Non-homogeneous Model Research Articles

Heat transfer enhancement compared to entropy generation by imposing magnetic field and hybrid nanoparticles in mixed convection of a Bingham plastic fluid in a ventilated enclosure

PurposeThe purpose of this study is to analyze the nonhomogeneous model on the mixed convection of Al2O3–Fe3O4 Bingham plastic hybrid nanofluid in a ventilated enclosure subject to an externally imposed uniform magnetic field. Entropy generation and the pressure drop are determined to analyze the performance of the heat transfer. The significance of Joule heating arising due to the applied magnetic field on the heat transfer of the yield stress fluid is described.Design/methodology/approachThe ventilation in the enclosure of heated walls is created by an opening on one vertical wall through which cold fluid is injected and another opening on the opposite vertical wall through which fluid can flow out.FindingsThis study finds that the inclusion of Fe3O4 nanoparticles with the Al2O3-viscoplastic nanofluid augments the heat transfer. This rate of enhancement in heat transfer is higher than the rate by which the entropy generation is increased as well as the enhancement in the pressure drop. The yield stress has an adverse effect on the heat transfer; however, it favors thermal mixing. The magnetic field, which is acting opposite to the direction of the inlet jet, manifests heat transfer of the viscoplastic hybrid nanofluid. The horizontal jet of cold fluid produces the optimal heat transfer.Originality/valueThe objective of this study is to analyze the impact of the inclined cold jet of viscoplastic electrically conducting hybrid nanofluid on heat transfer from the enclosure in the presence of a uniform magnetic field. The combined effect of hybrid nanoparticles and a magnetic field to enhance heat transfer of a viscoplastic fluid in a ventilated enclosure has not been addressed before.

Non-homogeneous Poisson and linear regression models as approaches to study time series with change-points

In this study we consider some stochastic models and a Bayesian approach to analyze count time series data in the presence of one or more change-points. When the observed count data are all different of zero, it is possible to perform an analysis using linear regression models with normal distribution errors for the log-transformed data. When we have the presence of zero counts at different times, the statistical model based on the log-transformation is not suitable. Hence, in this case, it is possible to consider non-homogeneous Poisson processes (NHPP) models with a suitable rate function. In the present work we consider both models (linear regression and Poisson) to analyze three data sets. These sets are data recording the monthly visitors to New Zealand with the purpose of education, yearly tuberculosis incidence data from New York City, and monthly measles incidence data from Brazil. When the NHPP model is used a PLP (power law process) model is assumed for the intensity function. Additionally, in both models, the presence of change-points will be allowed.

Steerable Music Generation which Satisfies Long-Range Dependency Constraints

Although music is full of repetitive motifs and themes, artificially intelligent temporal sequence models have yet to demonstrate the ability to model or generate musical compositions that satisfy steerable, long-range constraints needed to evoke such repetitions. Markovian approaches inherently assume a strictly limited range of memory while neural approaches—despite recent advances in evoking long-range dependencies—remain largely unsteerable. More recent models have been published that attempt to evoke repetitive motifs by imposing unary constraints at intervals or by collating copies of musical segments. Although the results of these methods satisfy long-range dependencies, they come with significant—potentially prohibitive—sacrifices in the musical coherence of the generated composition or in the breadth of satisfying compositions which the model can create. We present R<small>EGUALR</small> non-homogeneous Markov models as a solution to the long-range dependency problem which uses R<small>ELATIONAL</small> automata to enforce binary constraints to compose music with repeating motifs. The solution we present preserves musical coherence (i.e., Markovian constraints) for the duration of the generated compositions and significantly increases the range of satisfying compositions that can be generated.

