Unsteady Flow of Fluids With Arbitrarily Time-Dependent Rheological Behavior

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Irene Daprà ◽  
Giambattista Scarpi
Keyword(s):  
Analytical Solution ◽  
Kinematic Viscosity ◽  
Applied Pressure ◽  
Gibbs Phenomenon ◽  
Momentum Equation ◽  
Unsteady Motion ◽  
Circular Pipes ◽  
Direct Numerical Solution ◽  
The Difference ◽  
Radial Variable

This paper presents an analytical solution of the momentum equation for the unsteady motion of fluids in circular pipes, in which the kinematic viscosity is allowed to change arbitrarily in time. Velocity and flow rate are expressed as a series expansion of Bessel and Kelvin functions of the radial variable, whereas the dependence on time is expressed as Fourierlike series. The analytical solution for the velocity is compared with the direct numerical solution of the momentum equation in a particular case, verifying that the difference between analytical and numerical values of axial velocity is less than 1%, except near the discontinuity of the applied pressure gradient, where the typical behavior due to the Gibbs phenomenon is to be noted.

scholarly journals An Exact Solution for Power-Law Fluids in a Slit Microchannel with Different Zeta Potentials under Electroosmotic Forces

Micromachines ◽  
2018 ◽  
Vol 9 (10) ◽  
pp. 504 ◽  
Author(s):  
Du-Soon Choi ◽  
Sungchan Yun ◽  
WooSeok Choi
Keyword(s):  
Power Law ◽  
Applied Pressure ◽  
Debye Length ◽  
Momentum Equation ◽  
Microfluidic System ◽  
Zeta Potentials ◽  
Power Law Fluids ◽  
Poisson Boltzmann ◽  
The Difference ◽  
Poisson Boltzmann Equation

Electroosmotic flow (EOF) is one of the most important techniques in a microfluidic system. Many microfluidic devices are made from a combination of different materials, and thus asymmetric electrochemical boundary conditions should be applied for the reasonable analysis of the EOF. In this study, the EOF of power-law fluids in a slit microchannel with different zeta potentials at the top and bottom walls are studied analytically. The flow is assumed to be steady, fully developed, and unidirectional with no applied pressure. The continuity equation, the Cauchy momentum equation, and the linearized Poisson-Boltzmann equation are solved for the velocity field. The exact solutions of the velocity distribution are obtained in terms of the Appell’s first hypergeometric functions. The velocity distributions are investigated and discussed as a function of the fluid behavior index, Debye length, and the difference in the zeta potential between the top and bottom.

Blood Pressure Estimation with Considering of Stroke Volume Effect

2008 ◽  
pp. 173-180
Author(s):  
Moha’med O. Al-Jaafreh ◽  
Adel A. Al-Jumaily
Keyword(s):  
Blood Pressure ◽  
Stroke Volume ◽  
Applied Pressure ◽  
Peripheral Resistance ◽  
Volume Effect ◽  
Signal Features ◽  
Measure Blood Pressure ◽  
The Mean ◽  
The Difference ◽  
Blood Pressure Estimation

The mean arterial pressure (MAP) is a very important cardiovascular parameter for physicians to diagnose various cardiovascular diseases. Many algorithms were used to estimate MAP with different accuracy. These algorithms used different factors, such as blood level, pulses, and external applied pressure, photo-plethysmography (PPG) signal features, heart rate (HR), and other factors. In addition, some natural-based techniques were employed to minimize the difference between estimated and measured blood pressure, as well as to measure blood pressure continuously. This article presents an algorithm to estimate MAP, utilizing the HR, Stroke Volume (SV), and Total Peripheral Resistance (TPR), with considering SV changing influence; this consideration is investigated mathematically, and by the Particle Swarm Optimization (PSO) technique.

scholarly journals Pulsating Flow of an Ostwald—De Waele Fluid between Parallel Plates

