Zeitschriftenartikel: „Viscous flow Mathematical models“

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Nazarov, Serdar, Muhammetberdi Rakhimov, and Gurbanyaz Khekimov. "Linearization of the Navier-Stokes equations." E3S Web of Conferences 216 (2020): 01060. http://dx.doi.org/10.1051/e3sconf/202021601060.

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This paper studies mathematical models of the heat transfer process of a viscous incompressible fluid. Optimal control methods are used to solve the problem of optimal modeling. Questions of linearization of the Navier-Stokes equation for a plane fluid flow are considered. The optimal modes (optimal functional dependencies) of the pump and heating device are found depending on the fluid flow rate.

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Ali, Azhar, Dil Nawaz Khan Marwat, and Saleem Asghar. "Viscous flow over a stretching (shrinking) and porous cylinder of non-uniform radius." Advances in Mechanical Engineering 11, no. 9 (September 2019): 168781401987984. http://dx.doi.org/10.1177/1687814019879842.

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The classical models of viscous flows and heat transfer are reformulated in this article. The physical problem describes flow and heat transfer over a stretching (shrinking) and porous cylinder of non-uniform radius. The mathematical model is presented in the form of new equations and dimensionless parameters by means of reframing techniques. A porous and heated cylinder of a non-uniform diameter is stretched (shrunk) with variable stretching (shrinking) velocities. The governing equations and their physical geometrical perspectives are summarized into simplest boundary value ordinary differential equations. A set of unseen, generalized, and convenient transformations are used to solve the complex problem. The current formulation accumulates all the previous models of axisymmetric flow and heat transfer toward stretching (shrinking) and porous cylinder presented in the literature and prevails over all such models. The current model can be easily transformed into classical simulations for particular values of the parameters. The problem is solved numerically and the results were compared with the benchmark solutions. Velocity, temperature, skin friction coefficient, and Nusselt number profiles are plotted and analyzed for different values of the parameters. Moreover, coupling effects of all parameters are seen on flow and heat transfer characteristics and new results are explored and discussed.

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Nazarov, Serdar, Muhammetberdi Rakhimov, and Gurbanyaz Khekimov. "Optimal modeling of the heat transfer of a viscous incompressible liquid." E3S Web of Conferences 216 (2020): 01059. http://dx.doi.org/10.1051/e3sconf/202021601059.

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This paper discusses mathematical models of the heat transfer process of a viscous incompressible fluid. Optimal control methods are used to solve the problem of optimal modeling. Questions of linearization of the Navier - Stokes equation are considered. The optimal modes (optimal functional dependencies) of the pump and heating device are found depending on the fluid flow rate.

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Socolowsky, Jürgen. "On the Nusselt Solution of a Nonisothermal Two-Fluid Inclined Film Flow." International Journal of Mathematics and Mathematical Sciences 2009 (2009): 1–8. http://dx.doi.org/10.1155/2009/981983.

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Nonisothermal viscous two-fluid flows occur in numerous kinds of coating devices. The corresponding mathematical models often represent two-dimensional free boundary value problems for the Navier-Stokes equations or their modifications. In the present paper we are concerned with a particular problem of coupled heat and mass transfer. Marangoni convection is incorporated, too. The solvability of a corresponding stationary problem is discussed. The obtained results generalize previous results for a similar isothermal problem.

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Xie, Fangwei, Diancheng Wu, Yaowen Tong, Bing Zhang, and Jie Zhu. "Effects of structural parameters of oil groove on transmission characteristics of hydro-viscous clutch based on viscosity-temperature property of oil film." Industrial Lubrication and Tribology 69, no. 5 (September 4, 2017): 690–700. http://dx.doi.org/10.1108/ilt-12-2015-0207.

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Purpose The purpose of this paper is to study the influence of structural parameters of oil groove (such as central angle number, depth and so on) on pressure, flow, load capacity and transmitted torque between friction pairs of hydro-viscous clutch. Design/methodology/approach According to the working process of friction pairs of hydro-viscous clutch, mathematical models of hydrodynamic load capacity and torque transmitted by the oil film were built based on viscosity-temperature property. Then analytical solutions of pressure, flow, load capacity and transmitted torque were obtained; effects of central angle of oil groove zone and friction contact zone, oil film thickness, number of oil grooves on pressure, flow, load capacity and torque were studied theoretically. Findings The research found that the central angle of oil groove zone, number of oil grooves and oil groove depth have similar effects on flow, which means that with the increase of central angle, number or depth of oil grooves, the flow also increases; pressure in friction contact zone and oil groove zone drops along radial direction, whereas its value in oil groove zone is higher. With the increase of the central angle of oil groove zone, pressure in friction contact zone and friction contact zone rises, and the load capacity increases, whereas the transmitted torque drops. Number of oil grooves has little effect on load capacity. When the oil film thickness increases, its flow increases accordingly, whereas the pressure, load capacity and transmitted torque drops. Meanwhile, the transmitted torque decreases with the increase of number of oil grooves, whereas the oil groove depth nearly has no effects on transmitted torque. Originality/value In this paper, mathematical models of hydrodynamic load capacity and torque transmitted by oil film were built based on viscosity-temperature property in the working process of hydro-viscous clutch, and their analytical solutions were obtained; effects of structural parameters of oil groove on transmission characteristics of hydro-viscous clutch based on viscosity-temperature property were revealed. The research results are of great value to the theory development of hydro-viscous drive technology, the design of high-power hydro-viscous clutch and relative control strategy.

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CHAI, ZHEN-HUA, BAO-CHANG SHI, and LIN ZHENG. "LATTICE BOLTZMANN SIMULATION OF VISCOUS DISSIPATION IN ELECTRO-OSMOTIC FLOW IN MICROCHANNELS." International Journal of Modern Physics C 18, no. 07 (July 2007): 1119–31. http://dx.doi.org/10.1142/s0129183107011200.

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In this paper, the effects of viscous dissipation in electro-osmotic flow in microchannels are numerically analyzed with lattice Boltzmann method (LBM), and three different lattice Boltzmann models that can recover the macroscopic governing equations for electro-osmotic flow (EOF) are proposed. As the dimensions of the channels approach the microlevel, viscous dissipation could be significant due to a high velocity gradient in electric double layer (EDL). Numerical results show that viscous dissipation plays an important role in EOF in microchannels.

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Dorodnitsyn, L. V. "Acoustics in viscous subsonic flow models with nonreflecting boundary conditions." Computational Mathematics and Modeling 11, no. 4 (October 2000): 356–76. http://dx.doi.org/10.1007/bf02359300.