Effects of sediment diameter and concentration on cavitation characteristics and mechanism

The synergistic erosion caused by cavitation and abrasion is a common and severe problem for hydraulic machinery. In order to explore the mechanism of particles size and concentration effect on cavitation, taking the rotating disk as the research object. The solid-liquid-gas three-phase flow was calculated based on the non-homogeneous multiphase flow model, modified RNG k−εturbulence model, and ZGB model. The increase of particles size firstly inhibited the bubbles (0.02 mm ≤ d ≤ 0.1 mm) and then promoted the bubbles (0.1 mm <d ≤ 0.4 mm); When 0.27 mm < d ≤ 0.4 mm, both cavitation area and cavitation damage intensity are more significant than those of cavitation alone. When d = 0.1 mm, 1% ≤ Cv ≤ 10%, the increase of particles concentration promotes bubbles. However, that only enhances the cavitation area, but has little effect on the cavitation damage intensity. When particles severely inhibit the bubbles, the vortex rotation effect is the strongest, and the mainstream promotion and re-entrant jet inhibition effect are the strongest. The purpose of this paper is to provide some theoretical basis for exploring the mechanism of synergistic erosion.

Significance of Lorentz forces on Jeffrey nanofluid flows over a convectively heated flat surface featured by multiple velocity slips and dual stretching constraint: a homotopy analysis approach

Abstract Motivated by the temporal relaxation feature of the Jeffrey model and its practical uses in the rheological modeling of several vital liquids, this study aimed to present a theoretical analysis of three-dimensional MHD Jeffrey nanofluid flows over a dual stretching surface with velocity slip conditions. By adopting the nonhomogeneous nanofluid model along with the passive control approach of nanoparticles, the current flow problem is solved semi-analytically via the homotopy analysis method for convective heating and multiple slip conditions. Dynamically, the magnetic and viscoelastic parameters have a declining effect on the velocity distributions in both directions in the existence and absence of slip effects, while the Deborah number has generally an escalating influence on the flow distributions. On the other hand, the variations of the velocity profiles in both directions are always greater in the presence of slip effect as compared to the nonslip case. Besides, the velocity stretching factor rises the velocity profiles in both directions. Furthermore, this increasing impact is dominant for the velocity distribution along the $y{\rm{-}}$direction as compared to the velocity field along the $x{\rm{-}}$direction. Thermally, the greater Biot number increases the temperature distribution. However, the bigger Schmidt number reduces the concentration distribution.

MHD radiative ohmic heating nanofluid flow of a stretching penetrable wedge: A numerical analysis

AbstractThe present numerical investigation has focused on the magnetohydrodynamics flow of a viscous nanofluid over a stretching wedge with the boundary convective conditions, thermal radiation, and ohmic heating. Buongiorno's two‐component nonhomogeneous nanoscale model was used and a dilute nanofluid with spherical type particles is considered. Similarity transformations are used to render the system of governing partial differential equations into a system of coupled similarity equations. The transformed equations are solved numerically with the BVP4C method. Validation of solutions with previous studies based on special cases of the general model is included. The salient features of fluid velocity profile, temperature as well as concentration profiles are discussed in a graphical manner for various values of selected governing factors. The skin friction coefficient, mass, and heat transfer rates are calculated and summarized. It is worthwhile noticing that the validation results exhibit an excellent agreement with already existing reports. The modeling of the present problem is useful in the thermal processing of sheet‐like substances that is a necessary operation in paper procurement, wire drawing, drawing of plastic films, polymeric sheets, and metal spinning.

Modeling and simulation of needle electrical impedance myography in nonhomogeneous isotropic skeletal muscle.

Needle electrical impedance myography (EIM) is a recently developed technique for neuromuscular evaluation. Despite its preliminary successful clinical application, further understanding is needed to aid interpreting EIM outcomes in nonhomogeneous skeletal muscle measurements. The framework presented models needle EIM measurements in a bidomain isotropic model. Finite element method (FEM) simulations verify the validity of our model predictions studying two cases: a spherical volume surrounded by tissue and a two-layered tissue. Our models show that EIM is influenced by the vicinity of tissue with different electrical properties. The apparent resistance, reactance and phase relative errors between our theoretical predictions and FEM simulations in the spherical volume case study are ≤0.2%, ≤1.2% and ≤1.0%, respectively. For the two-layered tissue model case study, the relative errors are ≤2%. We propose a bio-physics driven analytical framework describing needle EIM measurements in a nonhomogeneous bidomain tissue model. Our theoretical predictions may lead to new ways for interpreting needle EIM data in neuromuscular diseases that cause compositional changes in muscle content, e.g. connective tissue deposition within the muscle. These changes will manifest themselves by changing the electric properties of the conductor media and will impact impedance values.