Water ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 932
Author(s):  
Rodrigo González ◽  
Aldo Tamburrino ◽  
Andrea Vacca ◽  
Michele Iervolino
Keyword(s):  
Shear Stress ◽  
Analytical Solution ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Velocity Distribution ◽  
Momentum Equation ◽  
Parallel Plates ◽  
Analytical Computation ◽  
Pulsatile Pressure ◽  
Pulsatile Pressure Gradient

The flow between two parallel plates driven by a pulsatile pressure gradient was studied analytically with a second-order velocity expansion. The resulting velocity distribution was compared with a numerical solution of the momentum equation to validate the analytical solution, with excellent agreement between the two approaches. From the velocity distribution, the analytical computation of the discharge, wall shear stress, discharge, and dispersion enhancements were also computed. The influence on the solution of the dimensionless governing parameters and of the value of the rheological index was discussed.

Mathematical Model Incorporated Fractal Geometry and Permeability of Compressed Peanut and Sesame for Oil Extraction

2012 ◽  
Vol 550-553 ◽  
pp. 676-681
Author(s):  
Xiao Zheng ◽  
Jing Zhou Wang ◽  
Guo Xiang Lin ◽  
Zhi Xian Sun ◽  
Don Ping He
Keyword(s):  
Mathematical Model ◽  
Fractal Dimension ◽  
Applied Pressure ◽  
Fractal Dimensions ◽  
Image Analyzer ◽  
Fractal Characteristic ◽  
Pore Size Distributions ◽  
The Difference ◽  
Sesame Cake ◽  
Box Counting Method

Considering the fractal characteristic of oilseed cake, the relationship between the permeability and the pore fractal dimension of peanut and sesame cake has been investigated. The microstructures of peanut and sesame cake under five applied pressures are measured by using stereo light microscope and Image-pro image analyzer. Using the box-counting method, the fractal dimensions of pore size distributions are measured. A mathematical model incorporated fractal dimension and permeability has been developed to predicate the permeability of compressed peanut and sesame under cold condition based upon combining Hagen-Poiseulle equation with Darcy’s law for flow of fluid through porous media. There is a prediction of permeability of peanut and sesame cake. Thus, a measurement is carried out for validation. The values of mean relative errors are 19.4% and 11.4 respectively. A fairly good agreement is obtained in the case of high applied pressure. And there exists a tendency that the value of the difference between the theoretical calculation and the permeability measurement decrease significantly with the increase of applied pressure.

Analytical Solution for Vibration of a Rotating Delaminated Composite Beam with End Mass

2016 ◽  
Vol 16 (06) ◽  
pp. 1550013 ◽  
Author(s):  
Ramazan-Ali Jafari-Talookolaei
Keyword(s):  
Analytical Solution ◽  
Natural Frequencies ◽  
Laminated Composite ◽  
Mode Shapes ◽  
Material Anisotropy ◽  
Rotating Speed ◽  
Multipliers Method ◽  
Free Mode ◽  
The Difference ◽  
Laminated Composite Beams

In this paper, the free vibration of rotating laminated composite beams (LCBs) with general lay-ups and single through-the-width delamination is analytically investigated. The Hamilton’s principle is used to derive the coupled governing differential equations and boundary conditions for the rotating delaminated beam, considering the effects of shear deformation, rotary inertia, material couplings (bending–tension, bending–twist and tension–twist couplings), and Poisson’s effect. Both the free mode and constrained mode assumptions are adopted. Analytical solution for the natural frequencies and mode shapes are presented by incorporating the constraint conditions using the Lagrange multipliers method. The accuracy is assured by the convergence of the natural frequencies, as well as by comparison with published results. The effects of various factors such as delamination parameter, fiber angle, hub radius, material anisotropy, end mass and rotating speed are studied in detail. The difference between the results based on the free mode and constrained mode assumptions is also investigated.