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Zhang, Guoping, and Mingchao Cai. "Normal mode analysis of 3D incompressible viscous fluid flow models." Applicable Analysis 100, no. 1 (March 25, 2019): 116–34. http://dx.doi.org/10.1080/00036811.2019.1594201.

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Zhang, Bo-ning, Xiao-gang Li, Yu-long Zhao, Cheng Chang, and Jian Zheng. "A Review of Gas Flow and Its Mathematical Models in Shale Gas Reservoirs." Geofluids 2020 (November 30, 2020): 1–19. http://dx.doi.org/10.1155/2020/8877777.

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The application of horizontal wells with multistage hydraulic fracturing technologies has made the development of shale gas reservoirs become a worldwide economical hotspot in recent years. The gas transport mechanisms in shale gas reservoirs are complicated, due to the multiple types of pores with complex pore structure and special process of gas accumulation and transport. Although there have been many attempts to come up with a suitable and practical mathematical model to characterize the shale gas flow process, no unified model has yet been accepted by academia. In this paper, a comprehensive literature review on the mathematical models developed in recent years for describing gas flow in shale gas reservoirs is summarized. Five models incorporating different transport mechanisms are reviewed, including gas viscous flow in natural fractures or macropores, gas ad-desorption on shale organic, gas slippage, diffusion (Knudsen diffusion, Fick diffusion, and surface diffusion), stress dependence, real gas effect, and adsorption layer effect in the nanoshale matrix system, which is quite different from conventional gas reservoir. This review is very helpful to understand the complex gas flow behaviors in shale gas reservoirs and guide the efficient development of shale gas. In addition to the model description, we depicted the type curves of fractured horizontal well with different seepage models. From the review, it can be found that there is some misunderstanding about the essence of Knudsen/Fick diffusion and slippage, which makes different scholars adopt different weighting methods to consider them. Besides, the contribution of each mechanism on the transport mechanisms is still controversial, which needs further in-depth study in the future.

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Lei, Chen, Gao Junjie, Liu Gang, Zhai Keping, Zhang Yuyu, and Gao Jingyang. "Prediction of pipeline restart using different rheological models of gelled crude oil." Applied Rheology 29, no. 1 (January 1, 2019): 182–95. http://dx.doi.org/10.1515/arh-2019-0016.

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Abstract Shutdown of a waxy crude oil pipeline is unavoidable due to maintenance or emergency. It is critical to select the rheological models of gelled crude oil when investigating the pipeline restart process. Three crude oil rheological models are summarized based on previous researches in this paper, which are the viscoelastic model of a viscous type (Model 1), viscoelastic model of an elastic type (Model 2), and pure viscous thixotropic model without yield stress (Model 3). The same rheological data was fitted by the three models respectively. The critical state that pipeline can restart successfully is dominated by the slow creep of the gelled crude oil that can be regarded as an incompressible pipe flow, and this is verified by the pipe restart experiments under constant pressure conditions in this paper. To discuss the effects of the rheological models on calculation of pipeline restart separately, a simplified one-dimensional mathematical model with the pump boundary condition is established. The different calculated flow rate indicates that rheological models affect the judgement of the pipeline restart even though they are fitted from the same rheological data.

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Li, Xi Bing, Shi Gang Wang, Jian Hua Guo, and Dong Sheng Li. "A Mathematical Modeling Method on Micro Heat Pipe with a Trapezium-Grooved Wick Structure." Applied Mechanics and Materials 29-32 (August 2010): 1686–94. http://dx.doi.org/10.4028/www.scientific.net/amm.29-32.1686.

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With heat flux increasing and cooling space decreasing in the products in microelectronics and chemical engineering, micro heat pipe has become an ideal heat radiator for products with high heat flux. Through analyzing the factors influencing the structure, strength and heat transfer limits of circular micro heat pipe with trapezium-grooved wick structure, the heat transfer models are established in this paper, including the models of viscous limit, sonic limit, entrainment limit, capillary limit, condensing limit, boiling limit, continuous flow limit and frozen startup limit. The study lays a powerful theoretical foundation for the design and manufacture of circular micro heat pipe with a trapezium-grooved wick structure.

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Ayata, Muammer, and Ozan Özkan. "A new approach to mathematical models of Drinfeld-Sokolov-Wilson and coupled viscous Burgers’ equations in water flow." Physica Scripta 96, no. 9 (June 7, 2021): 095207. http://dx.doi.org/10.1088/1402-4896/ac05f4.

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Hamdan, M. H., and R. A. Ford. "Single-phase flow through porous channels part II: Flow models, critical length, and viscous separation." Applied Mathematics and Computation 69, no. 2-3 (May 1995): 241–54. http://dx.doi.org/10.1016/0096-3003(94)00132-n.

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Camassa, Roberto, and H. Reed Ogrosky. "On viscous film flows coating the interior of a tube: thin-film and long-wave models." Journal of Fluid Mechanics 772 (May 7, 2015): 569–99. http://dx.doi.org/10.1017/jfm.2015.221.

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A theoretical and numerical investigation of two classes of models for pressure-driven core–annular flow is presented. Both classes, referred to as ‘long-wave’ and ‘thin-film’ models, may be derived from a unified perspective using long-wave asymptotics, but are distinct from one another in the role played by the curved tube geometry with respect to the planar (limiting) case. Analytical and numerical techniques are used to show and quantify the significant differences between the behaviour of solutions to both model types. Temporal linear stability analysis of the constant solution is carried out first to pinpoint with closed-form mathematical expressions the different dynamical regimes associated with absolute or convective instabilities. Numerical simulations for the models are then performed and qualitative differences in the evolution of the free surface are explored. Mathematically, different levels of asymptotic accuracy are found to result in different regularizing properties affecting the long-time behaviour of generic numerical solutions. Travelling wave solutions are also studied, and qualitative differences in the topology of streamline patterns describing the flow of the film in a moving reference frame are discussed. These topological differences allow for further classification of the models. In particular, a transition from a regime in which waves trap a fluid core to one where waves travel faster than any parcel of the underlying fluid is documented for a variant of the primary model. In the corresponding thin-film model, no such transition is found to occur. The source of these differences is examined, and a comparison of the results with those of related models in the literature is given. A brief discussion of the merits of each class of models concludes this study.

