Values Of Power-law Index Research Articles

On behavioral response of ciliated cervical canal on the development of electroosmotic forces in spermatic fluid

The goal of this research is to conduct a theoretical investigation about the effect of the electroosmotic forces on the swimming of sperms throughout the cervical canal. To imitate male semen with self-propulsive spermatozoa, a hyperbolic tangent fluid is used as the base liquid. Swimming sperms move inside a ciliated cervical canal and peristalsis occurs due to the ciliated walls. The perturbation method is used to solve the controlling partial differential set of equations analytically. Due to selfpropulsion of swimmers and long wavelength assumption, a creeping flow protocol is used throughout the stream. The stream pattern, velocity distribution, and pressure gradient (above and below the swimming sheet) solutions are produced and displayed with the relevant parameters. The outcomes of this manuscript show that the rheological parameters of hyperbolic tangent fluid are more appropriate to simulate and discuss the motility of cervical fluid. Moreover, the motility of mucus velocity is more applicable for small values of power law index n at the upper swimming sheet of propulsive spermatozoa. In addition, the mucus velocity increases in both region (upper and lower region of swimming sheet) with an increase of the electroosmotic parameter me and Helmholtz-Smoluchowski velocity UHS. The present analysis provides a mathematical assessment to the swimmers’ interaction through the ciliated genital tract where the embryo is affected by the interaction of ciliary activity.

Study of Non-Newtonian biomagnetic blood flow in a stenosed bifurcated artery having elastic walls

Fluid structure interaction (FSI) gained attention of researchers and scientist due to its applications in science fields like biomedical engineering, mechanical engineering etc. One of the major application in FSI is to study elastic wall behavior of stenotic arteries. In this paper we discussed an incompressible Non-Newtonian blood flow analysis in an elastic bifurcated artery. A magnetic field is applied along x direction. For coupling of the problem an Arbitrary Lagrangian–Eulerian formulation is used by two-way fluid structure interaction. To discretize the problem, we employed P_{2} P_{1} finite element technique to approximate the velocity, displacement and pressure and then linearized system of equations is solved using Newton iteration method. Analysis is carried out for power law index, Reynolds number and Hartmann number. Hemodynamic effects on elastic walls, stenotic artery and bifurcated region are evaluated by using velocity profile, pressure and loads on the walls. Study shows there is significant increase in wall shear stresses with an increase in Power law index and Hartmann number. While as expected increase in Reynolds number decreases the wall shear stresses. Also load on the upper wall is calculated against Hartmann number for different values of power law index. Results show load increases as the Hartmann number and power law index increases. From hemodynamic point of view, the load on the walls is minimum for shear thinning case but when power law index increased i.e. for shear thickening case load on the walls increased.

Two dimensional unsteady flow past a square cylinder: Influence of proximal plane wall and power-law index

A numerical analysis using Ansys Fluent has been done to investigate the flow physics involved in both Newtonian and Power-law (shear-thinning) fluid flow over a square cylinder, placed near a wall with altered gap-to-side (G/a) ratios (where G represents the gap between the cylinder and the plane wall and a represents side of the square cylinder). At a constant Reynolds number, Re = 150, numerical calculations for unsteady, incompressible Navier-Stroke (N-S) equation with varying viscosity is carried out by using second-order upwind momentum and least square cell based pressure solver. It is found that for small G/a ratio shear-thinning fluid exhibits vortex shedding which was absent for Newtonian fluid. G/a ratio and power-law index have a strong influence on the coefficient of lift and coefficient of drag (CL and CD respectively). With the increase in gap-ratio, CD decreases and CL increases at a constant value of power-law (n) index. Also, CL increases and CD reduces with a decrease in n at a constant value of G/a. Detailed observation of instantaneous and mean vorticity and streamlines, coefficient of lift and drag, mean pressure distribution over the cylinder and the plane wall and recirculation length have been presented.