Effect of Materials on the Heat Transfer to Supercritical Pressure Fluids

2017 ◽  
Author(s):  
Xianliang Lei ◽  
Xiangfei Kong ◽  
Qian Zhang ◽  
Weiqiang Zhang ◽  
Huixiong Li
Keyword(s):  
Heat Transfer ◽  
Chemical Properties ◽  
Heating Surface ◽  
Supercritical Pressure ◽  
Operating Conditions ◽  
Inconel 600 ◽  
Heat Transfer Efficiency ◽  
Circular Pipes ◽  
The Difference ◽  
Aisi 321

Supercritical pressure fluids are widely used in many advanced single-phase thermosiphons as a working medium due to its high convective heat transfer efficiency and simpler design. However, the heat transfer in the pseudocritical region is very complex due to its steep variation of thermophysical properties and effect by the operating parameters. Under supercritical pressures, special heat transfer phenomenon can be observed in the heated tubes, three totally different heat transfer regimes present. As a result of the similarity between subcritical boiling phenomena and the deteriorated heat transfer behavior at supercritical pressure, scholars observed that heater with different materials but the same operating conditions, different types of free convection would be appeared by investigating the boiling-like phenomenon of carbon dioxide, which seems that boiling-like phenomena are specific to heater materials. The aim of this present study is to investigate the effects of thermophysical and chemical properties of heater materials upon heat transfer to supercritical water. In the present paper, two circular pipes with differential usual materials (AISI 321 and Inconel 600) are experimentally investigated by the electrically heating methods. The difference between AISI 321 and Inconel 600 in both enhanced and deteriorated heat transfer regimes are discussed respectively, then the heat transfer discrepancy caused by the materials analyzed. The results show that the heat transfer of supercritical pressure fluids dependent not only on the variation of the operating/boundary conditions but also on the materials of heating surface.

scholarly journals Analysis of the results of a computational experiment to restore the discontinuous functions of two variables using projections

2021 ◽  
pp. 12-17
Author(s):  
Oleg Lytvyn ◽  
Oleg Lytvyn ◽  
Oleksandra Lytvyn
Keyword(s):  
Differentiable Function ◽  
Fourier Coefficients ◽  
Gibbs Phenomenon ◽  
Discontinuous Function ◽  
Projection Data ◽  
Approximation Accuracy ◽  
Discontinuous Functions ◽  
Functions Of Two Variables ◽  
Fourier Sums ◽  
The Difference

This article presents the main statements of the method of approximation of discontinuous functions of two variables, describing an image of the surface of a 2D body or an image of the internal structure of a 3D body in a certain plane, using projections that come from a computer tomograph. The method is based on the use of discontinuous splines of two variables and finite Fourier sums, in which the Fourier coefficients are found using projection data. The method is based on the following idea: an approximated discontinuous function is replaced by the sum of two functions – a discontinuous spline and a continuous or differentiable function. A method is proposed for constructing a spline function, which has on the indicated lines the same discontinuities of the first kind as the approximated discontinuous function, and a method for finding the Fourier coefficients of the indicated continuous or differentiable function. That is, the difference between the function being approximated and the specified discontinuous spline is a function that can be approximated by finite Fourier sums without the Gibbs phenomenon. In the numerical experiment, it was assumed that the approximated function has discontinuities of the first kind on a given system of circles and ellipses nested into each other. The analysis of the calculation results showed their correspondence to the theoretical statements of the work. The proposed method makes it possible to obtain a given approximation accuracy with a smaller number of projections, that is, with less irradiation.

scholarly journals Stress Impact of the Annealing Procedure of Cu-Filled TSV Packaging on the Performance of Nano-Scaled MOSFETs Evaluated by an Analytical Solution and FEA-Based Submodeling Technique