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WANG, Y., Y. L. HE, Q. LI, G. H. TANG, and W. Q. TAO. "LATTICE BOLTZMANN MODEL FOR SIMULATING VISCOUS COMPRESSIBLE FLOWS." International Journal of Modern Physics C 21, no. 03 (March 2010): 383–407. http://dx.doi.org/10.1142/s0129183110015178.

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A lattice Boltzmann model is developed for viscous compressible flows with flexible specific-heat ratio and Prandtl number. Unlike the Maxwellian distribution function or circle function used in the existing lattice Boltzmann models, a polynomial kernel function in the phase space is introduced to recover the Navier–Stokes–Fourier equations. A discrete equilibrium density distribution function and a discrete equilibrium total energy distribution function are obtained from the discretization of the polynomial kernel function with Lagrangian interpolation. The equilibrium distribution functions are then coupled via the equation of state. In this framework, a model for viscous compressible flows is proposed. Several numerical tests from subsonic to supersonic flows, including the Sod shock tube, the double Mach reflection and the thermal Couette flow, are simulated to validate the present model. In particular, the discrete Boltzmann equation with the Bhatnagar–Gross–Krook approximation is solved by the finite-difference method. Numerical results agree well with the exact or analytic solutions. The present model has potential application in the study of complex fluid systems such as thermal compressible flows.

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Суровежко, А. С., and С. И. Мартыненко. "On optimization of technical devices based on a hierarchy of mathematical models." Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), no. 4 (September 10, 2019): 411–27. http://dx.doi.org/10.26089/nummet.v20r436.

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Рассмотрена задача о топливном коллекторе, которую можно отнести к обратным задачам гидродинамики: необходимо определить геометрию распределительного канала коллектора, обеспечивающего равномерную раздачу топлива. Однако профилирование коллектора на основе 3D стационарных уравнений Навье-Стокса для турбулентного течения несжимаемой вязкой среды в шероховатых каналах требует непрактичных вычислительных усилий. Использована иерархия математических моделей: 1D уравнения Навье-Стокса для профилирования и 3D уравнения Навье-Стокса для калибровки 1D модели. Показано, что используемая иерархия моделей позволяет существенно снизить объем вычислительной работы, необходимой для расчета оптимальной конструкции коллектора. Предложенный подход представляет интерес для оптимизации технических устройств различного назначения. A fuel collector problem is considered as an inverse problem of hydrodynamics: it is necessary to determine the distribution channel geometry of a collector for a uniform fuel distribution. However, the collector profiling based on the 3D stationary Navier-Stokes equations for turbulent flow of an incompressible viscous medium in rough channels requires impractical computational efforts. A hierarchy of mathematical models (1D Navier-Stokes equations for the collector profiling and 3D Navier-Stokes equations for 1D model validation) is used in this paper. It is shown that the hierarchy of models can significantly reduce amount of computational work needed for computing the optimal collector design. The developed approach is of interest for optimizing technical devices for various purposes.

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Perkins, Greg. "Mathematical modelling of in situ combustion and gasification." Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 232, no. 1 (August 2, 2017): 56–73. http://dx.doi.org/10.1177/0957650917721595.

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The total worldwide resources of oil sands, heavy oil, oil shale and coal far exceed those of conventional light oil. In situ combustion and gasification are techniques that can potentially recover the energy from these unconventional hydrocarbon resources. In situ combustion can be used to produce oil, especially viscous and immobile crudes, by heating the oil and reducing the viscosity of the hydrocarbon liquids allowing them to flow to production wells. In situ gasification can be used to convert deep carbonaceous materials into synthesis gas which can be used at surface for power generation and petrochemical applications. While both in situ combustion for oil recovery and in situ gasification of coal have been developed and demonstrated over many decades, the commercial applications of these techniques have been limited to date. There are many physical processes occurring during in situ combustion, including multi-phase flow, heat and mass transfer, chemical reactions in porous media and geomechanics. A key tool in analysing and optimising the technologies involves using numerical models to simulate the processes. This paper presents a brief review of mathematical modelling of in situ combustion and gasification with an emphasis on developing a generalised framework and describing some of the key challenges and opportunities.

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Bayly, P. V., and S. K. Dutcher. "Steady dynein forces induce flutter instability and propagating waves in mathematical models of flagella." Journal of The Royal Society Interface 13, no. 123 (October 2016): 20160523. http://dx.doi.org/10.1098/rsif.2016.0523.

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Cilia and flagella are highly conserved organelles that beat rhythmically with propulsive, oscillatory waveforms. The mechanism that produces these autonomous oscillations remains a mystery. It is widely believed that dynein activity must be dynamically regulated (switched on and off, or modulated) on opposite sides of the axoneme to produce oscillations. A variety of regulation mechanisms have been proposed based on feedback from mechanical deformation to dynein force. In this paper, we show that a much simpler interaction between dynein and the passive components of the axoneme can produce coordinated, propulsive oscillations. Steady, distributed axial forces, acting in opposite directions on coupled beams in viscous fluid, lead to dynamic structural instability and oscillatory, wave-like motion. This ‘flutter’ instability is a dynamic analogue to the well-known static instability, buckling. Flutter also occurs in slender beams subjected to tangential axial loads, in aircraft wings exposed to steady air flow and in flexible pipes conveying fluid. By analysis of the flagellar equations of motion and simulation of structural models of flagella, we demonstrate that dynein does not need to switch direction or inactivate to produce autonomous, propulsive oscillations, but must simply pull steadily above a critical threshold force.

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Zhurba Eremeeva, I. A., D. Scerrato, C. Cardillo, and A. Tran. "A MATHEMATICAL MODEL OF NONSTATIONARY MOTION OF A VISCOELASTIC FLUID IN ROLLER BEARINGS." Problems of strenght and plasticity 81, no. 4 (2019): 500–511. http://dx.doi.org/10.32326/1814-9146-2019-81-4-500-511.

