Values Of Power-law Index Research Articles

Unveiling the nature of compact object in the LMXB MAXI J1957+032 using Swift-xrt

MAXI J1957+032 is a transient Low-mass X-ray binary (LMXB) that underwent four short outbursts in 1.5 years since its discovery in 2015. The nature of the compact object in MAXI J1957+032 is not clear, but it was proposed to be a neutron star based on the short-duration of its outbursts. Here, we report the results obtained after performing spectral analysis using data obtained with the X-ray telescope aboard the Neil Gehrels Swift satellite. When describing the spectrum with an absorbed power law, we found that the spectra softens (the power-law index increases from $\sim$ 1.8 to 2.5) as the luminosity decreases. Near the end of its outbursts the observed value of power-law index ($\Gamma$) is $\sim$ 2.5. To identify the nature of the compact object in this system, we used $\Gamma$ as a tracer of the spectral evolution with luminosity. We found that for the distance of 4 kpc, our results suggest that the source harbours a neutron star.

The effect of the addition of a slip agent on the rheological properties of polyethylene: off-line and in-line measurements

Abstract The article describes an investigation into the effect of a slip agent on the rheological properties of low-density polyethylene. As a slip modifier, oleamide was used in the amounts of 0.5, 1.0, 2.0, 3.0 and 4.0 wt.%, respectively. The process of polymer modification was carried out in a twin-screw extrusion process. The effect of the slip agent on the mass flow rate index was determined. The specific plasticisation energy of the modified polymer was also assessed based on the change in the torque of a batch mixer. The assessment of the effect of the addition of oleamide on the change in the flow and viscosity curves was made using an off-line (plastometer) and an in-line (extruder rheometer) measuring technique. The rheological parameters were determined based on the Ostwald-de-Waele power law model. The operation of the plastometer was brought closer to the principles of operation of the capillary rheometer by applying variable piston loading. In in-line measurements, an extrusion head with replaceable cylindrical dies was used. Using two rheological measuring techniques made it possible to determine the low-density polyethylene viscosity variations and the values of flow power law index (n) and consistency factor (K) in a wide shear rate range.

Implication of fluid rheology on the hydrothermal and entropy generation characteristics for mixed convective flow in a backward facing step channel with baffle

The present study numerically investigates a two-dimensional, steady, laminar, incompressible and mixed convective flow of non-Newtonian fluid through a backward facing step channel with different baffle configurations. The power-law model is used to capture the confluence of fluid rheology and buoyancy for varying step to baffle distance, varying number of baffles and different arrangement (inline and staggered) of baffles. Different values of power-law index viz. n = 0.5, 0.8, 1, 1.2 and 1.5 are considered to encompass the shear-thinning (n < 1), shear-thickening (n > 1) as well as Newtonian fluids (n = 1) as a special case. The Reynolds number is fixed equal to 100 whereas the Richardson number has been varied within the range of 0.1–1 in the present investigation. The results obtained from the present investigation reveal the implications of power-law index, Richardson number and baffle configuration on the reattachment length, Nusselt number, pressure drop and entropy generation. The results show that the length of the recirculation zones formed in the backward facing step channel increases with increase in Richardson number and decreases with increase in power-law index. It is also found that the variation of heat transfer rate, pressure drop and entropy generation characteristics for varying step to baffle distance, different number of baffles and different arrangement and number of pairs of baffle is dictated by the interplay of power-law index and Richardson number. The findings of this study bear utility towards designing efficient thermodynamic system that can deliver maximum heat transfer with minimum irreversibility.

Steady-state performance of a circular journal bearing lubricated with a non-Newtonian fluid considering the elastic deformation of the liner

In this work, a numerical study of the effect of elastic deformation on the static characteristics of a circular journal bearing operating with non-Newtonian fluids obeying to the power law model is presented. The modified Reynolds equation has been derived taking into consideration the effect of non-Newtonian behavior of the fluids. To obtain the pressure distribution, the Reynolds equation has been solved using finite difference technique with appropriate iterative technique incorporating Reynolds boundary conditions. The static performance characteristics for finite-width journal bearing in terms of the load-carrying capacity, the attitude angle, friction coefficient, and the side leakage have been studied for various values of the non-Newtonian power law index n and the elastic coefficient. The results show that the increase of the power law index produces a higher load-carrying capacity, a higher side leakage, a lower attitude angle, and a lower friction coefficient. From this study, it can be concluded that the elastic deformation has an important influence on the static characteristics of the journal bearing lubricated with a non-Newtonian fluid, and this influence is more significant for the journal bearing operating at larger values of the eccentricity ratio.

