scholarly journals The Viscoelastic Swirled Flow in the Confusor

Polymers ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 630
Author(s):  
Aidar Kadyirov ◽  
Rinat Zaripov ◽  
Julia Karaeva ◽  
Ekaterina Vachagina
Keyword(s):  
Mathematical Model ◽  
Fluid Flows ◽  
Working Fluid ◽  
Giesekus Model ◽  
Mobility Factor ◽  
Special Cases ◽  
Swirl Intensity ◽  
Abrupt Contraction ◽  
The One ◽  
Swirled Flow

A two-dimensional mathematical model for a steady viscoelastic laminar flow in a confusor was developed under the condition of swirled flow imposed at the inlet. Low density polyethylene was considered as a working fluid. Its behavior was described by a two-mode Giesekus model. The proposed mathematical model was tested by comparing it with some special cases presented in the literature. Additionally, we propose a system of equations to find the nonlinear parameters of the multimode Giesekus model (mobility factor) based on experimental measurement. The obtained numerical results showed that in a confusor with the contraction rate of 4:1, an increase in the swirl intensity at Wi < 5.1 affects only the circumferential velocity, while the axial and radial velocities remain constant. The distribution pattern of the first normal stress difference in the confusor is qualitatively similar to the one in a channel with abrupt contraction, i.e., as the viscoelastic fluid flows in the confusor, the value of N1 increases and reaches a maximum at the end of the confusor. Dimensionless damping coefficients of swirl are used to estimate the swirl intensity. The results show that the swirl intensity decreases exponentially.

scholarly journals When to Substitute a Missing Upper Lateral With a Canine: A Simplified Approach

2021 ◽  
pp. 030157422098054
Author(s):  
Renu Datta
Keyword(s):  
Anterior Segment ◽  
Specific Treatment ◽  
Simplified Approach ◽  
Special Cases ◽  
Randomized Control ◽  
The One ◽  
Individual Presentation ◽  
Available Information ◽  
Missing Tooth ◽  
Made In

Introduction: The upper lateral incisor is the most commonly missing tooth in the anterior segment. It leads to esthetic and functional imbalance for the patients. The ideal solution is the one that is most conservative and which fulfills the functional and esthetic needs of the concerned individual. Canine substitution is evolving to be the treatment of choice in most of the cases, because of its various advantages. These are special cases that need more time and effort from the clinicians due to space discrepancy in the upper and lower arches, along with the presentation of individual malocclusion. Aims and Objectives: Malocclusion occurring due to missing laterals is more complex, needing more time and effort from the clinicians because of space discrepancy, esthetic compromise, and individual presentation of the malocclusion. An attempt has been made in this article to review, evaluate, and tabulate the important factors for the convenience of clinicians. Method: All articles related to canine substitution were searched in the electronic database PubMed, and the important factors influencing the decision were reviewed. After careful evaluation, the checklist was evolved. Result: The malocclusions in which canine substitution is the treatment of choice are indicated in the tabular form for the convenience of clinicians. Specific treatment-planning considerations and biomechanics that can lead to an efficient and long-lasting result are also discussed. Conclusion: The need of the hour is an evidence-based approach, along with a well-designed prospective randomized control trial to understand the importance of each factor influencing these cases. Until that time, giving the available information in a simplified way can be a quality approach to these cases.

scholarly journals Ultrasonic Waves in Bubbly Liquids: An Analytic Approach

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1309
Author(s):  
P. R. Gordoa ◽  
A. Pickering
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Acoustic Waves ◽  
Elliptic Functions ◽  
Coupled System ◽  
Ultrasonic Waves ◽  
Partial Differential ◽  
Special Cases ◽  
Spherical Bubbles

We consider the problem of the propagation of high-intensity acoustic waves in a bubble layer consisting of spherical bubbles of identical size with a uniform distribution. The mathematical model is a coupled system of partial differential equations for the acoustic pressure and the instantaneous radius of the bubbles consisting of the wave equation coupled with the Rayleigh–Plesset equation. We perform an analytic analysis based on the study of Lie symmetries for this system of equations, concentrating our attention on the traveling wave case. We then consider mappings of the resulting reductions onto equations defining elliptic functions, and special cases thereof, for example, solvable in terms of hyperbolic functions. In this way, we construct exact solutions of the system of partial differential equations under consideration. We believe this to be the first analytic study of this particular mathematical model.