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Nowadays, the emergence of new lubricants requires an enhancement of the rheological models and methods used for solution of corresponding initial boundary-value problems. In particular, models that take into account viscoelastic properties are of great interest. In the present paper we consider the mathematical model of nonstationary motion of a viscoelastic fluid in roller bearings. We used the Maxwell fluid model for the modeling of fluid properties. The viscoelastic properties are exhibited by many lubricants that use polymer additives. In addition, viscoelastic properties can be essential at high fluid speeds. Also, viscoelastic properties can be significant in the case of thin gaps. Maxwell's model is one of the most common models of viscoelastic materials. It combines the relative simplicity of constitutive equations with the ability to describe a stress relaxation. In addition, viscoelastic fluids also allow us to describe some effects that are missing in the case of viscous fluid. An example it is worth to mention the Weissenberg effect and a number of others. In particular, such effects can be used to increase the efficiency of the film carrier in the sliding bearings. Here we introduced characteristic assumptions on the form of the flow, allowing to significantly simplify the solution of the problem. We consider so-called self-similar solutions, which allows us to get a solution in an analytical form. As a result these assumptions, the formulae for pressure and friction forces are derived. Their dependency on time and Deborah number is analyzed. The limiting values of the flow characteristics were obtained. The latter can be used for steady state of the flow regime. Differences from the case of Newtonian fluid are discussed. It is shown that viscoelastic properties are most evident at the initial stage of flow, when the effects of non-stationarity are most important.

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Zhurba Eremeeva, I. A., D. Scerrato, C. Cardillo, and A. Tran. "A MATHEMATICAL MODEL OF NONSTATIONARY MOTION OF A VISCOELASTIC FLUID IN ROLLER BEARINGS." Problems of strenght and plasticity 81, no. 4 (2019): 501–12. http://dx.doi.org/10.32326/1814-9146-2019-81-4-501-512.

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Nowadays, the emergence of new lubricants requires an enhancement of the rheological models and methods used for solution of corresponding initial boundary-value problems. In particular, models that take into account viscoelastic properties are of great interest. In the present paper we consider the mathematical model of nonstationary motion of a viscoelastic fluid in roller bearings. We used the Maxwell fluid model for the modeling of fluid properties. The viscoelastic properties are exhibited by many lubricants that use polymer additives. In addition, viscoelastic properties can be essential at high fluid speeds. Also, viscoelastic properties can be significant in the case of thin gaps. Maxwell's model is one of the most common models of viscoelastic materials. It combines the relative simplicity of constitutive equations with the ability to describe a stress relaxation. In addition, viscoelastic fluids also allow us to describe some effects that are missing in the case of viscous fluid. An example it is worth to mention the Weissenberg effect and a number of others. In particular, such effects can be used to increase the efficiency of the film carrier in the sliding bearings. Here we introduced characteristic assumptions on the form of the flow, allowing to significantly simplify the solution of the problem. We consider so-called self-similar solutions, which allows us to get a solution in an analytical form. As a result these assumptions, the formulae for pressure and friction forces are derived. Their dependency on time and Deborah number is analyzed. The limiting values of the flow characteristics were obtained. The latter can be used for steady state of the flow regime. Differences from the case of Newtonian fluid are discussed. It is shown that viscoelastic properties are most evident at the initial stage of flow, when the effects of non-stationarity are most important.

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Průša, Vít, and K. R. Rajagopal. "Implicit Type Constitutive Relations for Elastic Solids and Their Use in the Development of Mathematical Models for Viscoelastic Fluids." Fluids 6, no. 3 (March 22, 2021): 131. http://dx.doi.org/10.3390/fluids6030131.

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Viscoelastic fluids are non-Newtonian fluids that exhibit both “viscous” and “elastic” characteristics in virtue of the mechanisms used to store energy and produce entropy. Usually, the energy storage properties of such fluids are modeled using the same concepts as in the classical theory of nonlinear solids. Recently, new models for elastic solids have been successfully developed by appealing to implicit constitutive relations, and these new models offer a different perspective to the old topic of the elastic response of materials. In particular, a sub-class of implicit constitutive relations, namely relations wherein the left Cauchy–Green tensor is expressed as a function of stress, is of interest. We show how to use this new perspective in the development of mathematical models for viscoelastic fluids, and we provide a discussion of the thermodynamic underpinnings of such models. We focus on the use of Gibbs free energy instead of Helmholtz free energy, and using the standard Giesekus/Oldroyd-B models, we show how the alternative approach works in the case of well-known models. The proposed approach is straightforward to generalize to more complex settings wherein the classical approach might be impractical or even inapplicable.

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Reddy, Kattamreddy Venugopal, Machireddy Gnaneswara Reddy, and Oluwole Daniel Makinde. "Heat and Mass Transfer of a Peristaltic Electro-osmotic Flow of a Couple Stress Fluid through an Inclined Asymmetric Channel with Effects of Thermal Radiation and Chemical Reaction." Periodica Polytechnica Mechanical Engineering 65, no. 2 (March 16, 2021): 151–62. http://dx.doi.org/10.3311/ppme.16760.

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The presented article addresses the electro-osmotic peristaltic flow of a couple stress fluid bounded in an inclined asymmetric micro-channel. The viscous dissipation, Joule heating and chemical reaction effects are employed simultaneously in the flow analysis. Heat and mass transfer have been studied under large wavelength and small Reynolds number. The resulting nonlinear systems are solved numerically. The influence of various dominant physical parameters is discussed for velocity, temperature distribution, concentration distribution and the pumping characteristics. Electro kinetic flow of fluids by micro-pumping through micro channels and micro peristaltic transport has accelerated considerable concern in accelerated medical technology and several areas of biomedical engineering. Deeper clarification of the fluid dynamics of such flow requires the continuous need for more delicate mathematical models and numerical simulations, in parallel with laboratory investigations.

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Zhong, Huiying, Weidong Zhang, Hongjun Yin, and Haoyang Liu. "Study on Mechanism of Viscoelastic Polymer Transient Flow in Porous Media." Geofluids 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/8763951.

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Oil recovery, including conventional and viscous oil, can be improved significantly by flooding with polymer solutions. This chemical flooding method can increase oil production, and it can improve the macrodisplacement efficiency and microsweep efficiencies. In this study, we establish physical models that include the dead-end and complex models based on the pore-network pattern etched into glass, using the snappyHexMesh solver in OpenFOAM. These models capture the complexity and topology of porous media geometry. We establish a mathematical model for transient flows of viscoelastic polymers using computational fluid dynamics simulations, and we study the distributions of pressure and velocity for different elasticity scenarios and different flooding process. The results demonstrate that the pressure difference increases as the relaxation time decreases, before the flow reaches its steady state. For a steady flow, elasticity can give rise to an additional pressure difference, which increases with increasing elasticity. Thus, the characteristics of pressure difference vary before and after the flow becomes steady; this phenomenon is very important. Velocity contours become more widely spaced with elasticity increase. This suggests that elasticity of the polymer solutions contributes to the microsweep efficiency. The results of the study provide the necessary theoretical foundation for laboratory experiments and development of methods for polymer flooding and can be helpful for the design and selection of polymers for polymer flooding.

