Search results for: variable volumetric expansion coefficient
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 5418

Search results for: variable volumetric expansion coefficient

5418 Thermal Radiation Effect on Mixed Convection Boundary Layer Flow over a Vertical Plate with Varying Density and Volumetric Expansion Coefficient

Authors: Sadia Siddiqa, Z. Khan, M. A. Hossain

Abstract:

In this article, the effect of thermal radiation on mixed convection boundary layer flow of a viscous fluid along a highly heated vertical flat plate is considered with varying density and volumetric expansion coefficient. The density of the fluid is assumed to vary exponentially with temperature, however; volumetric expansion coefficient depends linearly on temperature. Boundary layer equations are transformed into convenient form by introducing primitive variable formulations. Solutions of transformed system of equations are obtained numerically through implicit finite difference method along with Gaussian elimination technique. Results are discussed in view of various parameters, like thermal radiation parameter, volumetric expansion parameter and density variation parameter on the wall shear stress and heat transfer rate. It is concluded from the present investigation that increase in volumetric expansion parameter decreases wall shear stress and enhances heat transfer rate.

Keywords: thermal radiation, mixed convection, variable density, variable volumetric expansion coefficient

Procedia PDF Downloads 338
5417 Effect of Texture of Orthorhombic Martensite on Thermal Expansion of Metastable Titanium Alloy

Authors: E. Stepanova, N. Popov, S. Demakov, S. Stepanov

Abstract:

This paper examines the so-called invar-type behavior of metastable titanium alloy subjected to cold rolling. The effect was shown to occur due to the anisotropy of thermal expansion of titanium orthorhombic martensite. By means of X-ray diffraction analysis and dilatometry analyses, the influence of crystallographic texture of orthorhombic martensite on the coefficient of thermal expansion of sheets of metastable titanium alloy VT23 was examined. Anisotropy of the coefficient of thermal expansion has been revealed. It was lower in the rolling plane and higher along the transverse direction of the cold-rolled sheet comparing to the coefficient of thermal expansion of the unprocessed alloy.

Keywords: invar-type, cold rolling, metastable titanium alloy, texture

Procedia PDF Downloads 400
5416 Thermal Expansion Coefficient and Young’s Modulus of Silica-Reinforced Epoxy Composite

Authors: Hyu Sang Jo, Gyo Woo Lee

Abstract:

In this study, the evaluation of thermal stability of the micrometer-sized silica particle reinforced epoxy composite was carried out through the measurement of thermal expansion coefficient and Young’s modulus of the specimens. For all the specimens in this study from the baseline to those containing 50 wt% silica filler, the thermal expansion coefficients and the Young’s moduli were gradually decreased down to 20% and increased up to 41%, respectively. The experimental results were compared with filler-volume-based simple empirical relations. The experimental results of thermal expansion coefficients correspond with those of Thomas’s model which is modified from the rule of mixture. However, the measured result for Young’s modulus tends to be increased slightly. The differences in increments of the moduli between experimental and numerical model data are quite large.

Keywords: thermal stability, silica-reinforced, epoxy composite, coefficient of thermal expansion, empirical model

Procedia PDF Downloads 261
5415 Is It Important to Measure the Volumetric Mass Density of Nanofluids?

Authors: Z. Haddad, C. Abid, O. Rahli, O. Margeat, W. Dachraoui, A. Mataoui

Abstract:

The present study aims to measure the volumetric mass density of NiPd-heptane nanofluids synthesized using a one-step method known as thermal decomposition of metal-surfactant complexes. The particle concentration is up to 7.55 g/l and the temperature range of the experiment is from 20°C to 50°C. The measured values were compared with the mixture theory and good agreement between the theoretical equation and measurement were obtained. Moreover, the available nanofluids volumetric mass density data in the literature is reviewed.

Keywords: NiPd nanoparticles, nanofluids, volumetric mass density, stability

Procedia PDF Downloads 363
5414 Symbolic Computation on Variable-Coefficient Non-Linear Dispersive Wave Equations

Authors: Edris Rawashdeh, I. Abu-Falahah, H. M. Jaradat

Abstract:

The variable-coefficient non-linear dispersive wave equation is investigated with the aid of symbolic computation. By virtue of a newly developed simplified bilinear method, multi-soliton solutions for such an equation have been derived. Effects of the inhomogeneities of media and nonuniformities of boundaries, depicted by the variable coefficients, on the soliton behavior are discussed with the aid of the characteristic curve method and graphical analysis.