A two- and three-dimensional mesoscopic method for an updated non-homogeneous model of Newtonian and non-Newtonian nanofluids

A mesoscopic method based on a lattice Boltzmann method (LBM) for simulation of Newtonian and non-Newtonian nanofluids has been introduced. This investigation is a continuation of our recent study [G. H. R. Kefayati and A. Bassom, “A lattice Boltzmann method for single and two phase models of nanofluids: Newtonian and non-Newtonian nanofluids,” Phys. Fluids 33, 102008 (2021)], which proposed a two-dimensional LBM for a non-homogeneous model of nanofluids with Brownian diffusion and thermophoresis. Here, this model is improved by considering thermodynamic consistency, deposition rate, nanoparticle thermal dispersion, and hydrodynamic interactions around the nanoparticles, which are evaluated and reported in some thermodynamic and experimental observations. The proposed method is also developed for three-dimensional cases, applying all the above-mentioned elements. The revised macroscopic governing equations of mass (one for the carrier fluid and the other for the nanoparticles), momentum, and energy by considering the newly mentioned elements are presented, and then the proposed LBM, which has the ability to recover equations, is introduced while the derivations and proofs are provided. Different elements of the present code are validated with previous studies and demonstrated good agreement. To apply and evaluate the model in a case study, natural convection of Newtonian, shear-thinning, and viscoplastic nanofluids in a side-heated two-dimensional square enclosure and in a cubic cavity are investigated. The results for various volume fractions of nanofluids and Grashof numbers are shown in the formats of isotherms, streamlines, nanoparticle distributions, and local and average Nusselt numbers on the hot wall. In addition, the yielded/unyielded regions for viscoplastic nanofluids are defined and depicted.

Heat and mass transfer of a molten polymer conveying nanoparticles in a wire coating process with temperature-dependent fluid properties: Optimization using Response surface method

Heat and mass transfer rates play a significant role in achieving a high-efficiency, low-cost wire coating process. Therefore, the flow analysis of molten polymer (polyvinyl chloride) carrying nanoparticles inside a pressure-type die is presented. The third-grade liquid model is used for the constitutive equation of the polyvinyl chloride (PVC), while the non-homogeneous biphasic model is used for nanoparticles. The properties of PVC are temperature-dependent. The melt flow is governed by the modified Navier-Stokes equation for the third-grade fluid, energy conservation, and nanoparticles' continuity equation. The finite difference method-based routine is applied to solve the nonlinear differential equations that include nine physical parameters. The Response Surface Method (RSM) is implemented to optimize the heat/mass transfer rate coated wire's eminence depends on the coating material's rheological characteristics of PVC. Full quadratic correlation models for heat/mass transfer rate of melt are proposed through central-composite-design (CCD). The optimal level of third-grade fluid factor and nanofluid factors was determined to achieve an optimum heat/mass transfer rate of the melt. The rheological characteristics of PVC have been improved due to the temperature-dependent viscosity and shear thickening/thinning property of the melt. The nanofluid factors improve the thermal field and subsequently reduce the Nusselt number. Maximum heat transfer occurs for a low level of Brownian factor, a high level of thermophoresis factor, and a third-grade fluid factor of 0.2177, also reaching the maximum mass transfer simultaneously.

Remarks on Analytical Solutions of a Non-Homogeneous Gas Dynamic Model via Successive Approximation Method

The Successive Approximation Method (SAM) is introduced in this research to solve the non-homogeneous Gas Dynamic Equation (GDE). This GDE’s analytical solution is expressed via the SAM, in series form, with readily computed components. The proposed technique is used directly, without transformation, discretization, linearization, or any restrictive assumptions.