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Du, Dong Xing, Fa Hu Zhang, Dian Cai Geng, and Ying Ge Li. "Numerical Study on Film Foam Flow Characteristics in a Straight Duct." Key Engineering Materials 561 (July 2013): 472–77. http://dx.doi.org/10.4028/www.scientific.net/kem.561.472.

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Straight ducts capture some essential features of the motion of foam in porous media in petroleum industry. In this paper, Surface Evolver was employed to build the mathematical model to study the flow behavior of lamellas in the duct with different models. Numerical results show good agreement with experiments and some important features of lamella flow behavior in straight ducts are obtained. It is concluded that, the physical model with viscous force can adequately describe the flow characteristics of reality foam in the experiment. The actual pressure difference consists of the pressure difference caused by the curvature of the lamellas and the drag force on the boundary wall. Under the ideal condition of without drag force along the wall, the pressure drop for lamella flow in the duct is zero, and the shape and the velocity of the lamellas will maintain constant.

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Tai, Chang-Hsien, Yuh-Long Tian, and Jtm-Lun Liou. "High-resolution upwind viscous flow solver on SOCBT configuration with turbulence models." Finite Elements in Analysis and Design 18, no. 1-3 (December 1994): 237–57. http://dx.doi.org/10.1016/0168-874x(94)90105-8.

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Deng, Wubing, and Igor B. Morozov. "Solid viscosity of fluid-saturated porous rock with squirt flows at seismic frequencies." GEOPHYSICS 81, no. 4 (July 2016): D395—D404. http://dx.doi.org/10.1190/geo2015-0406.1.

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We have developed a macroscopic model for a two-phase medium (solid porous rock frame plus saturating pore fluid) with squirt flows based on Lagrangian continuum mechanics. The model focuses on improved physics of rock deformation, including explicit differential equations in time domain, causality, linearity, frequency-independent parameters with clear physical meanings, and an absence of mathematical internal or memory variables. The approach shows that all existing squirt-flow models can be viewed as microscopic models of viscosity for solid rock. As in existing models, the pore space is differentiated into compliant and relatively stiff pores. At lower frequencies, the effects of fluid flows within compliant pores are described by bulk and shear solid viscosities of the effective porous frame. Squirt-flow effects are “Biot consistent,” which means that there exists a viscous coupling between the rock frame and the fluid in stiff pores. Biot’s poroelastic effects associated with stiff porosity and global flows are also fully included in the model. Comparisons with several squirt-flow models show good agreement in predicting wave attenuation to approximately 1 kHz frequencies. The squirt-flow viscosity for sandstone is estimated in the range of [Formula: see text], which is close to field observations. Because of its origins in rigorous mechanics, the model can be used to describe any wavelike and transient deformations of heterogeneous porous media or finite bodies encountered in many field and laboratory experiments. The model also leads to new numerical algorithms for wavefield modeling, which are illustrated by 1D finite-difference waveform modeling.

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Hu, Yumeng, Haiming Huang, and Zimao Zhang. "Numerical simulation of a hypersonic flow past a blunt body." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 6 (June 5, 2017): 1351–64. http://dx.doi.org/10.1108/hff-05-2016-0187.

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Purpose The purpose of this paper is to explore the characteristics of hypersonic flow past a blunt body. Design/methodology/approach The implicit finite volume schemes are derived from axisymmetric Navier–Stokes equations by means of AUSM+ and LU-SGS methods, and programmed in FORTRAN. Based on the verified result that a 2D axisymmetric chemical equilibrium flow has a good agreement with the literature, the characteristics of hypersonic flow past a sphere are simulated by using four different models which involve four factors, namely, viscous, inviscid, equilibrium and calorically perfect gas. Findings Compared with the calorically perfect gas under hypervelocity condition, the shock wave of the equilibrium gas is more close to the blunt body, gas density and pressure become bigger, but gas temperature is lower due to the effect of real gas. Viscous effects are not obvious in the calculations of the equilibrium gas or the calorically perfect gas. In a word, the model of equilibrium gas is more suitable for hypersonic flow and the calculation of viscous flow has a smaller error. Originality/value The computer codes are developed to simulate the characteristics of hypersonic flows, and this study will be helpful for the design of the thermal protection system in hypersonic vehicles.

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Wang, Da Zheng, Dan Wang, Lei Mei, and Wei Chao Shi. "The Hydrodynamic Analysis of Propeller Based on ANSYS-CFX." Advanced Materials Research 694-697 (May 2013): 673–77. http://dx.doi.org/10.4028/www.scientific.net/amr.694-697.673.

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In this paper, the open water performance of a pod propeller in the viscous flow fields is numerically simulated by the Computational Fluid Dynamics (CFD) method. Based on the coordinate transformation formula for transforming the local to the global coordinate, mathematical model of a propeller is created. Thrust and torque coefficients corresponding to different advance coefficients of the model are calculated by ANSYS-CFX with three different turbulence models. The pressure distributions on the blade surface are also presented. Comparisons show that experimental results and numerical results agree well, with SST k-ω and RNG k-ε more accurate than the standard k-ε.

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Fiorot, G. H., G. F. Maciel, and C. Kitano. "MATHEMATICAL MODEL AND EXPERIMENTAL PROCEEDINGS TO DETERMINE ROLL WAVES IN OPEN CHANNELS." Revista de Engenharia Térmica 10, no. 1-2 (December 31, 2011): 55. http://dx.doi.org/10.5380/reterm.v10i1-2.61953.

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The goal of this paper is consolidate a representative model previously developed by RMVP team (Rheological Studies on Viscous and Viscousplastic Materials) from UNESP - Ilha Solteira, for a typical phenomenonthat occurs on spillways, river's bed, landslides, mudflows, blood flows, for Newtonian and non-Newtonian fluids, known as roll waves. Another goal of this paper is present an experimental project designed for capturing measurements (amplitude and wavelength) of these instabilities. From a mathematical perspective, a first-order analytical model is showed, based on Cauchy's equations system, once developed by the team (Ferreira, 2007), which provides a generation condition for roll waves through temporal linear stability analysis. This model follows the remarkable work of Dressler (1949) and it is able to generate roll waves for many rheological configurations, from Newtonian to Herschel & Bulkley models, representing clean water up to muddy mixtures, respectively. A numerical routine developed in Matlab/Simulink is used to show some results that illustrate roll waves pattern. Due to the lack of roll waves data (amplitude and wavelength), the team started to focus on the experimental approach of the phenomenon, aiming to design an apparatus that would be capable to reproduce roll waves in special conditions of flow, isolated from external perturbations. This project is here presented along with a proposal of a photometric system to ascertain measures of the flow height through light absorption technique, based on experiments found in the literature. The final execution of this experiment and the correct obtaining of amplitude and wavelength will contribute for the validation of the model here presented.