Materials ◽  
2021 ◽  
Vol 14 (18) ◽  
pp. 5226
Author(s):  
Pei-Chen Huang ◽  
Chang-Chun Lee
Keyword(s):  
Analytical Solution ◽  
Silicon Germanium ◽  
Lattice Mismatch ◽  
Oxide Semiconductor ◽  
Element Analysis ◽  
Stress Solution ◽  
The Difference ◽  
Field Transistor ◽  
Interconnect Systems ◽  
P Type

Stress-induced performance change in electron packaging architecture is a major concern when the keep-out zone (KOZ) and corresponding integration density of interconnect systems and transistor devices are considered. In this study, a finite element analysis (FEA)-based submodeling approach is demonstrated to analyze the stress-affected zone of through-silicon via (TSV) and its influences on a planar metal oxide semiconductor field transistor (MOSFET) device. The feasibility of the widely adopted analytical solution for TSV stress-affected zone estimation, Lamé radial stress solution, is investigated and compared with the FEA-based submodeling approach. Analytic results reveal that the Lamé stress solution overestimates the TSV-induced stress in the concerned device by over 50%, and the difference in the estimated results of device performance between Lamé stress solution and FEA simulation can reach 22%. Moreover, a silicon–germanium-based lattice mismatch stressor is designed in a silicon p-type MOSFET, and its effects are analyzed and compared with those of TSV residual stress. The S/D stressor dominates the stress status of the device channel. The demonstrated FEA-based submodeling approach is effective in analyzing the stress impact from packaging and device-level components and estimating the KOZ issue in advanced electronic packaging.

Limit Load Solutions of the Orthotropic Thick-Walled Pipe Subjected to Internal Pressure, Bending Moment and Torsion Moment

2019 ◽  
Author(s):  
Min Xu ◽  
Yujie Zhao ◽  
Binbin Zhou ◽  
Xiaohua He ◽  
Changyu Zhou
Keyword(s):  
Analytical Solution ◽  
Yield Strength ◽  
Internal Pressure ◽  
Yield Criterion ◽  
Bending Moment ◽  
Limit Load ◽  
Pure Bending ◽  
Pure Torsion ◽  
Torsion Moment ◽  
The Difference

Abstract Based on the Hill yield criterion, the analytical solutions of the limit load of orthotropic thick-walled pipes under pure internal pressure, bending moment and torsion are given respectively. The simplified Mises analytical solution and finite element results of limit load for isotropic thick-walled pipe are obtained. The solution verifies the reliability of the analytical solution. The paper discusses the difference of limit load of isotropic and orthotropic pipes under the conditions of pure internal pressure, pure bending moment and pure torsion moment. It is concluded that the influence of material anisotropy on the limit load is significant. The limit load of pipe under pure internal pressure is mainly determined by circumferential yield strength, pure bending is only related to axial yield strength and pure torsion moment is related to the yield strength in the 45° direction and radial yield strength.

Boundary Conditions and Initial Value Lines for Unsteady Homentropic Flow Calculations

1970 ◽  
Vol 21 (2) ◽  
pp. 145-162 ◽  
Author(s):  
W. A. Woods ◽  
H. Daneshyar
Keyword(s):  
Boundary Condition ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Good Accuracy ◽  
Numerical Calculations ◽  
Time Dependent ◽  
Straight Pipe ◽  
Initial Value ◽  
Use Of Time ◽  
The Difference

SummaryA detailed discussion on the difference between an initial value line and a line characterised by a boundary condition has been presented. Two types of boundaries are described and illustrated. To examine each boundary, several different calculations have been performed for a straight pipe. The results of the numerical calculations are compared with an analytical solution. It is shown that known pressure and velocity at the pipe ends give the most accurate results. Comparisons are also made between several practical types of calculations which give similar findings. The use of time-dependent boundaries can lead to errors as large as 40 per cent in derived results. It is shown that good accuracy can be restored by converting the boundaries into initial value lines. It is concluded that in general no more than one time-dependent boundary should be used in any calculation. Finally it is demonstrated that errors are not revealed by means of pressure diagrams alone.

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