Keywords: dispersive wave equations, multiple soliton solution, Hirota Bilinear Method, symbolic computation

Procedia PDF Downloads 414
5413 Effect of Al Addition on Microstructure and Physical Properties of Fe-36Ni Invar Alloy

Authors: Seok Hong Min, Tae Kwon Ha

Abstract:

High strength Fe-36Ni-base Invar alloys containing Al contents up to 0.3 weight percent were cast into ingots and thermodynamic equilibrium during solidification has been investigated in this study. From the thermodynamic simulation using Thermo-Calc®, it has been revealed that equilibrium phases which can be formed are two kinds of MC-type precipitates, MoC, and M2C carbides. The mu phase was also expected to form by addition of aluminum. Microstructure observation revealed the coarse precipitates in the as-cast ingots, which was non-equilibrium phase and could be resolved by the successive heat treatment. With increasing Al contents up to 0.3 wt.%, tensile strength of Invar alloy increased as 1400MPa after cold rolling and thermal expansion coefficient increased significantly. Cold rolling appeared to dramatically decrease thermal expansion coefficient.

Keywords: invar alloy, aluminum, phase equilibrium, thermal expansion coefficient, microstructure, tensile properties

Procedia PDF Downloads 328
5412 Development of Al-5%Cu/Si₃N₄, B₄C or BN Composites for Piston Applications

Authors: Ahmed Lotfy, Andrey V. Pozdniakov, Vadim C. Zolotorevskiy

Abstract:

The purpose of this research is to provide a competitive alternative to aluminum silicon alloys used in automotive applications. This alternative was created by developing three types of composites Al-5%Cu- (B₄C, BN or Si₃N₄) particulates with a low coefficient of thermal expansion. Stir casting was used to synthesis composites containing 2, 5 and 7 wt. % of B₄C, Si₃N₄ and 2, 5 of BN followed by squeeze casting. The squeeze casting process decreased the porosity of the final composites. The composites exhibited a fairly uniform particle distribution throughout the matrix alloy. The microstructure and XRD results of the composites suggested a significant reaction occurred at the interface between the particles and alloy. Increasing the aging temperature from 200 to 250°C decreased the hardness values of the matrix and the composites and decreased the time required to reach the peak. Turner model was used to calculate the expected values of thermal expansion coefficient CTE of matrix and its composites. Deviations between calculated and experimental values of CTE were not exceeded 10%. Al-5%Cu-B₄C composites experimentally showed the lowest values of CTE (17-19)·10-6 °С-1 and (19-20) ·10-6 °С-1 in the temperature range 20-100 °С and 20-200 °С respectively.

Keywords: aluminum matrix composites, coefficient of thermal expansion, X-ray diffraction, squeeze casting, electron microscopy,

Procedia PDF Downloads 366
5411 Analysis of a Generalized Sharma-Tasso-Olver Equation with Variable Coefficients

Authors: Fadi Awawdeh, O. Alsayyed, S. Al-Shará

Abstract:

Considering the inhomogeneities of media, the variable-coefficient Sharma-Tasso-Olver (STO) equation is hereby investigated with the aid of symbolic computation. A newly developed simplified bilinear method is described for the solution of considered equation. Without any constraints on the coefficient functions, multiple kink solutions are obtained. Parametric analysis is carried out in order to analyze the effects of the coefficient functions on the stabilities and propagation characteristics of the solitonic waves.

Keywords: Hirota bilinear method, multiple kink solution, Sharma-Tasso-Olver equation, inhomogeneity of media

Procedia PDF Downloads 478
5410 The Application of Variable Coefficient Jacobian elliptic Function Method to Differential-Difference Equations

Authors: Chao-Qing Dai

Abstract:

In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.

Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation

Procedia PDF Downloads 626
5409 Quintic Spline Method for Variable Coefficient Fourth-Order Parabolic Partial Differential Equations

Authors: Reza Mohammadi, Mahdieh Sahebi

Abstract:

We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the proposed derived method. Numerical comparison with other existence methods shows the superiority of our presented scheme.

Keywords: fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points, stability analysis

Procedia PDF Downloads 327
5408 Artificial Neural Network in Predicting the Soil Response in the Discrete Element Method Simulation

Authors: Zhaofeng Li, Jun Kang Chow, Yu-Hsing Wang

Abstract:

This paper attempts to bridge the soil properties and the mechanical response of soil in the discrete element method (DEM) simulation. The artificial neural network (ANN) was therefore adopted, aiming to reproduce the stress-strain-volumetric response when soil properties are given. 31 biaxial shearing tests with varying soil parameters (e.g., initial void ratio and interparticle friction coefficient) were generated using the DEM simulations. Based on these 45 sets of training data, a three-layer neural network was established which can output the entire stress-strain-volumetric curve during the shearing process from the input soil parameters. Beyond the training data, 2 additional sets of data were generated to examine the validity of the network, and the stress-strain-volumetric curves for both cases were well reproduced using this network. Overall, the ANN was found promising in predicting the soil behavior and reducing repetitive simulation work.

Keywords: artificial neural network, discrete element method, soil properties, stress-strain-volumetric response

Procedia PDF Downloads 359
5407 Establishment and Validation of Correlation Equations to Estimate Volumetric Oxygen Mass Transfer Coefficient (KLa) from Process Parameters in Stirred-Tank Bioreactors Using Response Surface Methodology

Authors: Jantakan Jullawateelert, Korakod Haonoo, Sutipong Sananseang, Sarun Torpaiboon, Thanunthon Bowornsakulwong, Lalintip Hocharoen

Abstract:

Process scale-up is essential for the biological process to increase production capacity from bench-scale bioreactors to either pilot or commercial production. Scale-up based on constant volumetric oxygen mass transfer coefficient (KLa) is mostly used as a scale-up factor since oxygen supply is one of the key limiting factors for cell growth. However, to estimate KLa of culture vessels operated with different conditions are time-consuming since it is considerably influenced by a lot of factors. To overcome the issue, this study aimed to establish correlation equations of KLa and operating parameters in 0.5 L and 5 L bioreactor employed with pitched-blade impeller and gas sparger. Temperature, gas flow rate, agitation speed, and impeller position were selected as process parameters and equations were created using response surface methodology (RSM) based on central composite design (CCD). In addition, the effects of these parameters on KLa were also investigated. Based on RSM, second-order polynomial models for 0.5 L and 5 L bioreactor were obtained with an acceptable determination coefficient (R²) as 0.9736 and 0.9190, respectively. These models were validated, and experimental values showed differences less than 10% from the predicted values. Moreover, RSM revealed that gas flow rate is the most significant parameter while temperature and agitation speed were also found to greatly affect the KLa in both bioreactors. Nevertheless, impeller position was shown to influence KLa in only 5L system. To sum up, these modeled correlations can be used to accurately predict KLa within the specified range of process parameters of two different sizes of bioreactors for further scale-up application.

Keywords: response surface methodology, scale-up, stirred-tank bioreactor, volumetric oxygen mass transfer coefficient

Procedia PDF Downloads 166
5406 Single-Crystal Kerfless 2D Array Transducer for Volumetric Medical Imaging: Theoretical Study

Authors: Jurij Tasinkiewicz

Abstract:

The aim of this work is to present a theoretical analysis of a 2D ultrasound transducer comprised of crossed arrays of metal strips placed on both sides of thin piezoelectric layer (a). Such a structure is capable of electronic beam-steering of generated wave beam both in elevation and azimuth. In this paper, a semi-analytical model of the considered transducer is developed. It is based on generalization of the well-known BIS-expansion method. Specifically, applying the electrostatic approximation, the electric field components on the surface of the layer are expanded into fast converging series of double periodic spatial harmonics with corresponding amplitudes represented by the properly chosen Legendre polynomials. The problem is reduced to numerical solving of certain system of linear equations for unknown expansion coefficients.