Effects of force and moment actuation in active two dimensional VIV control of an elastic circular cylinder in power-law fluid flow

The coupled in-line/crosswise (2-DOF) Vortex-Induced Vibration (VIV) control of a flexibly-supported impenetrable circular cylinder immersed in uniform 2D laminar cross-flow of incompressible non-Newtonian power-law fluids is numerically investigated. Two effective active closed-loop control strategies are separately applied and compared in a real-time collaborative simulation framework that interactively connects the Fluent CFD solver with Matlab/Simulink. Numerical simulations reveal the important effects of power-law rheology and controller configuration on the key cylinder response/aerodynamic parameters and flow structure for a wide range of power-law index parameters (0.4≤n≤1.8). In the absence of the control system, the boundary layer thickness, the attached wake size/strength, and the length/thickness of the associated “shear stretching layer” (vortex shedding frequency) are found to noticeably increase (decrease) with increasing the power law index parameter. As the value of power-law index is largely increased, there is a notable shift of the synchronization (lock-in) region into the higher Reynolds number range besides its marked contraction which can passively complement the cylinder VIV control problem in the highly viscous shear-thickening fluid. When the active control system becomes operative, the superior performance and efficiency of the moment-based controller in effective and rapid mitigation of cylinder VIV and weakening of the vortex intensities through a desynchronization type of action with minimum actuator power requirements is demonstrated.

Thermal and Entropy generation analysis of magnetohydrodynamic tangent hyperbolic slip flow towards a stretching sheet

This article examined the effects of boundary layer flow and heat transport of a two-dimensional incompressible magnetohydrodynamic tangent hyperbolic fluid under slip boundary conditions and variable thermal conductivity. The entropy generation model is also analysed for the said fluid. Non-similarity transformations transformed the governing equations of the fluid and entropy generation model into dimensionless form. Maple software is used to solve the transformed equations numerically. Effects of different dimensionless parameters on entropy generation rate, Bejan number, velocity and temperature fields are studied thoroughly through graphs. It is observed that for higher values of velocity slip parameter and power-law index, the entropy generation rate decreases while the Bejan number increases. Also, for the Hartmann number, Weissenberg number and Brinkman number, we found an increase in the entropy generation rate, and reverse behaviour is observed for the Bejan number. Nusselt number, temperature profile and Bejan’s number increase with an increase in variable thermal conductivity.

Dynamics of Marangoni convection in radiative flow of power-law fluid with entropy optimization

The flow of non-Newtonian liquids and their heat transfer characteristic gained more importance due to their technological, industrial and in many engineering applications. Inspired by these applications, the magnetohydrodynamic (MHD) flow of non-Newtonian liquid characterized by a power-law model is scrutinized. Further, viscous dissipation, Marangoni convection and thermal radiation are taken into the account. In addition, the production of entropy is investigated as a function of temperature, velocity and concentration. For different flow parameters, the total entropy production (EP) rate is examined. The appropriate similarity transformations are used to reduce the modeled equations reduced into ordinary differential equations (ODEs). The Runge–Kutta–Fehlberg 45-order procedure is then used to solve these reduced equations numerically using the shooting technique. Results reveal that the escalating values of radiation parameter escalate the heat transference, but the contrary trend is portrayed for escalating values of power-law index. The augmented values of thermal Marangoni number decline the heat transference. The gain in values of radiation parameter progresses the entropy generation.

Mathematical modelling of classical Graetz–Nusselt problem for axisymmetric tube and flat channel using the Carreau fluid model: a numerical benchmark study

