow field with FLUENT software, studied the shear stress on interstitial cells＇ surface due to the interstitial fluid flow, and analyzed the effect of flow on protein space distribution around the ceils. The numerical simulation results show that the parallel nature of capillaries could lead to directional interstitial fluid flow in the direction of capillaries. Interstitial fluid flow would induce shear stress on the membrane of interstitial cells, up to 30 Pa or so, which reaches or exceeds the threshold values of cells＇ biological response observed in vitro. Interstitial fluid flow would induce nonuniform spacial distribution of secretion protein of mast cells. Shear tress on cells could be affected by capillary parameters such as the distance between the adjacent capillaries, blood pressure and the permeability coefficient of capillary＇s wall. The interstitial pressure and the interstitial porosity could also affect the shear stress on cells. In conclusion, numerical simulation provides an effective way for in vivo dynamic interstitial velocity research, helps to set up the vivid subtle interstitial flow environment of cells, and is beneficial to understanding the physiological functions of interstitial fluid flow.

NONLINEAR NUMERICAL ANALYSIS OF A FLEXIBLE ROTOR EQUIPPED WITH SQUEEZE COUPLE STRESS FLUID FILM JOURNAL BEARINGS

This study performs a dynamic analysis of a rotor supported by two squeeze couple stress fluid film journal bearings with nonlinear suspension. The numerical results show that the stability of the system varies with the non-dimensional speed ratios and the dimensionless parameter l＊. It is found that the system is more stable with higher dimensionless parameter l＊. Thus it can conclude that the rotor-bearing system lubricated with the couple stress fluid is more stable than that with the conventional Newtonian fluid. The modeling results thus obtained by using the method proposed in this paper can be used to predict the stability of the rotor-bearing system and the undesirable behavior of the rotor and bearing center can be avoided.

Flow of couple stress fluid with variable thermal conductivity

The steady flow and heat transfer of a couple stress fluid due to an inclined stretching cylinder are analyzed. The thermal conductivity is assumed to be temperature dependent. The governing equations for the flow and heat transfer are transformed into ordinary differential equations. Series solutions of the resulting problem are computed. The effects of various interested parameters, e.g., the couple stress parameter, the angle of inclination, the mixed convection parameter, the Prandtl number, the Reynolds number, the radiation parameter, and the variable thermal conductivity parameter, are illustrated. The skin friction coefficient and the local Nusselt number are computed and analyzed. It is observed that the heat transfer rate at the surface increases while the velocity and the shear stress decrease when the couple stress parameter and the Reynolds number increase. The temperature increases when the Reynolds number increases.

Heat transfer analysis of MHD and electroosmotic flow of non-Newtonian fluid in a rotating microfluidic channel:an exact solution

The heat transfer of the combined magnetohydrodynamic(MHD)and electroosmotic flow(EOF)of non-Newtonian fluid in a rotating microchannel is analyzed.A couple stress fluid model is scrutinized to simulate the rheological characteristics of the fluid.The exact solution for the energy transport equation is achieved.Subsequently,this solution is utilized to obtain the flow velocity and volume flow rates within the flow domain under appropriate boundary conditions.The obtained analytical solution results are compared with the previous data in the literature,and good agreement is obtained.A detailed parametric study of the effects of several factors,e.g.,the rotational Reynolds number,the Joule heating parameter,the couple stress parameter,the Hartmann number,and the buoyancy parameter,on the flow velocities and temperature is explored.It is unveiled that the elevation in a couple stress parameter enhances the EOF velocity in the axial direction.

The Analysis of Stability of Bingham Fluid Flowing Down an Inclined Plane

In this paper, the stability problem of Bingham fluids flowing down an inclinedplane is studied with respect to two dimensional disturbances. The crilical Reynolodsnumber is given in ihe case of long waves, and the effect of yield stress on stability isanalysed.

THE ANALYSIS OF STABILITY OF BINGHAM FLUID FLOWIGN DOWN AN INCLINED PLANE

In this paper the stability problem of Bingham flowing down an inclinedplane is studied with respect to two dimensional disturbances, The critical Reynolodsnumber is given in the. case. of long wayes and the effect of yield stress on stability isanalysed.