Keywords: beamforming, transducer array, BIS-expansion, piezoelectric layer

Procedia PDF Downloads 396
5405 Validity and Reliability of the Iranian Version of the Self-Expansion Questionnaire

Authors: Mehravar Javid, James Sexton, Farzaneh Amani, Kainaz Patravala

Abstract:

Self-expansion is a procedure through which people expand the dimensions of their self-concept by incorporating novel content into their sense and experience of identity. Greater self-expansion predicts positive consequences for individuals and romantic relationships. The self-expansion questionnaire (SEQ) originally developed by Lewandowski & Aron (2002) assumes that self-expansion is constituted of key components from the self-expansion model. This study aimed to confirm the factor structure of SEQ and adapt the questions of the scale to the Iranian culture. The sample included 190 participants who responded to 14 items and were selected by simple random sampling. Using Amos-21 and SPSS-21, descriptive statistics, Pearson correlation and Confirmatory Factor Analysis (CFA) were calculated. Cronbach’s alpha coefficient for total SEQ items was 0.92. Results of CFA supported the factor structure SEQ [RMSEA=0.08, GFI=0.88 and CFI=0.92] that showed the model has a good fit and also all the items of SEQ, have a high correlation and have a direct and significant relationship. So, the SEQ demonstrated acceptable psychometric properties in Tehran University students. Looking forward, it would be interesting and exciting to see the implications of the scale as applied to romantic relationships.

Keywords: validity, reliability, confirmatory factor analysis, self-expansion questionnaire

Procedia PDF Downloads 41
5404 Detection of Muscle Swelling Using the Cnts-Based Poc Wearable Strain Sensor

Authors: Nadeem Qaiser, Sherjeel Munsif Khan, Muhammad Mustafa Hussian, Vincent Tung

Abstract:

One of the emerging fields in the detection of chronic diseases is based on the point-of-care (POC) early monitoring of the symptoms and thus provides a state-of-the-art personalized healthcare system. Nowadays, wearable and flexible sensors are being used for analyzing sweat, glucose, blood pressure, and other skin conditions. However, localized jaw-bone swelling called parotid-swelling caused by some viruses has never been tracked before. To track physical motion or deformations, strain sensors, especially piezoresistive ones, are widely used. This work, for the first time, reports carbon nanotubes (CNTs)-based piezoresistive sensing patch that is highly flexible and stretchable and can record muscle deformations in real-time. The developed patch offers an excellent gauge factor for in-plane stretching and spatial expansion with low hysteresis. To calibrate the volumetric muscle expansion, we fabricated the pneumatic actuator that experienced volumetric expansion and thus redefined the gauge factor. Moreover, we employ a Bluetooth-low-energy system that can send information about muscle activity in real-time to a smartphone app. We utilized COMSOL calculations to reveal the mechanical robustness of the patch. The experiments showed the sensing patch's greater cyclability, making it a patch for personal healthcare and an excellent choice for monitoring the real-time POC monitoring of the human muscle swelling.

Keywords: piezoresistive strain sensor, FEM simulations, CNTs sensor, flexible

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5403 Asymptotic Expansion of the Korteweg-de Vries-Burgers Equation

Authors: Jian-Jun Shu

Abstract:

It is common knowledge that many physical problems (such as non-linear shallow-water waves and wave motion in plasmas) can be described by the Korteweg-de Vries (KdV) equation, which possesses certain special solutions, known as solitary waves or solitons. As a marriage of the KdV equation and the classical Burgers (KdVB) equation, the Korteweg-de Vries-Burgers (KdVB) equation is a mathematical model of waves on shallow water surfaces in the presence of viscous dissipation. Asymptotic analysis is a method of describing limiting behavior and is a key tool for exploring the differential equations which arise in the mathematical modeling of real-world phenomena. By using variable transformations, the asymptotic expansion of the KdVB equation is presented in this paper. The asymptotic expansion may provide a good gauge on the validation of the corresponding numerical scheme.