Abstract The thermal entrance problem (also known as the classical Graetz problem) is studied for the complex rheological Carreau fluid model. The solution of two-dimensional energy equation in the form of an infinite series is obtained by employing the separation of variables method. The ensuing eigenvalue problem (S–L problem) is solved for eigenvalues and corresponding eigenfunctions through MATLAB routine bvp5c. Numerical integration via Simpson’s rule is carried out to compute the coefficient of series solution. Current problem is also tackled by an alternative approach where numerical solution of eigenvalue problem is evaluated via the Runge–Kutta fourth order method. This problem is solved for both flat and circular confinements with two types of boundary conditions: (i) constant wall temperature and (ii) prescribed wall heat flux. The obtained results of both local and mean Nusselt numbers, fully developed temperature profile and average temperature are discussed for different values of Weissenberg number and power-law index through graphs and tables. This study is valid for typical range of Weissenberg number W e ≤ 1 $\left(We\le 1\right)$ and power-law index n < 1 $\left(n{< }1\right)$ for shear-thinning trend while n > 1 $\left(n{ >}1\right)$ for shear-thickening behaviour. The scope of the present study is broad in the context that the solution of the said problem is achieved by using two different approaches namely, the traditional Graetz approach and the solution procedure documented in M. D. Mikhailov and M. N. Ozisik, Unified Analysis and Solutions of Heat and Mass Diffusion, New York, Dover, 1994.

Selective localization of rice husk derived graphene in reactive compatibilized PP/PA6 blends: Influence on morphology, interface and mechanical properties

ABSTRACT Graphene is synthesized and characterized using rice husk as a source with carbonization and potassium hydroxide (KOH) activation process. It has functional groups at the edges with a smooth surface. Graphene is melt-mixed with 50/50 (wt/wt) polypropylene (PP)/polyamine-6 (PA6) in the presence and absence of a compatibilizer. The compatibilizer used is polypropylene grafted maleic anhydride (PP-g-MA). There is a reaction between PP-g-MA and PA6 phase as established from FTIR spectroscopy. All samples show the formation of complex morphology with compatibilization and graphene addition in 50/50 (wt/wt) PP/PA6 blend. Graphene is localized in PA6 phase of 50/50 (wt/wt) PP/PA6 blend and its nanocomposites in the presence and absence of PP-g-MA. All the samples have power-law index (n) value of less than one exhibiting pseudoplastic fluid behavior; n values are significantly higher after compatibilization and graphene addition in 50/50 (wt/wt) PP/PA6 blend as reveals from rheological measurements. Graphene addition influences the crystallization behavior with selective localization in PA6 phase and morphology development. Dynamic mechanical analysis (DMA) shows improved stiffness of 50/50 (wt/wt) PP/PA6 blend with an addition of graphene and PP-g-MA. Tensile and impact properties increases are highest with an addition of 1 wt.% of graphene in 50/50 (wt/wt) PP/PA6 blend in presence of PP-g-MA.

Study of non – Newtonian flow, heat transfer and entropy generation characteristics in trapezoidal corrugated channel

This study is focused on the thermo-hydraulic and entropy generation characteristics of a non-Newtonian fluid in a trapezoidal shaped wavy channel. The study has been conducted for different Reynolds number ranging from 25 – 100 and power law index varying from 0.5 – 1.5. The variation of average Nusselt number, pressure drop, thermal entropy generation, viscous entropy generation are being calculated. For the discretization of the governing equations, finite volume method is adopted in Ansys Fluent. Average Nusselt number value increases with an increase in the value of Reynolds number and decreases with an increase in power law index. On the other hand, pressure drop decreases on increasing the value of Reynolds number, whereas on increasing the value of power law index, pressure drop value showing a decreasing trend. Thermal entropy generation and viscous entropy generation follows almost the same trend but both having different order of magnitude. The trend shows that on increasing the value of Re both the entropy generations increases whereas on increasing the power law index, it decreases.

Improving ride comfort by optimizing the parameters of a quarter car model with a power law damper

Suspension systems play a very important role in the vehicle performance as they are directly linked to improve and enhance the comfort of passengers. The working of a suspension arrangement depends strongly on the selection of suspension parameters like the spring stiffness and the damping coefficient. In this present study the parameters of a passive suspension with a power law damper are optimized for motion over a bump using genetic algorithm technique keeping passenger comfort in mind. It is seen that the best combination of suspension parameters results in selection of higher damping, lower spring stiffness and a lower value of power law index. It is also seen that the increase in the values of damping power index will result in the reduction of the suspension performance.

