Increase In Power-law Index Research Articles

Competition between turbulence and thermal blooming of coherent vortex beam array propagating in non-Kolmogorov marine atmosphere.

The competition between turbulence and thermal blooming significantly affects the propagation characteristics of laser beams in the atmosphere. Here, taking the propagation of a vortex beam array in a non-Kolmogorov marine atmosphere as an example, we have quantitatively analyzed the competition between turbulence and thermal blooming. The atmospheric coherence length is adopted to evaluate the turbulence strength, while a modified thermal distortion parameter is developed to evaluate the thermal blooming strength of vortex beam arrays in non-Kolmogorov turbulence. Results indicate that, in strong turbulence, there is a significant variation in the beam characteristics at the target plane as the spectral power law index increases, whereas this relationship exhibits a smoother change in weak turbulence. More interestingly, our results suggest that for a fixed aperture of laser emission systems, increasing the initial power density may not always lead to a higher average power density at the target plane, and there exists an optimal value no matter what the intensity of the turbulence is, i.e., weak, moderate, and strong turbulence. We hope these results may provide useful guidance for laser communication, laser power transmission, etc.

Multiple-relaxation-time lattice boltzmann simulation of natural convection of ethylene Glycol -Al[formula omitted]O[formula omitted] power-law Non-newtonian nanofluid in an open enclosure with adiabatic fins

The heat transfer by natural convection of a nanofluid, which is ethylene glycol−Al2O3 has been analyzed in an open cavity numerically using the multiple-relaxation-time - lattice Boltzmann method by the graphics processing unit high-performance parallel computing. The right side of the cavity is open, and different boundary conditions have been applied to all the walls. Besides, one adiabatic fin has been installed on each side of the enclosure’s top and bottom sides. Here, the Prandtl number is fixed at 16.6, and the Rayleigh number changes from 104−106 with the nanoparticle volume fraction from 0%−5% has been used for numerical simulations. Besides, in this work, the power-law index is an important parameter as well, and 0.7, 0.8, 1, 1.2, and 1.4 are the values of this parameter. Results are presented concerning both the average and local Nusselt numbers in the form of streamlines, isotherms, temperature distributions, velocity distributions, heat transfer rate, and entropy production. It is observed when increases, average Nusselt number increases 607.94%, and for this reason, the overall heat transfer rate rises because of buoyancy force. In addition, the average Nusselt number falls by 83.28% when the power-law index rises; as a result, the total heat transfer rate falls because fluid viscosity increases with the power-law index. It is also observed that for shear-thickening fluids, the temperature gradient is higher. On the contrary, the temperature started decreasing with the increase of the power-law index. Additionally, the local Nusselt number value rises as power-law index falls. Moreover, the heat transfer rate increases by 7.08% when volume fraction increases. The intensity of buoyancy force reduces with the increase of volume fraction. Besides, the overall entropy generation rises when the Rayleigh number and the volume fraction increase, but it decreases when the power-law index increases. So, when the Rayleigh number is 106, the power-law index is 0.7, and the volume fraction is 0.00 then the entropy generation is the highest. This current research has many applications for example heat exchangers, electronic cooling equipment, solar heating systems, aerospace applications, medical devices, and entropy generation-related systems.

Finite element simulations of double diffusion in a staggered cavity filled with a power-law fluid

Double diffusion refers to a phenomenon where two different components of a fluid (such as heat and mass) exhibit distinct diffusive behaviors. In this study, we employ finite element-based numerical simulations to investigate the phenomenon of double diffusion in a non-Newtonian fluid within a staggered cavity. Mathematically, this system can be understood by coupling the two-dimensional continuity, momentum, energy, and concentration equations. Since the governing equations have been written in a dimensionless form, Galerkin's finite element method is used to find a solution. The velocity profile and temperature are calculated in a function space of quadratic polynomials (P2), while the pressure is calculated in a linear (P1) finite element function space. Discrete systems of nonlinear algebraic equations are resolved through the implementation of Newton's method with appropriate damping and PARDISO solver in the inner loops for solving the sparse linear systems. In this work, the data are presented graphically in the form of streamlines, isotherms, iso-concentration, average Nusselt numbers, average Sherwood numbers, and kinetic energy distribution. Code validation and grid independence study are also provided. Moreover, convective mass transfer is significantly correlated with the Lewis number, as demonstrated by the results. As the power-law index increases, convection also exhibits enhanced as a means of transmitting heat and mass.