Keywords: asymptotic expansion, differential equation, Korteweg-de Vries-Burgers (KdVB) equation, soliton

Procedia PDF Downloads 215
5402 Effects of Dimensional Sizes of Mould on the Volumetric Shrinkage Strain of Lateric Soil

Authors: John E. Sani, Moses George

Abstract:

The paper presents the result of a laboratory study carried out on lateritic soil to determine the effects of dimensional size on the volumetric shrinkage strain (VSS) using three mould sizes i.e. split former mould, proctor mould and California bearing ratio (CBR) mould at three energy levels; British standard light (BSL), West African standard (WAS) and British standard heavy (BSH) respectively. Compactions were done at different molding water content of -2 % to +6 % optimum moisture content (OMC). At -2% to +2% molding water content for the split former mould the volumetric shrinkage strain met the requirement of not more than 4% while at +4% and +6% only the WAS and BSH met the requirement. The proctor mould and the CBR mould on the other hand gave a lower value of volumetric shrinkage strain in all compactive effort and the values are lower than the 4% safe VSS value.

Keywords: lateritic soil, volumetric shrinkage strain, molding water content, compactive effort

Procedia PDF Downloads 491
5401 Evaluation of Spatial Correlation Length and Karhunen-Loeve Expansion Terms for Predicting Reliability Level of Long-Term Settlement in Soft Soils

Authors: Mehrnaz Alibeikloo, Hadi Khabbaz, Behzad Fatahi

Abstract:

The spectral random field method is one of the widely used methods to obtain more reliable and accurate results in geotechnical problems involving material variability. Karhunen-Loeve (K-L) expansion method was applied to perform random field discretization of cross-correlated creep parameters. Karhunen-Loeve expansion method is based on eigenfunctions and eigenvalues of covariance function adopting Kernel integral solution. In this paper, the accuracy of Karhunen-Loeve expansion was investigated to predict long-term settlement of soft soils adopting elastic visco-plastic creep model. For this purpose, a parametric study was carried to evaluate the effect of K-L expansion terms and spatial correlation length on the reliability of results. The results indicate that small values of spatial correlation length require more K-L expansion terms. Moreover, by increasing spatial correlation length, the coefficient of variation (COV) of creep settlement increases, confirming more conservative and safer prediction.

Keywords: Karhunen-Loeve expansion, long-term settlement, reliability analysis, spatial correlation length

Procedia PDF Downloads 124
5400 Modeling Studies on the Elevated Temperatures Formability of Tube Ends Using RSM

Authors: M. J. Davidson, N. Selvaraj, L. Venugopal

Abstract:

The elevated temperature forming studies on the expansion of thin walled tubes have been studied in the present work. The influence of process parameters namely the die angle, the die ratio and the operating temperatures on the expansion of tube ends at elevated temperatures is carried out. The range of operating parameters have been identified by perfoming extensive simulation studies. The hot forming parameters have been evaluated for AA2014 alloy for performing the simulation studies. Experimental matrix has been developed from the feasible range got from the simulation results. The design of experiments is used for the optimization of process parameters. Response Surface Method’s (RSM) and Box-Behenken design (BBD) is used for developing the mathematical model for expansion. Analysis of variance (ANOVA) is used to analyze the influence of process parameters on the expansion of tube ends. The effect of various process combinations of expansion are analyzed through graphical representations. The developed model is found to be appropriate as the coefficient of determination value is very high and is equal to 0.9726. The predicted values are found to coincide well with the experimental results, within acceptable error limits.

Keywords: expansion, optimization, Response Surface Method (RSM), ANOVA, bbd, residuals, regression, tube

Procedia PDF Downloads 476
5399 Optimization of Alkali Silicate Glass Heat Treatment for the Improvement of Thermal Expansion and Flexural Strength

Authors: Stephanie Guerra-Arias, Stephani Nevarez, Calvin Stewart, Rachel Grodsky, Denis Eichorst

Abstract:

The objective of this study is to describe the framework for optimizing the heat treatment of alkali silicate glasses, to enhance the performance of hermetic seals in extreme environments. When connectors are exposed to elevated temperatures, residual stresses develop due to the mismatch of thermal expansions between the glass, metal pin, and metal shell. Excessive thermal expansion mismatch compromises the reliability of hermetic seals. In this study, a series of heat treatment schedules will be performed on two commercial sealing glasses (one conventional sealing glass and one crystallizable sealing glass) using a design of experiments (DOE) approach. The coefficient of thermal expansion (CTE) will be measured pre- and post-heat treatment using thermomechanical analysis (TMA). Afterwards, the flexural strength of the specimen will be measured using a four-point bend fixture mounted in a static universal testing machine. The measured material properties will be statistically analyzed using MiniTab software to determine which factors of the heat treatment process have a strong correlation to the coefficient of thermal expansion and/or flexural strength. Finally, a heat-treatment will be designed and tested to ensure the optimal performance of the hermetic seals in connectors.