Effect of inclination angle on the forced convective flow of a power-law fluid in a 2-D planar branching channel

Branching T-channel is a very common element of a piping system for the transportation of liquids and gases. The brachesbranches of the T-channel can be inclined at different angles which affects the flow dynamics and heat transfer characteristics significantly. Thus, the present work focuses on the flow and thermal characteristics of the laminar forced convection of power-law fluids in a rectangular branching channel which have been numerically investigated over a wide range of parameters such as Reynolds number, 50 ≤ Re ≤ 300, Prandtl number, 10 ≤ Pr ≤ 50, inclination angle, 30° ≤ α ≤ 90° and power-law index, 0.2 ≤ n ≤ 1.4 (includes shear-thinning, n < 1, shear-thickening, n > 1 and Newtonian, n = 1 fluids). This is perhaps the first systematic study which examines the role of power-law fluid behaviour and of branch inclination on momentum and heat transfer characteristics. New extensive results for the flow and temperature fields are presented in terms of streamline contours and separated-flow zones, pressure coefficient, recirculation length, critical Reynolds number, isotherm contours, temperature profiles and local Nusselt number. The pressure coefficient is found to be higher for shear-thickening fluids than that for the Newtonian and shear-thinning fluids while the inclination angle has only a weak effect. The recirculation length bears a positive dependence on the Reynolds number and inclination angle while an inverse relationship is observed with power-law index in both branches. The critical Reynolds number, at which the onset of flow recirculation is observed, is found to be lower for higher inclination angles and a strong influence of the power-law index is also seen on the critical Reynolds number in both branches. Also, the local Nusselt number is seen to be higher at lower Prandtl numbers, low power-law index values and high inclination angles for both branches. Overall, the inclination angle plays a significant role in determining the heat transfer characteristics.

Numerical Simulation of Non-Newtonian Power-Law Fluid Flow in a Lid-Driven Skewed Cavity

Non-Newtonian laminar fluid flow in a lid-driven skewed cavity has been studied numerically using power-law viscosity model. The governing two-dimensional unsteady incompressible Navier–Stokes equations were initially non-dimensionalized using appropriate transformation, and then the dimensionless form is transformed to generalized curvilinear coordinates to simulate complex geometry. The transformed equations are discretized using finite volume method with the collocated grid arrangement. The code is first validated against the existing benchmark results for two-dimensional lid-driven square cavity problem considering both Newtonian and non-Newtonian fluids. The validation has also been carried out for a lid-driven skewed cavity in the case of a Newtonian fluid. Then the code is applied to the skewed cavity problem involving non-Newtonian fluid flow which can be described by the power-law viscosity model. Moreover, grid independence test has been performed for a skewed cavity for different values of power-law index. In the present case, the skewness of the geometry has been changed by changing the skew angle for both shear-thinning and shear-thickening fluids. The consequent numerical results are presented in terms of the velocity as well as streamlines for the different values of the power-law index $$n=0.5$$ , 1 and 1.5, Reynolds number $$Re = 100, 200, 300$$ and 500 as well as for the different angles of the skewed cavity ( $$\alpha =15^{\circ }$$ to $$165^{\circ }$$ ).

Application of in-line rheological measurements for characterization of polypropylene/opoka rock powder composites

The rheological properties of the composites of polypropylene (PP) with a new natural powder hybrid filler – carbonate-silicate rock called opoka – were investigated. Opoka rock is industrial waste originating (as a subsieve fraction) from the production of sorbents used in water treatment processes. The effect of opoka addition (1, 5 and 10 wt %) on the processability of PP was determined during the extrusion process using an in-line measuring stand. The testing instrument was an extruder rheometer equipped with a rheological measuring head with exchangeable dies. Cylindrical measuring dies with a radius of 1.5 mm and a length of L = 20, 30, 40 and 50 mm, respectively, were used in the measurements. The rheological parameters of the composites were determined based on the Ostwald-de-Waele power--law model at a temperature of 230 °C. The effect of the addition of opoka on the extruder operating characteristic, flow curves, viscosity curves, and the values of power law index (n), consistency factor (K), mass flow rate (MFR) and volume flow rate (MVR) have been determined.