Magnetohydrodynamic convection-entropy generation of a non-Newtonian nanofluid in a 3D chamber filled with a porous medium

Magnetohydrodynamic (MHD) mixed convection in a 3D (three dimensional) lid-driven cavity loaded with a power-law nanofluid is examined. The bottom wavy wall is maintained at a hot temperature, while the upper lid is at a uniformly cold temperature. The vertical walls are kept in adiabatic conditions. The steady and three-dimensional flow of nanofluids is quantitatively studied utilizing thermophysical properties and the Galerkin Finite Element Method (GFEM). The findings were shown for a variety of Grashof numbers (Gr = 103-105), Hartmann numbers (Ha = 0–20), Reynolds numbers (Re = 10–500), power-law indexes (n = 0.8,1,1.6), and undulation numbers (N = 1–4). The influence of the various parameters on flow, heat transfer, and entropy generation is illustrated by the streamlines, isotherms, and isentropic contours. Higher Re, γ, N, φ, and lower Ha enhance the heat transfer. Entropy generation is mostly due to heat transfer but also fluid-friction and magneto effects contribute. Also, the increase in Re from 50 to 500 gives an enhancement in Nuav up to 87.5 %. Furthermore, the increase in power-law index (n) from 0.8 to 1 gives a reduction in Nusselt number up to 10.58 %.

Numerical Investigation of a Combustible Polymer in a Rectangular Stockpile: A Spectral Approach

Despite the wide application of combustion in reactive materials, one of the challenges faced globally is the auto-ignition of such materials, resulting in fire and explosion hazards. To avoid this unfortunate occurrence, a mathematical model describing the thermal decomposition of combustible polymer material in a rectangular stockpile is formulated. A nonlinear momentum equation is provided with the assumption that the combustible polymer follows a Carreau constitutive relation. The chemical reaction of the polymer material is assumed to be exothermic; therefore, Arrhenius’s kinetic theory is considered in the energy balance equation. The bivariate spectral local linearization scheme (BSLLS) is utilized to provide a numerical solution for the dimensionless equations governing the problem. The obtained results are validated by the collocation weighted residual method (CWRM), and a good agreement is achieved. Dimensionless velocity, temperature, and thermal stability results are presented and explained comprehensively with suitable applications. Some of the obtained results show that thermal criticality increases with increasing power law index (n) and radiation (Ra) values and decreases with increasing variable viscosity (β1) and material parameter (We) values.

SIMPLE INCREMENTAL APPROACH FOR ANALYSING OPTIMAL NON-PRISMATIC FUNCTIONALLY GRADED BEAMS

This paper presents a simple incremental approach of analysing the static behaviour of functionally graded tapered beams. This approach involves dividing the non-uniform beam into segments with uniform cross-sections, and using two separate finite element models to analyse the structural behavior of slender beams (Euler-Bernoulli model) and deep beams (Timoshenko beam theory). The material properties of the beam vary according to a power law distribution through the thickness, resulting in smooth variations in the mechanical properties. The finite element system of equations is obtained using the principle of virtual work. Detailed information on the shape functions and stiffness matrix of the beam is provided, and the numerical results are evaluated and validated using data from the literature. The comparison demonstrates that the response of the functionally graded tapered beams is accurately assessed by the proposed approach. Additionally, the effects of material distribution, boundary conditions, and tapering parameter on the deflection behavior are presented. Results show that an increase in the power law index increases the flexibility of the functionally graded tapered beams, resulting in higher deflection. Furthermore, lower tapering parameters also result in higher deflection. Compared to other boundary conditions, clamped-clamped boundary conditions demonstrate the best performance in terms of maximum deflection.

Numerical analysis of unsteady momentum and heat flow of dusty tangent hyperbolic fluid in three dimensions

This paper explores the impact of MHD and viscous dissipation with joule heating on convective stretching flow of dusty tangent hyperbolic fluid over a sheet in 3D. A time-dependent magnetic field is applied along the z-axis and the sheet being stretched along the xy-plane. The fluid and dust particles motions are coupled only through drag and heat transfer between them. The effect of viscous dissipation with convection is appreciable when the generated kinetic energy becomes appreciable as compared to the amount of heat transferred. A well known bvp4c method has been used to find the fruitful results. Graphs and tables show the facts and figures for physical properties according to different parameters. The main findings are that Increase in power law index, magnetic field, Weissenberg effect, concentration of dust particles, and unsteadiness parameter reduces the flow of fluid and solid granules.

