Advancements in Numerical Solutions:Fractal Runge-Kutta Approach to Model Time-Dependent MHD Newtonian Fluid with Rescaled Viscosity on Riga Plate

Fractal time-dependent issues in fluid dynamics provide a distinct difficulty in numerical analysis due to their complex characteristics,necessitating specialized computing techniques for precise and economical solutions.This study presents an innovative computational approach to tackle these difficulties.The main focus is applying the Fractal Runge-Kutta Method to model the time-dependent magnetohydrodynamic(MHD)Newtonian fluid with rescaled viscosity flow on Riga plates.An efficient computational scheme is proposed for handling fractal timedependent problems in flow phenomena.The scheme is comprised of three stages and constructed using three different time levels.The stability of the scheme is shown by employing the Fourier series analysis to solve scalar problems.The scheme’s convergence is guaranteed for a time fractal partial differential equations system.The scheme is applied to the dimensionless fractal heat and mass transfer model of incompressible,unsteady,laminar,Newtonian fluid with rescaled viscosity flow over the flat and oscillatory Riga plates under the effects of spaceand temperature-dependent heat sources.The first-order back differences discretize the continuity equation.The results show that skin friction local Nusselt number declines by raising the coefficient of the temperature-dependent term of heat source and Eckert number.The numerical simulations provide valuable insights into fluid dynamics,explicitly highlighting the influence of the temperature-dependent coefficient of the heat source and the Eckert number on skin friction and local Nusselt number.

Influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel

The influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel is investigated.The DarcyBrinkman model is used to characterize the fluid flow dynamics in porous materials.The analytical solutions are obtained for the unidirectional and completely developed flow.Based on a normal mode analysis,the generalized eigenvalue problem under a perturbed state is solved.The eigenvalue problem is then solved by the spectral method.Finally,the critical Rayleigh number with the corresponding wavenumber is evaluated at the assigned values of the other flow-governing parameters.The results show that increasing the Darcy number,the Lewis number,the Dufour parameter,or the Soret parameter increases the stability of the system,whereas increasing the inclination angle of the channel destabilizes the flow.Besides,the flow is the most unstable when the channel is vertically oriented.

GLOBAL SOLUTIONS TO 1D COMPRESSIBLE NAVIER-STOKES/ALLEN-CAHN SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND FREE-BOUNDARY

This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.

Modeling time-dependent mechanical behavior of hard rock considering excavation-induced damage and complex 3D stress states

To investigate the long-term stability of deep rocks,a three-dimensional(3D)time-dependent model that accounts for excavation-induced damage and complex stress state is developed.This model comprises three main components:a 3D viscoplastic isotropic constitutive relation that considers excavation damage and complex stress state,a quantitative relationship between critical irreversible deformation and complex stress state,and evolution characteristics of strength parameters.The proposed model is implemented in a self-developed numerical code,i.e.CASRock.The reliability of the model is validated through experiments.It is indicated that the time-dependent fracturing potential index(xTFPI)at a given time during the attenuation creep stage shows a negative correlation with the extent of excavationinduced damage.The time-dependent fracturing process of rock demonstrates a distinct interval effect of the intermediate principal stress,thereby highlighting the 3D stress-dependent characteristic of the model.Finally,the influence of excavation-induced damage and intermediate principal stress on the time-dependent fracturing characteristics of the surrounding rocks around the tunnel is discussed.

Impact of different interaction behavior on epidemic spreading in time-dependent social networks

We investigate the impact of pairwise and group interactions on the spread of epidemics through an activity-driven model based on time-dependent networks.The effects of pairwise/group interaction proportion and pairwise/group interaction intensity are explored by extensive simulation and theoretical analysis.It is demonstrated that altering the group interaction proportion can either hinder or enhance the spread of epidemics,depending on the relative social intensity of group and pairwise interactions.As the group interaction proportion decreases,the impact of reducing group social intensity diminishes.The ratio of group and pairwise social intensity can affect the effect of group interaction proportion on the scale of infection.A weak heterogeneous activity distribution can raise the epidemic threshold,and reduce the scale of infection.These results benefit the design of epidemic control strategy.