Lattice Boltzmann model of gas-liquid two-phase flow of incomprssible power-law fluid and its application in the displacement problem of porous media

A new incompressible gas-liquid two-phase flow model for non-Newtonian power-law fluid is proposed based on an incompressible lattice Boltzmann model. And the fundamental physical mechanism of Newtonian fluid displacing non-Newtonian power-law fluid liquid in porous medium is studied by using the proposed model. The effects of capillary number &lt;i&gt;Ca&lt;/i&gt;, dynamic viscosity ratio &lt;i&gt;M&lt;/i&gt;, surface wettability &lt;i&gt;θ&lt;/i&gt;, porous medium geometry, and power law index &lt;i&gt;n&lt;/i&gt; on the displacement process are investigated. The comprehensive results show that with the increase of capillary number, the displacement process turns faster, the fingering phenomenon becomes more obvious and the displacement efficiency decreases. However, for different values of power-law index &lt;i&gt;n&lt;/i&gt;, the effects of the &lt;i&gt;Ca&lt;/i&gt; on the displacement process have some differences. Specially, the decrease rate of displacement efficiency becomes slow if the displaced fluid is shear thickening fluid as compared with that if the displaced fluid is shear thinning fluid. On the other hand, the displacement efficiency decreases as dynamic viscosity ratio &lt;i&gt;M&lt;/i&gt; increases. And the effect of the viscosity ratio on the displacement process becomes more obvious for the low value of the power-law index &lt;i&gt;n&lt;/i&gt;. Moreover, the effect of the surface wettability of the porous medium on the displacement process is also related to the size of the power-law index. With the increase of the contact angle of the porous medium, the fingering phenomenon turns less obvious, and the displacement efficiency increases. However, with the increase of power-law index &lt;i&gt;n&lt;/i&gt;, the influence of the contact angle on the displacement process decreases. Besides, the displacement processes with different geometric types of the porous media are also studied in the work. The results show that comparing with the case of porous medium denoted by circle shape and square shape, the fingering phenomenon obtained by the case of triangular shape is most obvious, and the displacement efficiency is lowest.

A critical study of bending and thermo-mechanical stresses of a FG Timoshenko beam with various boundary conditions

Abstract A beam made up of functionally graded material is studied for its deformation and stress response under various thermo-mechanical loading conditions. The governing equations have been derived using the principle of virtual work within the framework of Timoshenko beams subjected to thermo-mechanical load. The material properties are assumed to vary according to power law equation; modulus of elasticity, modulus of rigidity, coefficient of thermal expansion and thermal conductivity vary across the beam height, while Poisson’s ratio is assumed to be a constant. The top and bottom surfaces of the beam are at elevated temperatures so as to have a thermal gradient across the height of beam. Exact solutions of the fourth order differential equation for the deformation and stress have been obtained for generalized boundary conditions. Comparative studies for purely thermal, purely mechanical and thermo-mechanical load have been reported to cover various ranges of temperatures with uniform, linear and non-linear temperature distributions. Transverse deflection and axial stress are plotted for a wide range of temperature gradients and power law index values for various boundary conditions for a given aspect ratio has been reported.

Two-phase mixed convection heat transfer and entropy generation analysis of a non-Newtonian nanofluid inside a cavity with internal rotating heater and cooler

In this study, mixed convection inside a square cavity filled with Cu-water nanofluid is simulated using the Eulerian two-phase mixture model. The base fluid is considered to be non-Newtonian and obeys from the power law. Two rotating cylinders are placed inside the heat exchanger and heat is transferred through the nanofluid from the hot cylinder to the cold one. In addition to the natural convection heat transfer inside the heat exchanger, rotation of the internal cylinders can provide forced convection heat transfer. The direction of rotation of cylinders can strengthen or weaken the natural convection effects in different regions, hence, four cases with various rotation directions for the cylinders are considered. The effects of changes in the value of imposed angular velocity (in terms of Richardson number), non-Newtonian power-law index, Rayleigh number and nanofluid volume fraction on both the heat transfer and entropy generation are discussed. The results have been illustrated that the shear-thinning or shear-thickening behavior of the non-Newtonian nanofluid can noticeably change the effect of forced convection on the heat transfer efficiency. Besides, regarding the values of Rayleigh number, Richardson number and non-Newtonian power-law index, the addition of nanoparticles into the non-Newtonian base fluid might adversely affect the heat transfer efficiency. In addition, to investigate irreversibilities, total entropy generation is discussed. It is indicated that shear-thinning nanofluids result in higher values of total entropy generation.