Investigating Static Deflection of Non-Prismatic Axially Functionally Graded Beam

In this study, the static deflection of non-prismatic axial function graded tapered beam (A-FGB) under distribution load has been analyzed using ANSYS workbench (17.2). According to a power-law model, the elastic modulus of the beam varies continuously in the axial direction of the beam. Also, the beam’s geometry, i.e., width, thickness, or both width and thickness of the beam, varies linearly in the axial direction with different values of non-uniformity parameter (1, 0.5,0, −0.5, and −0.75). The effects of martial distribution, i.e., power-law index, and non-uniformity parameter on the static deflection for A-FGB with different boundary conditions, in such free-clamped, clamped-free, and simply-supported, are studied. This research deals with functionally graded materials FGMs in more than one aspect in terms of using different boundary conditions; in addition, it studies the response of the non-prismatic beam non-uniformity parameter (α); therefore, this research studies comprehensively the deflection of the beam. The results show that the increase in power-law index causes decreasing in dimensionless deflection and its rate of change depends on the supporting types of the beam and non-uniformity parameters. The variation in both width and thickness for a free-clamped axial function–graded beam gives a significant decrease in dimensionless deflection at decreasing in non-uniformity parameter, whereas the variation in thickness for clamped-free axial function graded beam gives a significant decrease in dimensionless deflection at decreasing of non-uniformity parameter.

Cattaneo-Christov dual diffusive non-Newtonian nanoliquid flow featuring nonlinear convection

A theoretical study is presented of the transport characteristics in double diffusive tangent hyperbolic (non-Newtonian) nanofluid boundary layer flow from a stretching flat surface. The Cattaneo–Christov (non-Fourier and non-Fickian) double diffusion model is deployed in the formulations for energy and species conservation, to determine more precisely temperature and concentration distributions with thermal and solutual relaxation times. Non–linear mixed convection and heat generation/absorption are included. The nanofluid approach combines Brownian motion and thermophoresis. Suitable transformations are deployed to render the nonlinear partial differential system into a system of dimensionless coupled ordinary nonlinear differential equations. The non-dimensional boundary value problem is then solved with the homotopic analysis method (HAM). The distributions of velocity, temperature and concentration of nanoparticles are depicted and investigated for the effects of multiple emerging parameters. Velocity is reduced (and momentum boundary layer thickness elevated) with increasing power–law index and Weissenberg number whereas velocity is elevated (and momentum boundary layer thickness reduced) with increment in mixed convection variable. Temperature is suppressed (and thermal boundary layer thickness depleted) with increasing thermal relaxation variable, heat sink parameter, Prandtl number whereas temperature is enhanced (and thermal boundary layer thickness boosted) with greater heat source parameter, Brownian motion parameter and thermophoresis parameter. Nanoparticle concentration is depleted (and concentration boundary layer thickness reduced) with greater Schmidt number and Brownian motion parameter whereas the opposite effect is induced with greater thermophoresis parameter and solutal relaxation time. Skin friction is strongly reduced with increasing values of nonlinear thermal and concentration convection variables. The simulations are relevant to nano-polymer coating operations.

Stability Analysis of Thin Power-Law Fluid Film Flowing down a Moving Plane in a Vertical Direction

This paper analyses the stability of thin power-law fluid flowing down a moving plane in a vertical direction by using the long-wave perturbation method. Linear and nonlinear stability are discussed. The linear stable region increases as the downward speed increases and the power-law index increases. More accurate results are obtained on the coefficients of the nonlinear generalized kinematic equation in the power-law part. The regions of sub-critical instability and absolute stability are expanded when the downward movement of plane increases, or the power-law index increases, and meanwhile the parts of supercritical stability and explosive supercritical instability are compressed. By substituting the power-law index and moving speed into the generalized nonlinear kinematic equation of the power-law film on the free surface, the results can be applied to estimate the stability of the thin film flow in the field of engineering.