A process-oriented approach for identifying potential landslides considering time-dependent behaviors beyond geomorphological features

Geomorphological features are commonly used to identify potential landslides.Nevertheless,overemphasis on these features could lead to misjudgment.This research proposes a process-oriented approach for potential landslide identification that considers time-dependent behaviors.The method integrates comprehensive remote sensing and geological analysis to qualitatively assess slope stability,and employs numerical analysis to quantitatively calculate aging stability.Specifically,a time-dependent stability calculation method for anticlinal slopes is developed and implemented in discrete element software,incorporating time-dependent mechanical and strength reduction calculations.By considering the time-dependent evolution of slopes,this method highlights the importance of both geomorphological features and time-dependent behaviors in landslide identification.This method has been applied to the Jiarishan slope(JRS)on the Qinghai-Tibet Plateau as a case study.The results show that the JRS,despite having landslide geomorphology,is a stable slope,highlighting the risk of misjudgment when relying solely on geomorphological features.This work provides insights into the geomorphological characterization and evolution history of the JRS and offers valuable guidance for studying slopes with similar landslide geomorphology.Furthermore,the process-oriented method incorporating timedependent evolution provides a means to evaluate potential landslides,reducing misjudgment due to excessive reliance on geomorphological features.

Numerical Simulation and Entropy Production Analysis of Centrifugal Pump with Various Viscosity

The fluid’s viscosity significantly affects the performance of a centrifugal pump.The entropy production method and leakage are employed to analyze the performance changes under various viscosities by numerical simulation and validated by experiments.The results showed that increasing viscosity reduces both the pump head and efficiency.In addition,the optimal operating point shifts to the left.Leakage is influenced by vortex distribution in the front chamber and boundary layer thickness in wear-ring clearance,leading to an initial increase and subsequent decrease in leakage with increasing viscosity.The total entropy production Spro,Total inside the pump rises with increasing viscosity.The different mechanisms dominate under varying conditions:Turbulent dissipation dominates at low viscosity.Under high-viscosity conditions,energy loss is primarily caused by direct dissipation Spro,D and wall entropy production Spro,W.This study provides a deeper and more objective understanding of the energy characteristics of centrifugal pumps handling fluids of various viscosity,potentially aiding in optimizing pump design and improving energy conversion efficiency.

Determination of liquid viscosity based on dual-frequency-bandparticle tracking

An optical-tweezers-based dual-frequency-band particle tracking system was designed and fabricated for liquid viscositydetection. On the basis of the liquid viscosity dependent model of the particle’s restricted Brownian motion with theFax´en correction taken into account, the liquid viscosity and optical trap stiffness were determined by fitting the theoreticalprediction with the measured power spectral densities of the particle’s displacement and velocity that were derived from thedual-frequency-band particle tracking data. When the SiO2 beads were employed as probe particles in the measurements ofdifferent kinds of liquids, the measurement results exhibit a good agreement with the reported results, as well as a detectionuncertainty better than 4.6%. This kind of noninvasive economical technique can be applied in diverse environments forboth in situ and ex situ viscosity detection of liquids.

Construction of coal pitch-based HA-K grafted poly condensates and their excellent anti-temperature and viscosity-reducing properties

Humic acids(HAs)are widely used as filtrate and viscosity reducers in drilling fluids.However,their practical utility is limited due to poor stability in salt resistance and high-temperature resistance.Hightemperature coal pitch(CP)is a by-product from coal pyrolysis above 650℃.The substance's molecular structure is characterized by a dense arrangement of aromatic hydrocarbon and alkyl substituents.This unique structure gives it unique chemical properties and excellent drilling performance,surpassing traditional humic acids in drilling operations.Potassium humate is prepared from CP(CP-HA-K)by thermal catalysis.A new type of high-quality humic acid temperature-resistant viscosity-reducer(Graft CP-HA-K polymer)is synthesized with CP-HA-K,hydrolyzed polyacrylonitrile sodium salt(Na-HPAN),urea,formaldehyde,phenol and acrylamide(AAM)as raw materials.The experimental results demonstrate that the most favorable conditions for the catalytic preparation of CP-HA-K are 1 wt%catalyst dosage,30 wt%KOH dosage,a reaction temperature of 250℃,and a reaction time of 2 h,resulting in a maximum yield of CP-HA-K of 39.58%.The temperature resistance of the Graft CP-HA-K polymer is measured to be 177.39℃,which is 55.39℃ higher than that of commercial HA-K.This is due to the abundant presence of amide,hydroxyl,and amine functional groups in the Graft CP-HA-K polymer,which increase the length of the carbon chains,enhance the electrostatic repulsion on the surface of solid particles.After being aged to 120℃ for a specified duration,the Graft CP-HA-K polymer demonstrates significantly higher viscosity reduction(42.12%)compared to commercial HA-K(C-HA-K).Furthermore,the Graft CP-HA-K polymer can tolerate a high salt concentration of 8000 mg.L-1,measured after the addition of optimum amount of 3 wt%Graft CP-HA-K polymer.The action mechanism of Graft CP-HA-K polymer on high-temperature drilling fluid is that the Graft CP-HA-K polymer can increase the repulsive force between solid particles and disrupt bentonite's reticulation structure.Overall,this research provides novelty insights into the synthesis of artificial humic acid materials and the development of temperature-resistant viscosity reducers,offering a new avenue for the utilization of CP resources.