Non-linear radiative heat transfer analysis during the flow of Carreau nanofluid due to wedge-geometry: A revised model

In this article, an innovative revised Buongiorno's model is employed to investigate the flow of Carreau nanofluids generated by a wedge-shaped geometry. Moreover, heat and mass transfer characteristics are explored under the influence of non-linear thermal radiation. At first, the developed flow equations are made dimensionless via suitable transformations and then resulting set of nonlinear ordinary differential equations are solved numerically using built-in MATLAB solver bvp4c. It is observed that the solution of current flow problem is highly dependent on the contribution of several physical parameters like Weissenberg number, power-law index, wedge angle parameter, velocity ratio parameter, non-linear radiation parameter, suction parameter, Brownian motion and thermophoresis parameters, Lewis and Prandtl numbers. Detailed analysis for the novel results of dimensionless velocity, temperature and nanoparticles concentration with in the boundary layer region is exhibited graphically. The core physical implication of the computed results is that the thermal boundary layer is thinned by higher radiation parameter. This study reveals that an enhancement in the local Nusselt number is noted with higher temperature ratio parameter. On the other hand, an incremental skin friction ate the wall can be achieved by growing values of power-law index. The obtained data is distinguished with earlier studies and admirable agreement has been noted.

Fourier Power Spectra of Solar Noise Storms

We analyzed three noise storms recorded on 200 – 400 MHz Trieste Callisto radio spectra on 2 July 2012, 8 July 2012, and 16 July 2012 by the Fourier method. We divided intervals of the noise storms into five-minute intervals, and in these intervals we computed the mean Fourier spectra as a function of the wave numbers in the frequency and height-scale spaces. We found that these Fourier spectra, where the spectrum from the quiet-activity interval was subtracted, are power-law spectra. The mean power-law index of these spectra in the range $\ln(k_{z}) = [1.8, 2.9]$ (where $k_{z}$ is the wave number in the height-scale space) is $-1.7\pm0.14$ , $-1.6\pm0.14$ , and $-1.5 \pm0.12$ for the 2 July 2012, the 8 July 2012, and the 16 July 2012 noise storms, respectively. It appears that as the number of Type-I bursts in the studied interval increases, the power-law index becomes closer to $-5/3$ ; this is known as the Kolmogorov spectral index. The power-law index of the noise storms is very similar to that of the narrowband dm-spikes found in our previous studies. Furthermore, we found a break in the power spectra at $\ln(k_{z}) \approx2.9$ , and the mean power-law index values above this break are $-2.9\pm0.46$ , $-3.1\pm0.65$ , and $-3.4\pm0.98$ , respectively.

Analyzing primary resonant dynamics of functionally graded nanoplates based on a surface third-order shear deformation model

In the context of Gurtin-Murdoch (GM) surface elasticity theory, a size-dependent third-order shear deformable plate model is developed herein in order to study the nonlinear forced vibration behavior of rectangular nanoplates with considering surface stress effect. Nanoplates are assumed to be made of functionally graded materials (FGMs) whose properties are graded in the thickness direction based on a power-law distribution. First, the constitutive relations of GM model are matricized. Then, Hamilton’s principle is used to derive the governing equations. The variational differential quadrature, a numerical Galerkin, time periodic discretization, and pseudo arc-length methods are also employed for numerical solution of the geometrically nonlinear forced vibration problem. The frequency-response curves of rectangular nanoplates with different boundary conditions are investigated for different values of thickness, power-law index, surface constants and side length-to-thickness ratio. The results reveal that the surface stress has an important influence on the frequency-response curve of nanoplates at very small scales.