Mixed convection of nanofluid by two-phase model in an inclined cavity with variable aspect ratio

In this numerical study, the laminar mixed cross-convection of incompressible nanofluid in a two-dimensional inclined cavity with various aspect ratios is investigated. A nonhomogeneous Buongiorno's model is taken into account. Transport mechanisms incorporating the effects of Brownian motion, thermophoresis diffusion, Soret-Dufour effect are analyzed. The energy governing equation includes both regular diffusion and cross-diffusion terms. The numerical analysis is performed by the collocation spectral method (CSM) based on the fast cosine transformation (FCT). The improved projection scheme (IPS) is specially modified with help of FCT to decouple the pressure and the velocities. The combined effects of inclined cavity angle γ, aspect ratio A, thermophoresis parameters Nt, Brownian motion parameter Nb, Dufour diffusicity Df, Soret diffusicity Sr, along with Re, Gr, Pr, Le, Ln and buoyancy ratios Br, Nb, Nr, etc., on the developments of streamlines, isotherms, solutal isoconcentrations and nanoparticle isoconcentrations as well as on the average Nusselt and Sherwood numbers, are analyzed and discussed in detail. The results indicate that the above parameters, especially γ and A, have substantial effects on the flow, heat and mass transfer. The distributions of temperature, solutal concentration and nanoparticle concentration are changed completely. The cross-diffusive effects including Dufour-Soret effect can't be ignored.

Nonhomogeneous poisson process model of summer high temperature extremes over China

In this study, nonhomogeneous Poisson process (NHPP) models arising from the extreme value theory have been fitted to summer high temperature extremes (HTEs) at 321 meteorological stations over China. The seasonality and six prominent atmospheric teleconnection patterns in Northern Hemisphere are incorporated in the NHPP models reflecting the non-stationarity of occurrence rate in Poisson process of HTEs. In addition, Poisson regression model has also been applied to link HTEs and these teleconnection patterns. The linkages of HTEs and teleconnection patterns have been identified in both NHPP modeling and Poisson regression. Composite maps of differences of 500-hPa geopotential height and wind fields in the positive and negative phases of teleconnection patterns are constructed to show the impacts of atmospheric circulation patterns on extreme heat events. The spatial pattern of the associated anticyclonic or cyclonic circulations with teleconnection patterns partly explains the spatial variability of the occurrences of summer HTEs over China.

Modeling and validation of nonlinear voltage-current characteristics of ITER PF joint sample tested in the SULTAN facility

The International Thermonuclear Experimental Reactor poloidal field (PF) coils are wound into double pancakes with NbTi cable-in-conduit conductors, which are connected by joints in shaking hands lap-type configuration. The coils are operating in pulsed mode with a maximum operating current of 55 kA and peak magnetic field of 6.4 T, utilizing electromagnetic load on the conductors and joints. A series of PF qualification joint samples modified in praying hands configuration is measured in the SULTAN facility. For some samples, a nonlinear voltage-current (VI) characteristic is observed during the assessment of joint resistance. The growth of joint resistance versus the B× I product is larger than what is expected from the magneto-resistant copper contribution. Two non-homogeneous contact resistance models are developed and combined to quantitatively evaluate the reason for the nonlinear VI behavior in combination with the relevant power dissipation and current redistribution in the joint. The simulations reveal that, for the particular pre-qualification PFJEU2 sample with resistance variation up to 3.5 nΩ, the most probable reason for the nonlinear VI characteristic is a widely spread defective connection between copper sole and shim. The electromagnetic force involves a separation effect on the mechanically and electrically weakly connected parts, resulting into a varying resistance depending on transport current and background field. The hypothesis and models are validated by an experiment on a similar sample PFJEU3 and a post-mortem examination of the PFJEU2 sample.

Maintenance Decision Optimization of Multi-State System Considering Imperfect Maintenance

In the maintenance decision-making problem of a multi-state system, it is more in line with the actual situation to consider imperfect maintenance. However, under the influence of imperfect maintenance, the failure mechanism and maintenance process of the multi-state system are more complicated. Further discussion is needed about how to deal with the relationship between the states of various components and the overall state of the system, and how to make the optimal maintenance strategy. To address this issue, this paper proposes a multi-state system maintenance decision optimization method considering imperfect maintenance. Firstly, an imperfect maintenance model is established based on quasi-renewal theory. Secondly, the mapping relationship between the state of the components and the system is decoupled combining universal generating function with the non-homogeneous continuous-time Markov model, the reliability evaluation of the multi-state system is realized. Finally, the maintenance decision optimizing model considering imperfect maintenance is constructed, the optimal maintenance strategy of the multi-state system is obtained by optimizing the number of imperfect maintenance actions to maximize the expected benefit of the whole life cycle.