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Strzelecki, Tomasz, and Michał Strzelecki. "Relation Between Filtration and Soil Consolidation Theories." Studia Geotechnica et Mechanica 37, no. 1 (March 1, 2015): 105–14. http://dx.doi.org/10.1515/sgem-2015-0012.

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Abstract This paper presents a different, than commonly used, form of equations describing the filtration of a viscous compressible fluid through a porous medium in isothermal conditions. This mathematical model is compared with the liquid flow equations used in the theory of consolidation. It is shown that the current commonly used filtration model representation significantly differs from the filtration process representation in Biot’s and Terzaghi’s soil consolidation models, which has a bearing on the use of the methods of determining the filtration coefficient on the basis of oedometer test results. The present analysis of the filtration theory equations should help interpret effective parameters of the non-steady filtration model. Moreover, equations for the flow of a gas through a porous medium and an interpretation of the filtration model effective parameters in this case are presented.

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Hunt, Barry. "Knowledge-Based Nonlinear Boundary Integral Models of Compressible Viscous Flows Over Arbitrary Bodies: Taking CFD Back to Basics." Applied Mechanics Reviews 44, no. 11S (November 1, 1991): S130—S142. http://dx.doi.org/10.1115/1.3121345.

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The paper starts with a discussion of a knowledge-based CFD methodology. A new incompressible formulation known as SAVER is first introduced, employing a novel relaxation approach. This is then generalized through a modification of the boundary conditions to the GENESIS methodology, for analysis or design in compressible, rotational flow. A discussion is presented of how the basic causal nature of integral methods offers new insights into certain flow phenomena, such as shocks and separations, and facilitates aerodynamic sensitivity analysis. The paper presents a new class of vector fields approximating the Euler equations for transonic flows, and shows how GENESIS can be used to construct first an exact solution of these approximate fields, then a numerical solution of the residual error fields. The explicit representation of a shock discontinuity on the body boundary exploits its causal link with conditions at the sonic point to suppress, non-dissipatively, the mathematically-valid but physically-impossible formation of an expansion shock.

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Centeno, R., K. S. Varyani, and C. Guedes Soares. "Experimental Study on the Influence of Hull Spacing on Hard-Chine Catamaran Motions." Journal of Ship Research 45, no. 03 (September 1, 2001): 216–27. http://dx.doi.org/10.5957/jsr.2001.45.3.216.

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An experimental program was performed with hard-chine catamaran models in regular waves. The distance between the demi-hulls of the models was changed to assess its effects on the wave-induced motions. The results allowed the study of some aspects related to catamaran motions, like the interference between the hulls and resonance frequencies. The experimental results are compared with calculations performed with a recently developed code based on a two-dimensional potential flow theory in which viscous forces are included through a cross-flow drag approach. The effect of the hull distance in the heave and pitch motion responses and the importance of the viscous forces in such hull configurations are shown.

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TIAN, ZHI-WEI, CHUN ZOU, H. J. LIU, Z. H. LIU, Z. L. GUO, and C. G. ZHENG. "THERMAL LATTICE BOLTZMANN MODEL WITH VISCOUS HEAT DISSIPATION IN THE INCOMPRESSIBLE LIMIT." International Journal of Modern Physics C 17, no. 08 (August 2006): 1131–39. http://dx.doi.org/10.1142/s0129183106009631.

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A novel thermal lattice Boltzmann (LB) model is proposed to obtain the viscous heat term expediently. Unlike the existing thermal LB models, this model is entirely based on the framework of the LB method and directly derived from the macro temperature equation. Moreover, the computation cost decreases because the computation of complicated material derivative term has been avoided successfully. To testify the simulation capability of this model, the thermal Couette flow is simulated and the results indicate agreement with the analytical solutions.

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Shchuryk, Volodymyr, Leonid Serilko, Leonid Voitovych, and Zoia Sasiuk. "MATHEMATICAL MODEL OF DYNAMICS OF CENTRIFUGE FOR FORMATION OF CONCRETE TUBULAR PRODUCTS." Vibrations in engineering and technology, no. 4(95) (November 20, 2019): 72–79. http://dx.doi.org/10.37128/2306-8744-2019-4-9.

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The paper presents an advanced complex mathematical model of centrifuge dynamics for the formation of tubular products made of concrete or any other plastic and viscous confining mixtures. In the two-dimensional (plane) formulation of the problem, the studied mechanical system consists of a framework form (hollow rotor) with a partial confining filling, its elastic-damping suspension and power drive. It is assumed that the rotor is rigid, of correct design, has a certain static imbalance and can be both horizontal and vertical. The used filling is a concrete or some other mixture as a quasi-homogeneous plastic and viscous rheological body, which spreads slowly and in a shear flow over the inner surface of the rotor under the action of gravity forces and transfer forces of inertia. The rotor suspension is a roller lever type, but can be of any design, with certain inertial, rigid and damping characteristics. The variable power drive provides application of a variable torque to the rotor. The general theorems and dynamics equations, including the theorem on the motion of the mass center and the differential equation of rotation at the plane motion of a body with a pole other than the mass center, are used to construct differential equations of rotor dynamics. This eliminates the shortcomings of the known mathematical models with the similar problem statement. The proposed mathematical model can be implemented according to the well-known algorithms for numerical integration and used to develop or adjust the appropriate software. This enables the centrifuge dynamics to be studied more fully, to take into account and optimize its important parameters and characteristics.

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Astafiev, V. I., M. G. Kakhidze, V. I. Popkov, and A. V. Popkova. "MULTI-SCALE STRESS-DEFORMATION STATUS OF POROUS GEOLOGICAL STRUCTURE AS RELATED TO WELL FILTRATION FLOWS." Vestnik of Samara University. Natural Science Series 19, no. 9.2 (June 6, 2017): 153–69. http://dx.doi.org/10.18287/2541-7525-2013-19-9.2-153-169.