Numerical study of viscous dissipation and non-Boussinesq model effects on CMC–TiO2 fluid flow over backward facing step with baffle

The present work examined numerically the mixed convection of a non-Newtonian nanofluid flow through backward facing step with baffle. The Boussinesq and non-Boussinesq models are used to formulate the momentum equation, and the viscous dissipation is taken into account in the energy equation. The governing equations are discretized using the finite volume method. Effects of different key parameters such as Richardson number, temperature–viscosity coefficient, Brinkman number and power law index on both the heat transfer and the fluid flow characteristics are investigated. The results are presented in term of streamlines and isotherms contours as well as the average Nusselt number. The results show that both viscous dissipation and buoyancy forces affect greatly the flow and heat transfer structures. A multicellular zone is observed behind the step when considering the non-Boussinesq approximation for Ri ≥ 5 and taking into account viscous dissipation (Br = 0.5). In addition, the flow behavior for both Boussinesq and non-Boussinesq approximations is identical for Ri = 1 and totally different for Ri ≥ 5. Furthermore, in contrast of the non-Boussinesq approximation, considering the Boussinesq one overestimates the heat transfer rate, especially for low power law index values.

Numerical simulation of forced convective power law nanofluid through circular annulus sector

In this article, we have studied effect of two types of solid nanoparticles (i.e., TiO $$_{2}$$ and Cu) on the forced convective power law fluid flow through the annular sector duct. Finite volume method is used to transform governing nonlinear partial differential equations in algebraic form. A code is developed to solve resulting algebraic system of coupled equations with the help of strongly implicit procedure. Effect of concentration of solid nanoparticles on the velocity and temperature profiles is presented both in graphical and tabular form for different values of power law index. It has been observed that nanoparticles have pronounced effect in pseudo-plastic fluid as compared to dilatant fluid.

Enhanced dust emissivity power-law index along the western H α filament of NGC 1569

We used a data set from AKARI and Herschel images at wavelengths from 7 $\mu$m to 500 $\mu$m to catch the evidence of dust processing in galactic winds in NGC 1569. Images show a diffuse infrared (IR) emission extending from the galactic disk into the halo region. The most prominent filamentary structure seen in the diffuse IR emission is spatially in good agreement with the western H$\alpha$ filament (western arm). The spatial distribution of the $F_\mathrm{350}/F_\mathrm{500}$ map shows high values in regions around the super-star clusters (SSCs) and towards the western arm, which are not found in the $F_\mathrm{250}/F_\mathrm{350}$ map. The color-color diagram of $F_\mathrm{250}/F_\mathrm{350}$-$F_\mathrm{350}/F_\mathrm{500}$ indicates high values of the emissivity power-law index ($\beta_\mathrm{c}$) of the cold dust component in those regions. From a spectral decomposition analysis on a pixel-by-pixel basis, a $\beta_\mathrm{c}$ map shows values ranging from $\sim1$ to $\sim2$ over the whole galaxy. In particular, high $\beta_\mathrm{c}$ values of $\sim2$ are only observed in the regions indicated by the color-color diagram. Since the average cold dust temperature in NGC 1569 is $\sim30$ K, $\beta_\mathrm{c}<2.0$ in the far-IR and sub-mm region theoretically suggests emission from amorphous grains, while $\beta_\mathrm{c}=2.0$ suggests that from crystal grains. Given that the enhanced $\beta_\mathrm{c}$ regions are spatially confined by the HI ridge that is considered to be a birthplace of the SSCs, the spatial coincidences may indicate that dust grains around the SSCs are grains of relatively high crystallinity injected by massive stars originating from starburst activities and that those grains are blown away along the HI ridge and thus the western arm.

Effect of Bejan and Prandtl numbers on the design of tube arrangements in forced convection of shear thinning fluids: A numerical approach motivated by constructal theory

In this work, the effects of the pressure drop (i.e. the Bejan number in dimensionless term) and of the Prandtl number have been investigated with reference to optimal geometries for maximizing the heat transfer density under forced convection of shear thinning fluids. Constructal Design associated with Design of Experiments and Response Surface methodologies have been employed to search computationally for the optimals. More specifically, after having fixed the power law index value, n, equal to 0.4, we studied the effect of the Bejan number, Be, ranging from 104 to 105 (for Pr = 1) and the effect of the Prandtl number, Pr, ranging from 1 to 10 (for Be = 105) on the maximum dimensionless heat transfer density. The optimal geometries here detected differ much from those referred to Newtonian fluids, as a consequence of the non-linear stress behavior with respect to strain rate. We observed that the optimal aspect ratio of the elliptical tubes, ropt, highlights different (opposite) behaviours with the augmentation of Be and Pr: while ropt deacreases as Be increases, it augments with higher Pr, suggesting that for flows characterized by thermal diffusivity the tubes should be more slender horizontally for better heat transfer performance. In the meantime, assigned ropt, the dimensionless optimal distance between tubes, S˜0, proved to be practically indepent of all the tested values of Bejan number and Prandtl number.