The application of an optimized fractional order accumulated grey model with variable parameters in the total energy consumption of Jiangsu Province and the consumption level of Chinese residents

&lt;abstract&gt; &lt;p&gt;Fractional order imply the idea of "in between", the grey model generated by fractional accumulation has better prediction and adaptability than that generated by first-order accumulation. General grey model of the differential equation of the left is a cumulative function derivative of time, in order to improve the adaptability of the model and prediction ability, general fractional order differential equation model is presented. In this paper, on the basis of the derivation of time $ t $ extensions to the derivation of $ {t^u} $, added a variable coefficient, and through the integral differential equation and tectonic background value. We establish an optimized fractional order cumulative grey model with variable parameters, i.e., optimized fractional order accumulated grey model (FOGM (1, 1)). By using the Particle swarm optimization (PSO) algorithm, we search for the order and variable parameters of the optimal fractional order. Then we apply the proposed model to predict the total energy consumption of Jiangsu province and the consumption level of Chinese residents. The results indicate that the proposed model has high fitting and prediction accuracy compared to other classical grey prediction models, such as grey model (GM (1, 1)), non-homogeneous grey model (NGM (1, 1)) and fractional order accumulated grey model (FGM (1, 1)). It also validates that the proposed model is a practical and promising model for forecasting the energy consumption as well as the consumption level of Chinese residents.&lt;/p&gt; &lt;/abstract&gt;

Experimental Study on Microbial Induced Calcium Carbonate Precipitation to Enhance Reservoir Recovery.

Background: Bacillus subtilis can produce urease in the presence of urea as the main carbon source and induce mineralization in the presence of precipitable cations.Objectives: The objective of our study was to demonstrate that Bacillus subtilis catabolizes glucose first in the presence of both glucose and urea carbon sources. Using its feature of catabolizing glucose first to delay the mineralization time, it proved its potential application in enhancing the recovery of heterogeneous reservoirs.Material and Methods: The metabolic process of Bacillus subtilis was monitored by changing the glucose content in the bacterial medium by UV spectrophotometer and pH meter. Using a non-homogeneous physical model, experiments were conducted to improve reservoir recovery by microbial mineralization after polymer oil drive.Results: The higher the glucose content in the medium, the longer the time for the pH of the bacterial solution to reach 7 and the longer the end of the logarithmic phase of growth. the glucose content of the 48 h medium was significantly correlated with the consumption of the bacteria and the quality of the precipitation. In the oil drive experiment the permeability of the high permeability model was reduced from 1200 md to 136 md with a reduction rate of 88.6 %, and the permeability of the low permeability model was reduced by 22 md, and the crude oil recovery was increased by 7.9 %. Conclusions: It was demonstrated that the addition of glucose to the culture medium retarded the mineralization of bacteria. Only 0.2 times the pore volume of the bacterial solution and the cementing solution is required to form an effective seal, thus improving the recovery of crude oil.

Exponential bounds of ruin probabilities for non-homogeneous risk models

Exponential bounds of ruin probabilities for non-homogeneous risk models

Towards a new MHD non-homogeneous convective nanofluid flow model for simulating a rotating inclined thin layer of sodium alginate-based Iron oxide exposed to incident solar energy