Studies of the Movement Mechanism of Droplets in Power-Law Fluids in a T-Junction Microchannel by the Lattice Boltzmann Method

The movement mechanisms of Newtonian droplets in power-law fluids in T-junction microchannels were studied with the lattice Boltzmann method. The effects of power-law index <i>n</i> , capillary number <i>C</i>_a, flow ratio <i>Q</i> , viscosity ratio <i>M</i>, and surface wettability <i>θ</i> on the droplet formation size, the formation time and the deformation index (<i>D</i>_I) were investigated in detail. The results show that, first, with the increase of power-law index n from 0.4 to 1.6, the droplet formation size decreases almost linearly, and both the droplet formation time and the deformation index decrease quickly at first and then much more slowly. Second, the influences of the viscosity ratio on the droplet formation size, the formation time and the deformation index are basically the same as those of the power law index. In addition, with the increases of <i>C</i>_a and <i>θ</i> of the main channel, the droplet formation size decreases almost linearly, while the droplet formation time and deformation index decrease rapidly at first and then slowly, and the decreasing rates weaken with the increase of the power-law index. At last, with the increase of flow ratio <i>Q</i> of the continuous phase over the dispersed phase, the droplet formation size increases, and the droplet formation time as well as the deformation index decrease.

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.

Thermally induced instability on asymmetric buckling analysis of pinned-fixed FG-GPLRC arches

In the present work, an analytical study on the asymmetric static and dynamic buckling of a pinned-fixed functionally graded graphene nanoplatelet reinforced composite (FG-GPLRC) arch under thermal conditions is presented. The reinforcement of graphene nanoplatelets (GPLs) is dispersed along arch thickness by following a power law distribution. Making use of the modified Halpin–Tsai micromechanical model and energy method, the static buckling load of the arch under an arbitrary radial point load and the dynamic buckling load of the arch under an arbitrary radial step point load can be derived, which could be applied to determine the existence of dynamic buckling and the phenomenon of multiple limit points under a static state. A numerical analysis is conducted to verify the accuracy of the analytical method, a good prediction on the static and dynamic buckling of the pinned-fixed FG-GPLRC arch is demonstrated. In this study, the influence of GPLs weight fraction, concentration and geometry on the static and dynamic buckling of the arch is comprehensively discussed. The dynamic and static buckling loads of the arch are found to be sensitive to applied load position under various elevated temperatures. Arch buckling load decreases as the power law index increases, but it increases as temperature rises. It is also found that the present approach is able to trace the postbuckling paths of the arch for stability analysis. Besides, accurate first-known thermal buckling solutions are also presented.

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.

Controlling the flow and heat transfer characteristics of power-law fluids in T-junctions using a rotating cylinder

In this work, the combined influence of the power-law rheology and isothermal rotating cylinder has been investigated numerically on the flow and heat transfer characteristics in a T-channel. The cylinder placed at the T-junction imitates the functioning of a rotating valve which controls the flow rate and the enthalpy distribution of the exiting streams in two branches. The range of parameters considered in this work is as: Reynolds number, 1 < Re ≤ 50, power-law index, 0.2 ≤ n ≤ 1, Prandtl number, 10 ≤ Pr ≤ 100 and non-dimensional circumferential velocity of the cylinder, −5 ≤ α ≤ 5. Results suggest that the rotating cylinder can be used as a technique to create and/or reduce the formation of momentum and thermal boundary layers in the flow domain. The rotational velocity (α) and power-law flow index (n) are seen to have a strong effect on the critical Reynolds number for both the main and side branches. The hydrodynamic forces acting over the cylinder surface exerted by the fluid in the flow and perpendicular to the flow direction show a strong relationship with the cylinder rotation. For a particular combination of the studied parameters, these forces are also seen to be negative. Further, it is interesting to note that as the power-law index increases, the flow split ratio decreases while it shows an opposite trend with the Reynolds number. It can also be varied by switching the rotation direction. The dimensionless exiting temperature and enthalpy distribution are seen to have a strong relationship with the direction of rotation, fluid power-law index, Reynolds and Prandtl numbers. The mean values of the Nusselt number are seen to increase and/or decrease with the rotational velocity. For the anticlockwise rotation, the maximum suppression in the heat transfer is seen to be 79% while 62% for the clockwise rotation for the Newtonian fluid behaviour at low Prandtl number and high Reynolds numbers.