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Mono-harmonic junction in the interaction of porous space rock stress in oil/gas saturated reservoirs and averaged hydro-dynamic flows of viscous oil towards wells obtained as a result of innovative decisions in oil industry in general is presented. Within the frames of block homogeneous models of a well through the application of 3D linear theory of wave diffusion along the surface of geophysical emission layer, mathematical statement of asymmetrical filtration challenge with finite velocity of effect is presented. Dispersive ratios for constrained and resonant dissipative structures in a shear layer of viscous-elastic filtration at the edge of a slug of water-oil displacement are given. The redistribution results for the averaged inflow profile of viscous Newtonian filtration into asymmetrical energy-stable stress-deformation status inside the saturated porous media at various constraints: in conditions of enclosed or capillary-clamped boundary and in non-constrained conditions - at the frontier of displacement or with stimulation of water-flood displacement in zones of stagnation is presented.

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PIYASENA, PUNIDADAS, та ROBIN C. McKELLAR. "Influence of Guar Gum on the Thermal Stability of Listeria innocua, Listeria monocytogenes, and γ-Glutamyl Transpeptidase during High-Temperature Short-Time Pasteurization of Bovine Milk". Journal of Food Protection 62, № 8 (1 серпня 1999): 861–66. http://dx.doi.org/10.4315/0362-028x-62.8.861.

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Mathematical models describing the thermal inactivation of γ-glutamyl transpeptidase (TP) and Listeria innocua in milk during high-temperature short-time (HTST) pasteurization were validated with data from TP, L. innocua, and L. monocytogenes trials in guar gum–milk. Holding tube times were determined for turbulent flow using water, and for laminar flow using a guar gum (0.27% wt/wt)–sucrose (5.3% wt/wt)–water mixture. Inactivation of TP and L. innocua was lower in a solution of guar gum (0.25% wt/wt) in whole milk than was predicted by models derived from studies with whole milk alone. Use of laminar flow timings improved model fit but did not completely account for the observed protective effect. L. monocytogenes survival was close to that predicted by the L. innocua model, although some protection was afforded this pathogen under laminar flow. Considerable intertrial variability was noted for L. monocytogenes. Risk analysis simulations using @RISK, a Lotus 1-2–3W add-in, were used to account for intertrial variability. Simulated log10 %reductions consistently underpredicted experimental L. monocytogenes survival (fail-safe), thus the L. innocua model derived in milk is suitable for estimating L. monocytogenes survival in viscous products. Increased thermal tolerance during laminar flow may be attributed to the protective effect of stabilizer.

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DAMSGAARD, ANDERS, JENNY SUCKALE, JAN A. PIOTROWSKI, MORGANE HOUSSAIS, MATTHEW R. SIEGFRIED, and HELEN A. FRICKER. "Sediment behavior controls equilibrium width of subglacial channels." Journal of Glaciology 63, no. 242 (November 27, 2017): 1034–48. http://dx.doi.org/10.1017/jog.2017.71.

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ABSTRACTFlow-frictional resistance at the base of glaciers and ice sheets is strongly linked to subglacial water pressure. Understanding the physical mechanisms that govern meltwater fluxes in subglacial channels is hence critical for constraining variations in ice flow. Previous mathematical descriptions of soft-bed subglacial channels assume a viscous till rheology, which is inconsistent with laboratory data and the majority of field studies. Here, we use a grain-scale numerical formulation coupled to pore-water dynamics to analyze the structural stability of channels carved into soft beds. Contrary to the soft-bed channel models assuming viscous till rheology, we show that the flanks of till channels can support substantial ice loads without creep closure of the channel, because the sediment has finite frictional strength. Increased normal stress on the channel flanks causes plastic failure of the sediment, and the channel rapidly shrinks to increase the ice-bed contact area. We derive a new parameterization for subglacial channelized flow on soft beds and show that channel dynamics are dominated by fluvial erosion and deposition processes with thresholds linked to the plastic rheology of subglacial tills. We infer that the described limits to channel size may cause subglacial drainage to arrange in networks of multiple closely spaced channels.

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Deng, Wubing, and Igor B. Morozov. "A simple and general macroscopic model for local-deformation effects in fluid-saturated porous rock." Geophysical Journal International 220, no. 3 (December 6, 2019): 1893–903. http://dx.doi.org/10.1093/gji/ggz552.

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SUMMARY Wave-induced fluid flows (WIFF) can be viewed as cases of broader local-deformation (LD) phenomena and represent the principal causes of seismic-wave attenuation in fluid-saturated porous rock. Most existing WIFF models refer to greatly simplified microstructures and specific flow patterns, such as planar divergent flows within thin cracks (squirt flows, SF) or flows within patchy-saturation zones. However, such microstructures represent only idealized mathematical models that may be impossible to consistently identify within a given rock. At the same time, most details of such microstructures are insignificant for seismic waves, which are only sensitive to averaged properties of the medium. To perform microstructure-independent modelling of LD effects, we develop a simple yet general approach based entirely on a macroscopic local-deformation variable. This variable is broadly analogous to Biot's fluid content and is illustrated for two specific microstructural models. The macroscopic model is Biot-consistent and uses only time- and frequency-independent material properties. Both local and global (Biot's) pore flows and all types of waves and deformations are explained in a rigorous and consistent manner. The model allows constraining a minimal set of material properties responsible for all observed elastic and anelastic effects in porous rock. Because of making no assumptions about the microstructures and their spatial scales, this approach should comprise at least some of the existing WIFF models. In particular, this model accurately reproduces all attenuation and velocity dispersion spectra predicted by a broadly used SF model. The model also contains effects not considered previously, such as bulk viscosity of pore fluid and viscous coupling between the rock frame and fluid-filled pores. The model offers straightforward extensions to multiple porosities and cases of viscous fluids in primary pores. Based on the resulting differential equations, physically consistent schemes for numerical modelling of seismic wavefields can be developed for porous rock with arbitrary LD effects.

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Leclaire, Sébastien, Andrea Parmigiani, Bastien Chopard, and Jonas Latt. "Three-dimensional lattice Boltzmann method benchmarks between color-gradient and pseudo-potential immiscible multi-component models." International Journal of Modern Physics C 28, no. 07 (July 2017): 1750085. http://dx.doi.org/10.1142/s0129183117500851.

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In this paper, a lattice Boltzmann color-gradient method is compared with a multi-component pseudo-potential lattice Boltzmann model for two test problems: a droplet deformation in a shear flow and a rising bubble subject to buoyancy forces. With the help of these two problems, the behavior of the two models is compared in situations of competing viscous, capillary and gravity forces. It is found that both models are able to generate relevant scientific results. However, while the color-gradient model is more complex than the pseudo-potential approach, numerical experiments show that it is also more powerful and suffers fewer limitations.