Keywords: glass-ceramics, design of experiment, hermetic connectors, material characterization

Procedia PDF Downloads 119
5398 Durability and Early-Age Behavior of Sprayed Concrete with an Expansion Admixture

Authors: Kyong-Ku Yun, Kyeo-Re Lee, Kyong Namkung, Seung-Yeon Han, Pan-Gil Choi

Abstract:

Sprayed concrete is a way to spray a concrete using a machinery with high air pressure. There are insufficient studies on the durability and early-age behavior of sprayed concrete using high quality expansion agent. A series of an experiment were executed with 5 varying expansion agent replacement rates, while all the other conditions were kept constant, including cement binder content and water-cement ratio. The tests includes early-age shrinkage test, rapid chloride permeability test, and image analysis of air void structure. The early-age expansion test with the variation of expansion agent show that the expansion strain increases as the ratio of expansion agent increases. The rapid chloride permeability test shows that it decrease as the expansion agent increase. Therefore, expansion agent affects into the rapid chloride permeability in a better way. As expansion agent content increased, spacing factor slightly decreased while specific surface kept relatively stable. As a results, the optimum ratio of expansion agent would be selected between 7 % and 11%.

Keywords: sprayed concrete, durability, early-age behavior, expansion admixture

Procedia PDF Downloads 477
5397 Exact Solutions of Discrete Sine-Gordon Equation

Authors: Chao-Qing Dai

Abstract:

Two families of exact travelling solutions for the discrete sine-Gordon equation are constructed based on the variable-coefficient Jacobian elliptic function method and different transformations. When the modulus of Jacobian elliptic function solutions tends to 1, soliton solutions can be obtained. Some soliton solutions degenerate into the known solutions in literatures. Moreover, dynamical properties of exact solutions are investigated. Our analysis and results may have potential values for certain applications in modern nonlinear science and textile engineering.

Keywords: exact solutions, variable-coefficient Jacobian elliptic function method, discrete sine-Gordon equation, dynamical behaviors

Procedia PDF Downloads 379
5396 Design of Tube Expanders with Groove Shapes to Reduce Deformation of Tube Inner Grooves in Copper Tube Expansion

Authors: I. Sin, H. Kim, S. Park

Abstract:

Fin-tube heat exchangers have grooves inside tubes to improve heat exchange performance. However, during the tube expansion process, heat exchange efficiency is decreased due to large deformation of tube inner grooves. Therefore, the objective of this study is to design a tube expander with groove shapes on its outer surface to minimize deformation of the inner grooves in copper tube expansion for fin-tube heat exchangers. In order to achieve this goal, first, we have tried to calculate tube inner groove deformation by the currently used tube expander without groove shapes on its surface. The tube inner groove deformation was acquired by elastoplastic finite element analysis from the boundary conditions with one tube end fixed and friction between the tube and tube expander (friction coefficient: 0.15). The tube expansion process was simulated by inserting the tube expander into the tube with a speed of 90 mm/s. The analysis results showed that tube inner groove heights were decreased by approximately 8 % from 0.15 mm to 0.138 mm with stress concentrations observed at the groove end, consistent with experimental results. Based on the current results, we are trying to design a novel shape of the tube expander with grooves to further reduce deformation tube inner grooves in copper tube expansion. For this, we will select major design variables of tube expander groove shapes by conducting sensitivity analysis and then optimize the design variables using the Taguchi method.