A Numerical Study of Unsteady Natural Convection in a Rectangular Enclosure: The Effect of Compressibility

2004 ◽  
Author(s):  
K. M. Akyuzlu ◽  
Y. Pavri ◽  
A. Antoniou
Keyword(s):  
Mathematical Model ◽  
Stokes Equations ◽  
Numerical Study ◽  
Vertical Wall ◽  
Ideal Gas ◽  
Working Fluid ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Rectangular Enclosure ◽  
Circulation Patterns

A two-dimensional, mathematical model is adopted to investigate the development of buoyancy driven circulation patterns and temperature contours inside a rectangular enclosure filled with a compressible fluid (Pr=1.0). One of the vertical walls of the enclosure is kept at a higher temperature then the opposing vertical wall. The top and the bottom of the enclosure are assumed insulated. The physics based mathematical model for this problem consists of conservation of mass, momentum (two-dimensional Navier-Stokes equations) and energy equations for the enclosed fluid subjected to appropriate boundary conditions. The working fluid is assumed to be compressible through a simple ideal gas relation. The governing equations are discretized using second order accurate central differencing for spatial derivatives and first order forward finite differencing for time derivatives where the computation domain is represented by a uniform orthogonal mesh. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns (primitive variables) of the problem. A numerical experiment is carried out for a benchmark case (driven cavity flow) to verify the accuracy of the proposed solution procedure. Numerical experiments are then carried out using the proposed compressible flow model to simulate the development of the buoyancy driven circulation patterns for Rayleigh numbers between 103 and 105. Finally, an attempt is made to determine the effect of compressibility of the working fluid by comparing the results of the proposed model to that of models that use incompressible flow assumptions together with Boussinesq approximation.

scholarly journals Spreading of chemical substance after its accidental spillage onto the soil surface under unsaturated conditions and variable porosity

2019 ◽  
pp. 41-44
Author(s):  
Olena Kozhushko ◽  
Petro Martyniuk
Keyword(s):  
Mathematical Model ◽  
Soil Moisture ◽  
Soil Profile ◽  
Moisture Transport ◽  
Soil Surface ◽  
Chemical Substance ◽  
High Concentration ◽  
Solute Transfer ◽  
Variable Porosity ◽  
The One

In this paper we study a mathematical model of soil moisture transport with variable porosity. The problem is set for the case of highly concentrated solute spilled onto soil surface. We investigate the way solute transfer, adsorption of contaminant by soil particles and variable porosity influence infiltration of solute into the soil profile. For that purpose, two models are used: a classical one and the one with consideration of mentioned factors. By comparing the results of both models, we established that high concentration of solute causes moisture transport to transpire more slowly, and the pollutant to remain on the soil surface for longer time. Numerical results indicate that porosity can vary considerably under the conditions of intensive contamination with salts.

Tsunamis

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Mathematical Model ◽  
Large Scale ◽  
Volcanic Eruptions ◽  
Ocean Waves ◽  
The Other ◽  
Tsunami Generation ◽  
Sea Waves ◽  
Tsunami Propagation ◽  
Tidal Waves ◽  
Special Cases

This chapter describes a mathematical model of tsunami propagation (transient waves). A tsunami is a series of ocean waves triggered by large-scale disturbances of the ocean, including earthquakes, as well as landslides, volcanic eruptions, and meteorites. Tsunamis have very long wavelengths (typically hundreds of kilometers). They have also been called “tidal waves” or “seismic sea waves,” but both terms are misleading. The chapter first considers the boundary-value problem before modeling two special cases of tsunami generation, one due to an initial displacement on the free surface and the other due to tilting of the seafloor. It also discusses surface waves on deep water and how fast the wave energy propagates and concludes with an analysis of leading waves due to a transient disturbance.