Study on dehydration kinetics of mango kernel

This study was aimed to study the dehydration kinetics of mango kernel with specific reference to sample thickness, drying temperature and mango varieties, and was performed prior to preparation of flour from mango kernel. Kernels of four mango varieties (Boishakhi, Amrapali, Fazli and Ashwina) were separated manually and dried at 65˚C by slicing into 4, 6 and 8 mm thickness to know the thickness effect on drying kinetics. Again, 6 mm thick slices of kernels were dried at 55, 60 and 65˚C to know the temperature effect. Kinetics analysis resulted that drying rate decreased with the increasing of thickness and decreasing of temperature. Ashwina’s kernels having the highest initial moisture content (M0) had the highest drying rate constant (m), while the lowest m was noticed for Boishakhi’s kernels having the lowest M0. The values of power law index (n) of drying model were 0.83, 0.32, 0.31 and 0.70 for kernels of Boishakhi, Amrapali, Fazli and Ashwina mango, respectively. Activation energy of water diffusion was in the range of 7.002-7.515 KCal/g-mole. Conclusively, this study revealed that moisture diffusivity and drying rate are greatly influenced by drying parameters and kernel varieties.

Impact of non-Newtonian fluid behavior on hydrodynamics and mass transfer in spacer-filled channels

Spiral wound membrane modules operate as filtration modules in the food, beverage, and pharmaceutical industries. As many fluids are non-Newtonian or become non-Newtonian during concentration, it is essential to gain an understanding of the effect of a shear-rate dependent viscosity. This computational work examines the impact of the fluid rheology and the Reynolds number on the hydrodynamics and the mass transfer in zigzag and cavity spacer-filled channels under laminar flow conditions. To describe the rheology of the working fluid, we utilized the well-known power-law model. The power-law index values corresponded to 0.7, 1, and 1.3, representing shear-thinning, Newtonian, and shear-thickening behavior, respectively. The Reynolds number was varied up to 160 whereas the Schmidt number was kept constant at 500. A standard convection–diffusion equation with a constant wall concentration was employed to describe the mass transfer. In agreement with previous works on Newtonian fluids, the zigzag spacer was found to be the most promising spacer type, because of the enhanced mass transfer in the reattachment regions. Whereas the mass transfer was only slightly affected by the rheology, the shear thinning fluid produced the smallest pressure drop. As a direct consequence of the positive effect on the pressure drop, the spacer efficiency was highest in all configurations. The results of this first numerical investigation in the context of non-Newtonian fluid flow through spacer-filled channels emphasize the importance of taking into account a varying fluid viscosity in the design and operation of the filtration process.

MWCNT and graphene nanoparticles additives for energy efficiency in engine oil with regression modeling

Quality of engine oil plays vital role in reducing frictional energy loss and enhancing durability. Recently, concept of nanolubricants, which is the suspension of nanoparticles in base lubricants, widely attempted. In the present study, experimental and regression approach has been used to evaluate the rheological properties of graphene/engine oil and MWCNT–graphene/engine oil nanolubricants. Power law index and consistency index values reveal non-Newtonian and shear thinning behavior of the samples. Result shows that dispersion of 1.8% particle volume fraction makes 155.06% and 62.85% increment in viscosity for MWCNT–graphene/engine oil and graphene/engine oil nanolubricant, respectively. A novel regression model for the dynamic viscosity of nanolubricant is proposed with temperature, nanoparticle volume fraction and shear rate as parameters. The proposed regression model provides viscosity prediction with deviation within 2.57% (R2, 0.99887). MWCNT–graphene/engine oil nanolubricants and regression model provide a cost-effective and eco-friendly approach for enhancement in the properties of lubricant.