Keywords: tube expansion, tube expander, heat exchanger, finite element

Procedia PDF Downloads 282
5395 High Accuracy Analytic Approximations for Modified Bessel Functions I₀(x)

Authors: Pablo Martin, Jorge Olivares, Fernando Maass

Abstract:

A method to obtain analytic approximations for special function of interest in engineering and physics is described here. Each approximate function will be valid for every positive value of the variable and accuracy will be high and increasing with the number of parameters to determine. The general technique will be shown through an application to the modified Bessel function of order zero, I₀(x). The form and the calculation of the parameters are performed with the simultaneous use of the power series and asymptotic expansion. As in Padé method rational functions are used, but now they are combined with other elementary functions as; fractional powers, hyperbolic, trigonometric and exponential functions, and others. The elementary function is determined, considering that the approximate function should be a bridge between the power series and the asymptotic expansion. In the case of the I₀(x) function two analytic approximations have been already determined. The simplest one is (1+x²/4)⁻¹/⁴(1+0.24273x²) cosh(x)/(1+0.43023x²). The parameters of I₀(x) were determined using the leading term of the asymptotic expansion and two coefficients of the power series, and the maximum relative error is 0.05. In a second case, two terms of the asymptotic expansion were used and 4 of the power series and the maximum relative error is 0.001 at x≈9.5. Approximations with much higher accuracy will be also shown. In conclusion a new technique is described to obtain analytic approximations to some functions of interest in sciences, such that they have a high accuracy, they are valid for every positive value of the variable, they can be integrated and differentiated as the usual, functions, and furthermore they can be calculated easily even with a regular pocket calculator.

Keywords: analytic approximations, mathematical-physics applications, quasi-rational functions, special functions

Procedia PDF Downloads 217
5394 Quintic Spline Solution of Fourth-Order Parabolic Equations Arising in Beam Theory

Authors: Reza Mohammadi, Mahdieh Sahebi

Abstract:

We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme.

Keywords: fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points

Procedia PDF Downloads 314
5393 Simulation of Cure Kinetics and Process-Induced Stresses in Carbon Fibre Composite Laminate Manufactured by a Liquid Composite Molding Technique

Authors: Jayaraman Muniyappan, Bachchan Kr Mishra, Gautam Salkar, Swetha Manian Sridhar

Abstract:

Vacuum Assisted Resin Transfer Molding (VARTM), a cost effective method of Liquid Composite Molding (LCM), is a single step process where the resin, at atmospheric pressure, is infused through a preform that is maintained under vacuum. This hydrodynamic pressure gradient is responsible for the flow of resin through the dry fabric preform. The current study has a slight variation to traditional VARTM, wherein, the resin infuses through the fabric placed on a heated mold to reduce its viscosity. The saturated preform is subjected to a cure cycle where the resin hardens as it undergoes curing. During this cycle, an uneven temperature distribution through the thickness of the composite and excess exothermic heat released due to different cure rates result in non-uniform curing. Additionally, there is a difference in thermal expansion coefficient between fiber and resin in a given plane and between adjacent plies. All these effects coupled with orthotropic coefficient of thermal expansion of the composite give rise to process-induced stresses in the laminate. Such stresses lead to part deformation when the laminate tries to relieve them as the part is released off the mold. The current study looks at simulating resin infusion, cure kinetics and the structural response of composite laminate subject to process-induced stresses.

Keywords: cure kinetics, process-induced stresses, thermal expansion coefficient, vacuum assisted resin transfer molding

Procedia PDF Downloads 201
5392 A Summary of the Research on the Driving Mechanism of Space Expansion in China's National New District

Authors: Qin Xia

Abstract:

’National New District’ as a regional overall promotion of strategic thinking has become increasingly mature, but its spatial expansion is still chaotic and disorderly, so it is urgent to summarize the complex and unique driving mechanism contained in its spatial expansion to formulate sustainable urban expansion plan. Under the understanding of the general laws of the driving mechanism of China's space expansion, it is found that the existing research on the driving mechanism of the space expansion of national new districts is insufficient. The research area focuses on the research of the driving mechanism of the space expansion of a single new area. In terms of research methods, qualitative description is the main focus. In terms of research content, it is limited to the expansion speed, intensity, and area of the new district itself and does not involve the expansion and utilization efficiency of space and the spillover efficiency to surrounding cities. The specific connotations of social, economic, political, and geographical categories are not thoroughly explored. It is often a general explanation that a certain factor has promoted it. The logic is not rigorous and convincing, and the description is relatively static, with different time and space. There is less literature on scale interaction. Through the reflection on the key and difficult points of the drive mechanism of the space expansion of the national new area, it is clear that the existing research on the drive mechanism of the space expansion of the national new area should be continued to drive the sustainable expansion of space.