Performance Analysis of a Solar-Assisted Organic Rankine Cycle

2020 ◽  
Author(s):  
M. T. Nitsas ◽  
I. P. Koronaki
Keyword(s):  
Mathematical Model ◽  
Performance Analysis ◽  
Temporal Variation ◽  
Storage Tank ◽  
Organic Rankine Cycle ◽  
Rankine Cycle ◽  
Working Fluid ◽  
Evaporation Temperature ◽  
Solar Powered ◽  
The Mathematical Model

Abstract The objective of this paper is the thermodynamic analysis of a solar powered Organic Rankine Cycle (O.R.C.) and the investigation of potential working fluids in order to select the optimum one. A dynamic model for a solar O.R.C. with a storage tank, which produces electricity is developed. The mathematical model includes all the equations that describe the operation of the solar collectors, the storage tank, the Rankine Cycle and the feedback between them. The model runs for representative days throughout the year, calculating the net produced energy as a function of the selected evaporation temperature for every suitable working fluid. Above that, the temporal variation of the systems’ temperatures, collectors’ efficiency and net produced power, for the optimum organic fluid and evaporation temperature are presented.

Possibility of Evaluating a Depth of Defects as a Hole in a Composite Dielectric Sample by the Parameters of Electric Response to Pulse Mechanical Excitation

2018 ◽  
Vol 781 ◽  
pp. 155-158 ◽  
Author(s):  
Petr Khorsov ◽  
Anatoly Surzhikov ◽  
Vladimir Surzhikov ◽  
Roman Laas
Keyword(s):  
Mathematical Model ◽  
Electromagnetic Response ◽  
Electric Response ◽  
One Dimensional ◽  
Response Parameter ◽  
Dielectric Sample ◽  
Receiver System ◽  
Mechanoelectrical Transformations ◽  
Spurious Component ◽  
The One

The applicability of the method mechanoelectrical transformations (MET) to determine the depth of the macrodefects location in the sample on parameters of the electromagnetic response is evaluated. As the response parameter it was used the phase characteristic of the signal analytical representation.On the one-dimensional mathematical model it was shown the possibility to detect phase response changes when reflected from defect acoustic wave is mixed with the signal spurious component generated by a distributed MET sources. Experimental verification of mathematical model on a sample of concrete was conducted. It has been shown that the sensitivity of the method MET to evaluation of the macrodefect locate depth depends on the wavelength of the excitation pulse and the area of the macrodefect border closest to the emitter-receiver system.

Location of a multinational corporation in a cluster

2016 ◽  
Vol 24 (2) ◽  
pp. 144-167 ◽  
Author(s):  
Dorota Leszczyńska ◽  
Erick Pruchnicki
Keyword(s):  
Mathematical Model ◽  
Knowledge Transfer ◽  
Tacit Knowledge ◽  
Mathematical Expression ◽  
Decision Criterion ◽  
Specific Knowledge ◽  
Content Type ◽  
The One ◽  
Effective Transfer ◽  
The Impact

Purpose A multinational company (MNC) looking to locate within a cluster is mainly interested in gaining access to scarce and highly valuable tacit knowledge. The transfer of such resources first requires sharing a certain degree of architectural and specific knowledge. This paper aims to examine the transfer of systemic technological expertise (specific tacit knowledge) that is incorporated into organisational practices (architectural knowledge). To quantify the level of knowledge transfer involved, the present study defines the architectural distance between the MNC and the cluster. Design/methodology/approach The mathematical expression of acquisition performance is inferred from a conceptual study that formulates hypotheses regarding the impact of these variables on knowledge transfer. The MNC chooses its location in such a way as to maximise this performance. Findings Applying a mathematical model to knowledge transfer between two of the MNC units helps to determine if the locally acquired knowledge could benefit other units of the MNC. Research limitations/implications The present study defines the architectural distance between the MNC and the cluster. This architectural distance is defined by a vector composed of social, organisational, cultural, institutional, technological and geographic distances between the new acquisition and its network of local partners, on the one hand, and the MNC, on the other. Knowledge transfer also depends on the business players’ trust and motivation. Further research through a quantitative study would be useful to improve the links between the proposed mathematical model and the efficiency of an MNC’s location within a cluster. Practical implications The solution to the optimisation problem allows to put forward a simple decision criterion to assist a manager who has to face the problem of an optimal location choice. Originality/value First, this study contributes to a better understanding of how knowledge transfer effects may interact with cluster effects, while explaining a subsidiary’s performance with regard to location. Second, it provides an interpretation of the concept of knowledge embeddedness by showing that the effective transfer of architectural and specific knowledge involves the prior sharing of a certain amount of this knowledge.

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