In today's era, energy resources are among the essential objectives for the economic advancement of any developed country. Alternatively, fossil fuels that meet a large percentage of the world's energy needs are becoming increasingly rare and their quantity is dwindling. Solar systems which convert solar radiation into useable heat or electricity now play a vital part in the production of renewable energies. Solar energy, despite its somewhat higher operating costs, is a better alternative energy type when considering environmental safety and substantial uncertainty about future energy provisions. Due to the demand for solar radiation in nowadays era, the features of solar radiation towards the heat transfer of three-dimensional magnetohydrodynamic generalized and sodium alginate-based iron oxide Fe3O4- SA nanofluid flows past a spinning disk are investigated in this article. Furthermore, the Brownian motion and thermophoresis phenomena, and Arrhenius activation energy are taken into account. The obtained equations are altered from partial differential equations into ordinary differential equations with the help of reasonable similarity transformations. The transformed system is solved thereafter semi-analytically by the homotopy analysis method. The convergence area of the applied technique is displayed with the help of figures and tables. Here, we have found that the variation in sodium alginate-based iron oxide nanofluid due to film width is greater as compared to generalized nanofluid. The greater magnetic parameter has reduced the velocity profiles. Also, the generalized nanofluid has gained extraordinary velocity as compared to Fe3O4- SA nanofluid. On the other hand, the greater thermophoresis parameter has augmented the temperature profile while the opposing impact is observed for the concentration profile. Additionally, the generalized nanofluid has gained the greater variation in temperature profile as compared to Fe3O4- SA nanofluid, while no difference is found for concentration profile. The augmented absorption parameter, irradiance parameter, and thermal Biot number have amplified the temperature profile. In addition, the temperature profile of the generalized nanofluid increases significantly as compared to Fe3O4- SA nanofluid.

A Nonhomogeneous Bulk Flow Model for Gas in Liquid Flow Annular Seals: An Effort to Produce Engineering Results

Abstract Seals in multiple-phase rotordynamic pumps must operate without compromising system efficiency and stability. Both field operation and laboratory experiments show that seals supplied with a gas in liquid mixture (bubbly flow) can produce rotordynamic instability and excessive rotor vibrations. This paper advances a nonhomogeneous bulk flow model (NHBFM) for the prediction of the leakage and dynamic force coefficients of uniform clearance annular seals lubricated with gas in liquid mixtures. Compared to a homogeneous bulk flow model (HBFM), the current model includes diffusion coefficients in the momentum transport equations and a field equation for the transport of the gas volume fraction (GVF). Published experimental leakage and dynamic force coefficients for two seals supplied with an air in oil mixture whose GVF varies from 0% (pure liquid) to 20% serve to validate the novel model as well as to benchmark it against predictions from a HBFM. The first seal withstands a large pressure drop (∼38 bar) and the shaft speed equals 7.5 krpm. The second seal restricts a small pressure drop (1.6 bar) as the shaft turns at 3.5 krpm. The first seal is typical as a balance piston whereas the second seal is found as a neck-ring seal in an impeller. For the high pressure seal and inlet GVF = 0.1, the flow is mostly homogeneous as the maximum diffusion velocity at the seal exit plane is just ∼0.1% of the liquid flow velocity. Thus, both the NHBFM and HBFM predict similar flow fields, leakage (mass flow rate), and drag torque. The difference between the predicted leakage and measurement is less than 5%. The NHBFM direct stiffness (K) agrees with the experimental results and reduces faster with inlet GVF than the HBFM K. Both direct damping (C) and cross-coupled stiffness (k) increase with inlet GVF &amp;lt; 0.1. Compared to the test data, the two models generally under predict C and k by ∼25%. Both models deliver a whirl frequency ratio (fw) ∼ 0.3 for the pure liquid seal, hence closely matching the test data. fw raises to ∼0.35 as the GVF approaches 0.1. For the low-pressure seal, the flow is laminar; the experimental results and both NHBFM and HBFM predict a null direct stiffness (K). At an inlet GVF = 0.2, the NHBFM predicted added mass (M) is ∼30% below the experimental result while the HBFM predicts a null M. C and k predicted by both models are within the uncertainty of the experimental results. For operation with either a pure liquid or a mixture (GVF = 0.2), both models deliver fw = 0.5 and equal to the experimental finding. The comparisons of predictions against experimental data demonstrate that the NHBFM offers a marked improvement, in particular for the direct stiffness (K). The predictions reveal that the fluid flow maintains the homogeneous character known at the inlet condition.

Local well-posedness of nonhomogeneous incompressible liquid crystals model without compatibility condition

This paper is concerned with the nonhomogeneous incompressible model for the nematic liquid crystals in a smooth bounded domain Ω⊂R3 with vacuum being allowed. Compared with the results before, we proof the local existence of a unique strong solution without assuming any compatibility condition to the initial data.