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Curt, Paula, and Denisa Fericean. "A Special Class of Univalent Functions in Hele-Shaw Flow Problems." Abstract and Applied Analysis 2011 (2011): 1–10. http://dx.doi.org/10.1155/2011/948236.

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We study the time evolution of the free boundary of a viscous fluid for planar flows in Hele-Shaw cells under injection. Applying methods from the theory of univalent functions, we prove the invariance in time ofΦ-likeness property (a geometric property which includes starlikeness and spiral-likeness) for two basic cases: the inner problem and the outer problem. We study both zero and nonzero surface tension models. Certain particular cases are also presented.

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Li, Guo-Jie, Wen-Bin Shangguan, and Subhash Rakheja. "Modelling and analysis of a magneto-rheological damper featuring non-magnetized flow paths in the piston." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 234, no. 10-11 (April 8, 2020): 2665–79. http://dx.doi.org/10.1177/0954407020907487.

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The damping characteristics of a magneto-rheological damper featuring non-magnetized flow paths in the piston are analysed using the Eyring constitutive model considering both viscous and minor hydraulic losses. The force–displacement and force–velocity characteristics of the magneto-rheological damper with non-magnetized flow paths were experimentally evaluated under different excitations and magnetic field intensity. Experimental results revealed relatively largerpre-yield-like region, attributed to flows through the non-magnetized paths, which increased with an increase in the coil current. A mathematical model of the damper was subsequently formulated using the Eyring constitutive model considering pressure drop across the piston and viscous effect in addition to the current-dependent friction. The Eyring model parameters were identified as a function of the magnetic field intensity and thus the coil current. For this purpose, a finite element model was formulated to identify a relation between the coil current and the magnetic field intensity. The validity of the proposed model is demonstrated by comparing the model-predicted force–velocity characteristics with the measured data under different applied currents. The model results are also compared with those obtained from the widely reported modified Bouc–Wen model and the Bingham constitutive model. The comparisons showed that the Eyring constitutive model can yield more accurate predictions of the damping properties compared to the Bingham model but similar to those from the modified Bouc–Wen model, while the Bouc–Wen model involves identifications of considerably greater number of parameters. The proposed model provided more accurate prediction of the damping force in the pre-yield region compared to the other models.

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Alam, Aftab, Dil Nawaz Khan Marwat, and Saleem Asghar. "Flow over a non-uniform sheet with non-uniform stretching (shrinking) and porous velocities." Advances in Mechanical Engineering 12, no. 2 (February 2020): 168781402090900. http://dx.doi.org/10.1177/1687814020909000.

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Viscous flow over a porous and stretching (shrinking) surface of an arbitrary shape is investigated in this article. New dimensions of the modeled problem are explored through the existing mathematical analogies in such a way that it generalizes the classical simulations. The latest principles provide a framework for unification, and the consolidated approach modifies the classical formulations. A realistic model is presented with new features in order to explain variety of previous observations on the said problems. As a result, new and upgraded version of the problem is appeared for all such models. A set of new, unusual, and generalized transformations is formed for the velocity components and similarity variables. The modified transformations are equipped with generalized stretching (shrinking), porous velocities, and surface geometry. The boundary layer governing equations are reduced into a set of ordinary differential equations (ODEs) by using the unification procedure and technique. The set of ODEs has two unknown functions f and g. The modeled equations have five different parameters, which help us to reduce the problem into all previous formulations. The problem is solved analytically and numerically. The current simulation and its solutions are also compared with existing models for specific value of the parameters, and excellent agreement is found between the solutions.

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Butler, J. P., J. Huang, S. H. Loring, S. J. Lai-Fook, P. M. Wang, and T. A. Wilson. "Model for a pump that drives circulation of pleural fluid." Journal of Applied Physiology 78, no. 1 (January 1, 1995): 23–29. http://dx.doi.org/10.1152/jappl.1995.78.1.23.

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Physical and mathematical models were used to study a mechanism that could maintain the layer of pleural fluid that covers the surface of the lung. The pleural space was modeled as a thin layer of viscous fluid lying between a membrane carrying tension (T), representing the lung, and a rigid wall, representing the chest wall. Flow of the fluid was driven by sliding between the membrane and wall. The physical model consisted of a cylindrical balloon with strings stretched along its surface. When the balloon was inflated inside a vertical circular cylinder containing a viscous fluid, the strings formed narrow vertical channels between broad regions in which the balloon pressed against the outer cylinder. The channels simulated the pleural space in the regions of lobar margins. Oscillatory rotation of the outer cylinder maintained a lubricating layer of fluid between the balloon and the cylinder. The thickness of the fluid layer (h), measured by fluorescence videomicroscopy, was larger for larger fluid viscosity (mu), larger sliding velocity (U), and smaller pressure difference (delta P) between the layer and the channel. A mathematical model of the flow in a horizontal section was analyzed, and numerical solutions were obtained for parameter values of mu, U, delta P, and T that matched those of the physical model. The computed results agreed reasonably well with the experimental results. Scaling laws yield the prediction that h is approximately (T/delta P)(microU/T)2/3. For physiological values of the parameters, the predicted value of h is approximately 10(-3) cm, in good agreement with the observed thickness of the pleural space.

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Asif, Muhammad, Sami Ul Haq, Saeed Islam, Tawfeeq Abdullah Alkanhal, Zar Khan, Ilyas Khan, and Kottakkaran Nisar. "Unsteady Flow of Fractional Fluid between Two Parallel Walls with Arbitrary Wall Shear Stress Using Caputo–Fabrizio Derivative." Symmetry 11, no. 4 (April 1, 2019): 449. http://dx.doi.org/10.3390/sym11040449.

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In this article, unidirectional flows of fractional viscous fluids in a rectangular channel are studied. The flow is generated by the shear stress given on the bottom plate of the channel. The authors have developed a generalized model on the basis of constitutive equations described by the time-fractional Caputo–Fabrizio derivative. Many authors have published different results by applying the time-fractional derivative to the local part of acceleration in the momentum equation. This approach of the fractional models does not have sufficient physical background. By using fractional generalized constitutive equations, we have developed a proper model to investigate exact analytical solutions corresponding to the channel flow of a generalized viscous fluid. The exact solutions for velocity field and shear stress are obtained by using Laplace transform and Fourier integral transformation, for three different cases namely (i) constant shear, (ii) ramped type shear and (iii) oscillating shear. The results are plotted and discussed.

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