Keywords: national new district, space expansion, driving mechanism, existing research

Procedia PDF Downloads 137
5391 Effect of Transition Metal Addition on Aging Behavior of Invar Alloy

Authors: Young Sik Kim, Tae Kwon Ha

Abstract:

High strength Fe-36Ni-base Invar alloys containing Al contents up to 0.3 weight per cent were cast into ingots and thermodynamic equilibrium during solidification has been investigated in this study. From the thermodynamic simulation using Thermo-Calc®, it has been revealed that equilibrium phases which can be formed are two kinds of MC-type precipitates, MoC, and M2C carbides. The mu phase was also expected to form by addition of aluminum. Microstructure observation revealed the coarse precipitates in the as-cast ingots, which was non-equilibrium phase and could be resolved by the successive heat treatment. With increasing Al contents up to 0.3 wt.%, tensile strength of Invar alloy increased as 1400MPa after cold rolling and thermal expansion coefficient increased significantly. Cold rolling appeared to dramatically decrease thermal expansion coefficient.

Keywords: Invar alloy, transition metals, phase equilibrium, aging behavior, microstructure, hardness

Procedia PDF Downloads 501
5390 Heat-Induced Uncertainty of Industrial Computed Tomography Measuring a Stainless Steel Cylinder

Authors: Verena M. Moock, Darien E. Arce Chávez, Mariana M. Espejel González, Leopoldo Ruíz-Huerta, Crescencio García-Segundo

Abstract:

Uncertainty analysis in industrial computed tomography is commonly related to metrological trace tools, which offer precision measurements of external part features. Unfortunately, there is no such reference tool for internal measurements to profit from the unique imaging potential of X-rays. Uncertainty approximations for computed tomography are still based on general aspects of the industrial machine and do not adapt to acquisition parameters or part characteristics. The present study investigates the impact of the acquisition time on the dimensional uncertainty measuring a stainless steel cylinder with a circular tomography scan. The authors develop the figure difference method for X-ray radiography to evaluate the volumetric differences introduced within the projected absorption maps of the metal workpiece. The dimensional uncertainty is dominantly influenced by photon energy dissipated as heat causing the thermal expansion of the metal, as monitored by an infrared camera within the industrial tomograph. With the proposed methodology, we are able to show evolving temperature differences throughout the tomography acquisition. This is an early study showing that the number of projections in computer tomography induces dimensional error due to energy absorption. The error magnitude would depend on the thermal properties of the sample and the acquisition parameters by placing apparent non-uniform unwanted volumetric expansion. We introduce infrared imaging for the experimental display of metrological uncertainty in a particular metal part of symmetric geometry. We assess that the current results are of fundamental value to reach the balance between the number of projections and uncertainty tolerance when performing analysis with X-ray dimensional exploration in precision measurements with industrial tomography.

Keywords: computed tomography, digital metrology, infrared imaging, thermal expansion

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5389 Oxygen Transfer in Viscous Non-Newtonian Liquid in a Hybrid Bioreactor

Authors: Sérgio S. de Jesus, Aline Santana, Rubens Maciel Filho

Abstract:

Global oxygen transfer coefficient (kLa) was characterized in a mechanically agitated airlift bio reactor. The experiments were carried out in an airlift bio reactor (3.2 L) with internal re circulation (a concentric draft-tube airlift vessel device); the agitation is carried out through a turbine Rushton impeller located along with the gas sparger in the region comprised in the riser. The experiments were conducted using xanthan gum (0.6%) at 250 C and a constant rotation velocity of 0 and 800 rpm, as well as in the absence of agitation (airlift mode); the superficial gas velocity varied from 0.0157 to 0.0262 ms-1. The volumetric oxygen transfer coefficient dependence of the rotational speed revealed that the presence of agitation increased up to two times the kLa value.

Keywords: aeration, mass transfer, non-Newtonian fluids, stirred airlift bioreactor

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