Numerical analysis of flow and forced convection heat transfer of non-Newtonian fluid in a pipe based on fractional constitutive model

PurposeThis paper aims to use a fractional constitutive model with a nonlocal velocity gradient for replacing the nonlinear constitutive model to characterize its complex rheological behavior, where non-linear characteristics exist, for example, the inherent viscous behavior of the crude oil. The feasibility and flexibility of the fractional model are tested via a case study of non-Newtonian fluid. The finite element method is non-Newtonian used to numerically solve both momentum equation and energy equation to describe the fluid flow and convection heat transfer process.Design/methodology/approachThis paper provides a comprehensive theoretical and numerical study of flow and heat transfer of non-Newtonian fluids in a pipe based on the fractional constitutive model. Contrary to fractional order a, the rheological property of non-Newtonian fluid changes from shear-thinning to shear-thickening with the increase of power-law index n, therefore the flow and heat transfer are hindered to some extent.FindingsThis paper discusses two dimensionless parameters on flow regime and thermal patterns, including Reynolds number (Re) and Nusselt number (Nu) in evaluating the flow rate and heat transfer rate. Analysis results show that the viscosity of the non-Newtonian fluid decreases with the rheological index (order α) increasing. While large fractional (order α) corresponds to the enhancement of heat transfer capacity.Research limitations/implicationsFirst, it is observed that the increase of the Re results in an increase of the local Nusselt number (Nul). It means the heat transfer enhancement ratio increases with Re. Meanwhile, the increasement of the Nul indicating the enhancement in the heat transfer coefficient, produces a higher speed flow of crude oil.Originality/valueThis study presents a new numerical investigation on characteristics of steady-state pipe flow and forced convection heat transfer by using a fractional constitutive model. The influences of various non-dimensional characteristic parameters of fluid on the velocity and temperature fields are analyzed in detail.

Numerical Analysis and Entropy Generation of Electrokinetic Flow of Power-Law Fluid in a Microtriangular Prism

This research aims to study the characteristics of thermal transport and analyse the entropy generation of electroosmotic flow of power-law fluids in a microtriangular prism in the presence of pressure gradient. Considering a fully developed flow subject to constant wall heat flux, the nonlinear electric potential, momentum, and linear heat transfer equations are solved numerically by developing an iterative finite difference method with a nonuniform grid. The thermal efficiency of the model is explored under the light of the second law of thermodynamics. Effect/impact of governing physical parameters on velocity, temperature, Nusselt number, and entropy distributions is studied, and the results are demonstrated graphically; we found that the Nusselt number decreases with the increase of power-law index, and average entropy generation increases with power-law index. We believe that the obtained result in the present study shall be useful for design of energy efficient microsystems which utilize the dual electrokinetic and centrifugal pumping effects.

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.

Elasto-hydrodynamic analysis of journal bearing operating with nanolubricants

In this study, performance parameters of a rigid and flexible journal bearing using non-Newtonian nanolubricants have been investigated and compared. Krieger-Dougherty viscosity model has been implemented with a non-Newtonian model (power law) to evaluate the effective viscosity of nanolubricants. In order to attain the pressure field of nanolubricants, a numerical solution of the modified Reynolds equation has been derived with initial assumptions and boundary conditions using finite difference method. The static performance parameters for both the bearings have been examined at different values of power law index and eccentricity ratio. The results demonstrate that the load-carrying capacity, maximum pressure and friction force increase significantly using nanolubricant in comparison to base lubricant. Also, the values of these parameters increase with increase of power law index. An insignificant effect of elastic deformation is observed on performance parameters except attitude angle at a particular power law index value.

MHD effect on mixed convection of annulus circular enclosure filled with Non-Newtonian nanofluid

The fluid flow and mixed convection heat transfer of a non-Newtonian (Cu–water) nanofluid-filled circular annulus enclosure in a magnetic field are investigated numerically for a two-dimensional, steady-state, incompressible, laminar flow using the Galerkin finite element method (GFEM). The Prandtl number (Pr = 6.2) and Grashof number (Gr = 100) are assumed to be constants, whereas the Richardson number varies within a range of 0 ≤ Ri ≤ 1, the Hartman number within a range of 0 ≤ Ha ≤60, the Power law index within a range of 0.2 ≤ n ≤ 1.4, and the volume fraction within a range of 0 ≤ φ ≤ 1. The enclosure consists of an outer rotating cylinder that is kept at a cold temperature (Tc) and an inner non-rotating cylinder kept at a hot temperature (Th). The ratio of the inner circular diameter to the annulus space length is kept constant at 2. The results depict that the stream function increases with increasing power law index, even up to n = 1, which causes the fluid to behave as a Newtonian fluid. The magnetic field has a critical impact on the fluid flow pattern. The average Nusselt number increases with decreasing Richardson number, owing to the improved heat transfer by forced convection.