Numerical simulation of free convection of MHD non-Newtonian nanofluid within a square wavy enclosure using Meshfree method

In this article, flow and heat transfer of nanofluids inside a wavy square enclosure filled with non-Newtonian (shear thinning) nanofluid under magnetic field has been simulated numerically. Single-phase model is used. The governing equations have been solved numerically using element free Galerkin method. The results are obtained for isotherms, streamlines, and average Nusselt number for various values of Hartmann number, Rayleigh number, nanoparticles volume fraction, and power-law index. Here, the main objective is to explore the effect of power-law index, Rayleigh number, Hartmann number, and volume fraction on average Nusselt number. It is found that in the absence of magnetic field, Nusselt number drops on increasing the value of power-law index whereas in the presence of magnetic field, heat transfer rate increases with increase in power-law index. With the increase in Rayleigh number and volume fraction of nanoparticles, the heat transfer rate increase in all cases. This type of problem has a direct application in the coolant systems, solar collector where the structure used is wavy in order to increase the rate of heat flow. Here, EFGM is efficiently applied for simulation due to irregular domain, which creates a novelty in the work.

Fundamental frequency analysis of functionally graded plates with temperature-dependent properties based on improved exponential-trigonometric two-dimensional higher shear deformation theory

The objective of this paper is to provide a computational method to analyze free vibrations of advanced composite plates in thermal environments according to a recently developed higher-order shear deformation theory. This method is based upon the assumptions that displacements field include just four unknowns and considers a combination of trigonometric and exponential shear shape functions which satisfy shear stress free boundary conditions on the plate surfaces. The FG plates are simply supported and subjected to uniform, linear, nonlinear and sinusoidal temperature rise. The temperature field considered is assumed to vary in the thickness direction and constant in the axial directions of plates. It is supposed that the constituent materials possess temperature-dependent properties changing across the thickness with a simple power law function. The equations of motion are obtained by employing Hamilton’s principle and solved based on Navier’s method to determine natural frequencies of the FG plate. A parametric study for FGM plates with different values of power law index and under different sets of thermal environmental conditions has been carried out. The obtained results are compared for temperature-dependent and temperature-independent FG Plates and validated with available results in the literature.

Investigation of the mixed convection of power-law fluids between two horizontal concentric cylinders: Effect of various operating conditions

The purpose of this paper is to study numerically the mixed convection between two rotating circular cylinders under horizontal arrangement. The cylinders have a concentric position with a blockage ratio of d/D = 2.5. The annular space is completely filled with non-Newtonian power-law fluid. The surface of the inner cylinder is hot whereas the surface of the outer one is cold. Three cases are studied: in the first one, the inner cylinder has a constant rotational speed, while the outer cylinder is completely fixed; the second case: both cylinders are rotating in the same direction and at the same rotational speed; in the last case, both cylinders are rotating in opposite directions at a similar rotational speed. All studied cases are examined for various values of Reynolds number (Re = 1–10), Richardson number (Ri = 0–3), and power-law index (n = 0.6–1.6) at Prandtl number Pr = 50.

Functionally Graded Panels: A Review

Functionally gradedmaterials (FGMs) are not homogeneous materials. It consists of different(two or more) materials, engineered to have a continuously varying spatial composition profile. FGM is the one that can solve practical problems arising from the production and application of a new type of composite material. This paper describes the overview of FGM basic concepts, classification, properties, and its modeling which may focus on the static and dynamic analysis of functionally graded panels. The effective material properties of functionally graded materials for the panel are graded in the thickness direction from the bottom surface to the top surface according to the power-law distribution of volume fractions of the constituents. The use of structures like beams, plates, and shells, which are made from functionally graded (FG) materials, is increasing because of the smooth variation of material properties along with preferred directions. This variation gives continuous stress distribution in the FG structures. Therefore, an FGM can be effectively used in avoiding corrosion, fatigue, fracture, and stress corrosion cracking. The paper covers the literature study on static, buckling and free vibration, thermo-mechanical analysis of FGM panel. From this literature study it is found that, analysis of these problems is made using the constitutive relations and governing equations associated with the classical laminated theory structural model, the FSDT model, the HSDT model,Reissner and Sander theory,differential quadrature, finite element method and closed form solutions. Results are availableon different geometrical dimensional ratios variations, power-law index value n variationsand simply supported,clamped, free edges boundary conditionswith its combinations for FG panels. Lesser literatures are available for different edge boundary conditions such as SCSC, CSCS,SSSC, SFSF, SSSF, SCSF on curved panelfor free vibration, buckling and thermo-structural analysis.