A GENERALIZED SCALAR AUXILIARY VARIABLE METHOD FOR THE TIME-DEPENDENT GINZBURG-LANDAU EQUATIONS

This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.

Nuclear magnetic resonance experiments on the time-varying law of oil viscosity and wettability in high-multiple waterflooding sandstone cores

A simulated oil viscosity prediction model is established according to the relationship between simulated oil viscosity and geometric mean value of T2spectrum,and the time-varying law of simulated oil viscosity in porous media is quantitatively characterized by nuclear magnetic resonance(NMR)experiments of high multiple waterflooding.A new NMR wettability index formula is derived based on NMR relaxation theory to quantitatively characterize the time-varying law of rock wettability during waterflooding combined with high-multiple waterflooding experiment in sandstone cores.The remaining oil viscosity in the core is positively correlated with the displacing water multiple.The remaining oil viscosity increases rapidly when the displacing water multiple is low,and increases slowly when the displacing water multiple is high.The variation of remaining oil viscosity is related to the reservoir heterogeneity.The stronger the reservoir homogeneity,the higher the content of heavy components in the remaining oil and the higher the viscosity.The reservoir wettability changes after water injection:the oil-wet reservoir changes into water-wet reservoir,while the water-wet reservoir becomes more hydrophilic;the degree of change enhances with the increase of displacing water multiple.There is a high correlation between the time-varying oil viscosity and the time-varying wettability,and the change of oil viscosity cannot be ignored.The NMR wettability index calculated by considering the change of oil viscosity is more consistent with the tested Amott(spontaneous imbibition)wettability index,which agrees more with the time-varying law of reservoir wettability.

Numerical Simulation of Slurry Diffusion in Fractured Rocks Considering a Time-Varying Viscosity

To analyze the effects of a time-varying viscosity on the penetration length of grouting,in this study cement slur-ries with varying water-cement ratios have been investigated using the Bingham’sfluidflow equation and a dis-crete element method.Afluid-solid coupling numerical model has been introduced accordingly,and its accuracy has been validated through comparison of theoretical and numerical solutions.For different fracture forms(a single fracture,a branch fracture,and a fracture network),the influence of the time-varying viscosity on the slurry length range has been investigated,considering the change in the fracture aperture.The results show that under different fracture forms and the same grouting process conditions,the influence of the time-varying viscosity on the seepage length is 0.350 m.

Influences of clean fracturing fluid viscosity and horizontal in-situ stress difference on hydraulic fracture propagation and morphology in coal seam

The viscosity of fracturing fluid and in-situ stress difference are the two important factors that affect the hydraulic fracturing pressure and propagation morphology. In this study, raw coal was used to prepare coal samples for experiments, and clean fracturing fluid samples were prepared using CTAB surfactant. A series of hydraulic fracturing tests were conducted with an in-house developed triaxial hydraulic fracturing simulator and the fracturing process was monitored with an acoustic emission instrument to analyze the influences of fracturing fluid viscosity and horizontal in-situ stress difference on coal fracture propagation. The results show that the number of branched fractures decreased, the fracture pattern became simpler, the fractures width increased obviously, and the distribution of AE event points was concentrated with the increase of the fracturing fluid viscosity or the horizontal in-situ stress difference. The acoustic emission energy decreases with the increase of fracturing fluid viscosity and increases with the increase of horizontal in situ stress difference. The low viscosity clean fracturing fluid has strong elasticity and is easy to be compressed into the tip of fractures, resulting in complex fractures. The high viscosity clean fracturing fluids are the opposite. Our experimental results provide a reference and scientific basis for the design and optimization of field hydraulic fracturing parameters.

Catalytic Performance of Aquathermolysis and Viscosity Reduction of Heavy Oil over a WO_(3)/ZrO_(2) Solid Acid