Convective heat transfer and entropy generation analysis of non-Newtonian power-law fluid flows in parallel-plate and circular microchannels under slip boundary conditions

This study deals with convective heat transfer and entropy generation analysis of slip flow of non-Newtonian power-law fluids through parallel-plate and circular microchannels. The microchannels were subjected to uniform heat flux boundary condition at the wall. The governing equations relevant to both hydrodynamically and thermally fully developed laminar flows were analytically solved using non-linear slip boundary condition while also including viscous dissipation. Analytical closed form solution of the velocity profiles, temperature distributions, Nusselt number, entropy generation rate and Bejan number in terms of different parameters such as slip coefficient, power-law index and Brinkman number were obtained. The results indicate that increase of the slip coefficient leads to an increase in Nusselt number and a decrease in average entropy generation rate. The effect of slip coefficient on Bejan number is strongly affected by Brinkman number. Low values of either power-law index or Brinkman number result in better working performance of microfluidic systems. Under same conditions, parallel-plate microchannel produce more entropy than circular microchannel. Viscous dissipation significantly affects heat transfer and entropy generation characteristics and cannot be neglected. The results of current study are helpful in deep understanding of flow and heat transfer rates and also designing more thermally efficient microfluidic devices which utilize non-Newtonian fluids.

Heat transfer enhancement in suddenly expanding annular shear-thinning flows

Heat transfer enhancement in suddenly expanding annular pipe flows of Newtonian and shear-thinning non-Newtonian fluids is studied within the steady laminar flow regime. Conservation of mass, momentum, and energy equations, along with the power-law constitutive model are numerically solved. The impact of inflow inertia, annular-diameter-ratio, k, power-law index, n, and Prandtl numbers, is reported over the following range of parameters: Re = {50, 100, 150}, k = {0, 0.5, 0.7}; n = {1, 0.8, 0.6}; and Pr = {1, 10, 100}. Heat transfer enhancement downstream of the expansion plane, i.e., Nusselt numbers greater than the downstream fully developed value, Nu/Nufd > 1, is only observed for Pr = 10 and 100. In general, higher Prandtl numbers, power-law index values, and annular-diameter-ratios, result in more significant heat transfer enhancement downstream of the expansion plane. Heat transfer augmentation, for Pr = 10 and 100, increases with the annular-diameter-ratio. For a given annular-diameter-ratio and Reynolds numbers, increasing the Prandtl number from Pr = 10 to Pr = 100, always results in higher peak Nu values, Numax, for both Newtonian and shear-thinning flows. All Numax values are located downstream of the flow reattachment point, in the case of suddenly expanding round pipe flows, i.e., κ = 0. However, for suddenly expanding annular pipe flows, i.e., κ = 0.5 and 0.7, Numax values appear upstream the flow reattachment point. For Pr = 10 and 100, shear-thinning flows display two local peak Nu/Nufd values, in comparison with one peak value in the case of Newtonian flows. The highest heat transfer enhancement, Numax/Nufd ≈ 5, is observed at κ = 0.7, n = 0.6, and Pr = 100.

A critical study of stresses of FG Timoshenko Beams using B-spline Collocation

A functionally graded material beam of rectangular cross-section is studied for bending and shear stresses under uniformly distributed mechanical load. The gradation is assumed to be along the height of the beam and follows power law. The governing equations are derived using principle of virtual work in the framework of Timoshenko beams which is solved numerically using sixth order B-spline collocation technique with Greville abscissa as collocation points. The variation in the position of neutral axis, variations in bending (axial) and shear stresses at different positions along a cross-section corresponding to different power law index values have been reported. It has been observed that shift in neutral axis governs the stress distribution along the cross-section.