Soret and Dufour effects on MHD boundary layer flow of non-Newtonian Carreau fluid with mixed convective heat and mass transfer over a moving vertical plate

In this analysis, the mixed convection boundary layer MHD flow of non-Newtonian Carreau fluid subjected to Soret and Dufour effects over a moving vertical plate is studied. The governing flow equations are converted into a set of non-linear ordinary differential equations using suitable transformations. For numerical computations, bvp4c in MATLAB package is used to solve the resulting equations. Impacts of various involved parameters, such as Weissenberg number, power-law index, magnetic parameter, thermal buoyancy parameter, solutal buoyancy parameter, thermal radiation, Dufour number, Soret number and reaction rate parameter, on velocity, temperature and concentration are shown through figures. Also, the local skin-friction coefficient, local Nusselt number and local Sherwood number are calculated and shown graphically and in tabular form for different parameters. Some important facts are revealed during the investigation. The temperature and concentration show decreasing trends with increasing values of power-law index, whereas velocity shows reverse trend and these trends are more prominent for larger values of Weissenberg number. For stronger magnetic field, velocity decreases, while the temperature and concentration increase. It was also found that for shear thinning fluid the drag coefficient exhibits an increasing character when Weissenberg number increases, but for shear thickening fluid the drag coefficient shows the contrary nature. For small values of Dufour number, heat transfer rate enhances with increasing Soret number, but for higher values of Dufour number it slightly dies down with Soret number and the mass transfer rate reacts oppositely. In addition, due to increasing chemical reaction rate, the concentration and velocity decrease.

Analysis of rheological properties of MWCNT/SiO2 hydraulic oil nanolubricants using regression and artificial neural network

In this article, the rheological behavior of MWCNT/SiO2 based nano-hydraulic oil nanolubricant is evaluated using experimental and Artificial Neural Network (ANN) approach. Viscosities of the hybrid nanolubricant samples were measured at temperature and shear rate range of 10–80 °C and 10–200 s−1 respectively. A new regression model is being proposed to predict the dynamic viscosity of nanolubricants. The proposed regression model (R2 0.98338–0.99583) predicts the viscosity of nanolubricants closer to experimental results (least deviation 2.62%). Consistency index (m) and power law index (n) values reveal that nanolubricant samples are non-Newtonian fluid with shear thinning behavior. To improve the accuracy in predicting the viscosity of nanolubricants, the ANN model was designed having input variables among temperature, solid volume fraction and shear rate. In the first phase, temperature and solid volume fraction were taken as input variables, and in the second phase shear rate was introduced as an additional input parameter. The entire data was split into 70:30 proportions for the training and testing phases of the ANN model. The testing results of ANN revealed better accuracy than the proposed correlation in terms of average values of Root Mean Square Error (RMSE) and R2.

Thermohydrodynamic (THD) Analysis of Journal Bearing Operating with Bio-based Nanolubricants

The objective of current research is to study the adiabatic solutions of a plain journal bearing operating with bio-based lubricants containing nanoparticles. Estimation of pressure and temperature fields has been accomplished by simultaneous numerical solutions of the modified Reynolds equation and the adiabatic energy equation. These equations have been solved by adopting the finite difference method with suitable iterative scheme. The analysis has been carried out taking into account the heating effects and non-Newtonian rheology of bio-based nanolubricant following the power law model. The results have been investigated for temperature and pressure fields and the static performance parameters for a broad range of eccentricity ratio e and different power law index values. The calculated results present that the involvement of nanoparticles in bio-based lubricant significantly enhances the pressure, load carrying capacity and friction force. Moreover, the influence of thermal effects on performance parameters is seen to be maximum at higher values of power law index.