Tungstated zirconia(WO_(3)/ZrO_(2))solid acid catalysts with different WO_(3) contents were prepared by a hydrothermal method and then used in the catalytic aquathermolysis of heavy oil from Xinjiang.The WO_(3)/ZrO_(2) solid acid catalyst was characterized by a range of characterization methods,including X-ray diffraction,NH3-temperature programmed desorption,and pyridine infrared spectroscopy.The WO_(3) content of the WO_(3)/ZrO_(2) catalysts had an important impact on the structure and property of the catalysts.When the WO_(3) mass fraction was 20%,it facilitated the formation of tetragonal zirconia,thereby enhancing the creation of robust acidic sites.Acidity is considered to have a strong impact on the catalytic performance of the aquathermolysis of heavy oil.When the catalyst containing 20%WO_(3) was used to catalyze the aquathermolysis of heavy oil under conditions of 14.5 MPa,340℃,and 24 h,the viscosity of heavy oil decreased from 47266 to 5398 mPa·s and the viscosity reduction rate reached 88.6%.The physicochemical properties of heavy oil before and after the aquathermolysis were analyzed using a saturates,aromatics,resins,and asphaltenes analysis,gas chromatography,elemental analysis,densimeter etc.After the aquathermolysis,the saturate and aromatic contents significantly increased from 43.3%to 48.35%and 19.47%to 21.88%,respectively,with large reductions in the content of resin and asphaltene from 28.22%to 25.06%and 5.36%to 2.03%,respectively.The sulfur and nitrogen contents,and the density of the oil were significantly decreased.These factors were likely the main reasons for promoting the viscosity reduction of heavy oil during the aquathermolysis over the WO_(3)/ZrO_(2) solid acid catalysts.

Study of the Viscosity and Specific Gravity of the Ternary Used Frying Oil (UFO)-Bioethanol-Diesel System

Fossil fuels cover around 80% of global energy consumption. However, the problems linked to their use justify the choice of using biofuel. In order to reduce as much as possible, diesel rate, an increase in the number of additives may be considered. Thus, in this work, the study of the used frying oil (UFO), bioethanol and diesel ternary system was undertaken. It emerges from this study that the addition of bioethanol reduces the viscosity and the density of the ternary system and permits a 90% substitution rate for diesel between the UFO and bioethanol. Finally, the percentage of oil becomes 40% after adding alcohol compared to the binary diesel crude vegetable oil mixture where this rate is 30%.

Magnetohydrodynamic Conjugate Free Convective Heat Transfer Analysis of an Isothermal Horizontal Circular Cylinder with Temperature Dependent Viscosity

Heat transfers due to MHD-conjugate free convection from the isothermal horizontal circular cylinder while viscosity is a function of temperature is investigated. The governing equations of the flow and connected boundary conditions are made dimensionless using a set of non-dimensional parameters. The governing equations are solved numerically using the finite difference method. Numerical results are obtained for various values of viscosity variation parameter, Prandtl number, magnetic parameter, and conjugate conduction parameter for the velocity and the temperature within the boundary layer as well as the skin friction coefficients and heat transfer rate along the surface.

Thermomechanical Dynamics (TMD) and Bifurcation-Integration Solutions in Nonlinear Differential Equations with Time-Dependent Coefficients

The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple back-and-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD). The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general.

Non Existence of Shear in Bianchi Type-ⅢString Cosmological Models with Bulk Viscosity and Time-Dependent A Term

We study the non existence of shear in locally rotationally symmetric Bianchi type-Ⅲstring cosmological models with bulk viscosity and variable cosmological termΛ.Exact solutions of the field equations are obtained by assuming the conditions:the bulk viscosity is proportional to the expansion scalar,ξ∝θ,expansion scalar is proportional to shear scalar,θ∝σ,and A is proportional to the Hubble parameter.The coefficient of bulk viscosity is assumed to be a power function of mass density.The corresponding physical interpretations of the cosmological solutions are also discussed.

Bianchi Type-I String Cosmological Model with Bulk Viscosity and Time-Dependent Λ term

Einstein field equations with the cosmological constant is considered in the presence of bulk viscosity in a Bianchi type-I universe.Solutions of the field equations are obtained by assuming the following conditions:the bulk viscosity is proportional to the expansion scalarξ∝θ;the expansion scalar is proportional to shear scalarθ∝σ;andΛis proportional to the Hubble parameterΛ∝H.The corresponding interpretations of the cosmological solutions are also discussed.

Sample size adaptive strategy for time-dependent Monte Carlo particle transport simulation

When multiphysics coupling calculations contain time-dependent Monte Carlo particle transport simulations, these simulations often account for the largest part of the calculation time, which is insufferable in certain important cases. This study proposes an adaptive strategy for automatically adjusting the sample size to fulfil more reasonable simulations. This is realized based on an extension of the Shannon entropy concept and is essentially different from the popular methods in timeindependent Monte Carlo particle transport simulations, such as controlling the sample size according to the relative error of a target tally or by experience. The results of the two models show that this strategy can yield almost similar results while significantly reducing the calculation time. Considering the efficiency, the sample size should not be increased blindly if the efficiency cannot be enhanced further. The strategy proposed herein satisfies this requirement.