Exact solutions for the flow of second grade fluid in annulus between torsionally oscillating cylinders

The velocity field and the associated shear stress corresponding to the torsional oscillatory flow of a second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. At time t = 0, the fluid and both the cylinders are at rest and at t = 0 ＋ , cylinders suddenly begin to oscillate around their common axis in a simple harmonic way having angular frequencies ω 1 and ω 2 . The obtained solutions satisfy the governing differential equation and all imposed initial and boundary conditions. The solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for Newtonian fluid are also obtained as limiting cases of our general solutions.

The Effects of Post-Stenotic Dilatations on the Flow of Couple Stress Fluid through Stenosed Arteries

The flow of incompressible couple stress fluid in a circular tube with stenosis and dilatations has been investigated. The stenosis was assumed to be axially symmetric and mild. The flow equations have been linearized and the expressions for the resistance to the flow, velocity, pressure drop, wall shear stress have been derived. The effects of various parameters on these flow variables have been investigated. It is found that the resistance to the flow and pressure drop increase with height of the stenosis and decrease with post stenotic dilatation. Pressure drop decreases with couple stress fluid parameter for both stenosis and post stenotic dilatation. Further, the wall shear stress increases with height of the stenosis and couple stress parameter but decreases with post stenotic dilatation and couple stress fluid parameter.

Single-cell transcriptomic analysis reveals transcript enrichment in oxidative phosphorylation,fluid sheer stress,and inflammatory pathways in obesity-related glomerulopathy

Obesity-related glomerulopathy(ORG)is an independent risk factor for chronic kid-ney disease and even progression to end-stage renal disease.Efforts have been undertaken to elucidate the mechanisms underlying the development of ORG and substantial advances have been made in the treatment of ORG,but relatively little is known about cell-specific changes in gene expression.To define the transcriptomic landscape at single-cell resolution,we analyzed kidney samples from four patients with ORG and three obese control subjects without kidney disease using single-cell RNA sequencing.We report for the first time that immune cells,including T cells and B cells,are decreased in ORG patients.Further analysis indicated that SPP1 was significantly up-regulated in T cells and B cells.This gene is related to inflammation and cell proliferation.Analysis of differential gene expression in glomerular cells(endothelial cells,mesangial cells,and podocytes)showed that these cell types were mainly enriched in genes related to oxidative phosphorylation,cell adhesion,thermogenesis,and inflammatory pathways(PI3K-Akt signaling,MAPK signaling).Furthermore,we found that the podocytes of ORG patients were enriched in genes related to the fluid shear stress pathway.Moreover,an evaluation of cell-cell communications revealed that there were interactions between glomerular parietal epithelial cells and other cells in ORG patients,with major interactions between parietal epithelial cells and podocytes.Altogether,our identification of molecular events,cell types,and differentially expressed genes may facilitate the development of new preventive or therapeutic approaches for ORG.

Approximate Solution of Oil Film Load-carrying Capacity of Turbulent Journal Bearing with Couple Stress Flow

The instability of the rotor dynamic system supported by oil journal bearing is encountered frequently, such as the half speed whirl of the rotor, which is caused by oil film lubricant with nonlinearity. Currently, more attention is paid to the physical characteristics of oil film due to an oil-lubricated journal bearing being the important supporting component of the bearing-rotor systems and its nonlinear nature. In order to analyze the lubrication characteristics of journal bearings efficiently and save computational c[~brts, an approximate solution of nonlinear oil film forces of a finite length turbulent journal bearing with couple stress flow is proposed based on Sommerfeld and Ocvirk numbers. Reynolds equation in lubrication of a finite length turbulent .journal bearing is solved based on multi-parametric principle. Load-carrying capacity of nonlinear oil film is obtained, and the results obtained by different methods are compared. The validation of the proposed method is verified, meanwhile, the relationships of load-carrying capacity versus eccentricity ratio and width-to-diameter ratio under turbulent and couple stress working conditions are analyzed. The numerical results show that both couple stress flow and eccentricity ratio have obvious influence on oil film pressure distribution, and the proposed method approximates the load-carrying capacity of turbulent journal bearings efficiently with various width-to-diameter ratios. This research proposes an approximate solution of oil film load-carrying capacity of turbulent journal bearings with different width-to-diameter ratios, whicb are suitable for high eccentricity ratios and heavy loads.