Search results for: boundary layer fence

Authors: E. Livya, G. Anitha, P. Valli

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The main objective of aircraft aerodynamics is to enhance the aerodynamic characteristics and maneuverability of the aircraft. This enhancement includes the reduction in drag and stall phenomenon. The airfoil which contains dimples will have comparatively less drag than the plain airfoil. Introducing dimples on the aircraft wing will create turbulence by creating vortices which delays the boundary layer separation resulting in decrease of pressure drag and also increase in the angle of stall. In addition, wake reduction leads to reduction in acoustic emission. The overall objective of this paper is to improve the aircraft maneuverability by delaying the flow separation point at stall and thereby reducing the drag by applying the dimple effect over the aircraft wing. This project includes both computational and experimental analysis of dimple effect on aircraft wing, using NACA 0018 airfoil. Dimple shapes of Semi-sphere, hexagon, cylinder, square are selected for the analysis; airfoil is tested under the inlet velocity of 30m/s at different angle of attack (5˚, 10˚, 15˚, 20˚, and 25˚). This analysis favours the dimple effect by increasing L/D ratio and thereby providing the maximum aerodynamic efficiency, which provides the enhanced performance for the aircraft.

Keywords: airfoil, dimple effect, turbulence, boundary layer separation

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Authors: X. Wang, T. J. Craft, H. Iacovides

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When handling the near-wall regions of turbulent flows, it is necessary to account for the viscous effects which are important over the thin near-wall layers. Low-Reynolds- number turbulence models do this by including explicit viscous and also damping terms which become active in the near-wall regions, and using very fine near-wall grids to properly resolve the steep gradients present. In order to overcome the cost associated with the low-Re turbulence models, a more advanced wall function approach has been implemented within OpenFoam and tested together with a standard log-law based wall function in the prediction of flows which involve 2-D shock wave/turbulent boundary layer interactions (SWTBLIs). On the whole, from the calculation of the impinging shock interaction, the three turbulence modelling strategies, the Lauder-Sharma k-ε model with Yap correction (LS), the high-Re k-ε model with standard wall function (SWF) and analytical wall function (AWF), display good predictions of wall-pressure. However, the SWF approach tends to underestimate the tendency of the flow to separate as a result of the SWTBLI. The analytical wall function, on the other hand, is able to reproduce the shock-induced flow separation and returns predictions similar to those of the low-Re model, using a much coarser mesh.

Keywords: SWTBLIs, skin-friction, turbulence modeling, wall function

Procedia PDF Downloads 315

Authors: T. Arudchelvam, W. W. E. N. Fernando

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Mobile phone has become as an essential thing in our life. Therefore, security is the most important thing to be considered in mobile communication. Short message service is the cheapest way of communication via the mobile phones. Therefore, security is very important in the short message service as well. This paper presents a method to maintain the security at user level. Different types of encryption methods are used to implement the user level security in mobile phones. Caesar cipher, Rail Fence, Vigenere cipher and RSA are used as encryption methods in this work. Caesar cipher and the Rail Fence methods are enhanced and implemented. The beauty in this work is that the user can select the encryption method and the key. Therefore, by changing the encryption method and the key time to time, the user can ensure the security of messages. By this work, while users can safely send/receive messages, they can save their information from unauthorised and unwanted people in their own mobile phone as well.

Keywords: SMS, user level security, encryption, decryption, short message service, mobile communication

Procedia PDF Downloads 368

Authors: Roslinda Nazar, Amin Noor, Khamisah Jafar, Ioan Pop

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In this paper, the steady laminar three-dimensional boundary layer flow and heat transfer of a copper (Cu)-water nanofluid in the vicinity of a permeable shrinking flat surface in an otherwise quiescent fluid is studied. The nanofluid mathematical model in which the effect of the nanoparticle volume fraction is taken into account is considered. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using a similarity transformation which is then solved numerically using the function bvp4c from Matlab. Dual solutions (upper and lower branch solutions) are found for the similarity boundary layer equations for a certain range of the suction parameter. A stability analysis has been performed to show which branch solutions are stable and physically realizable. The numerical results for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are obtained, presented and discussed in detail for a range of various governing parameters.

Keywords: heat transfer, nanofluid, shrinking surface, stability analysis, three-dimensional flow

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Authors: Mostafa Shahriari, Theophile Chaumont-Frelet, David Pardo

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Resistivity measurements are used to characterize the Earth’s subsurface. They are categorized into two different groups: (a) those acquired on the Earth’s surface, for instance, controlled source electromagnetic (CSEM) and Magnetotellurics (MT), and (b) those recorded with borehole logging instruments such as Logging-While-Drilling (LWD) devices. LWD instruments are mostly used for geo-steering purposes, i.e., to adjust dip and azimuthal angles of a well trajectory to drill along a particular geological target. Modern LWD tools measure all nine components of the magnetic field corresponding to three orthogonal transmitter and receiver orientations. In order to map the Earth’s subsurface and perform geo-steering, we invert measurements using a gradient-based method that utilizes the derivatives of the recorded measurements with respect to the inversion variables. For resistivity measurements, these inversion variables are usually the constant resistivity value of each layer and the bed boundary positions. It is well-known how to compute derivatives with respect to the constant resistivity value of each layer using semi-analytic or numerical methods. However, similar formulas for computing the derivatives with respect to bed boundary positions are unavailable. The main contribution of this work is to provide an adjoint-based formulation for computing derivatives with respect to the bed boundary positions. The key idea to obtain the aforementioned adjoint state formulations for the derivatives is to separate the tangential and normal components of the field and treat them differently. This formulation allows us to compute the derivatives faster and more accurately than with traditional finite differences approximations. In the presentation, we shall first derive a formula for computing the derivatives with respect to the bed boundary positions for the potential equation. Then, we shall extend our formulation to 3D Maxwell’s equations. Finally, by considering a 1D domain and reducing the dimensionality of the problem, which is a common practice in the inversion of resistivity measurements, we shall derive a formulation to compute the derivatives of the measurements with respect to the bed boundary positions using a 1.5D variational formulation. Then, we shall illustrate the accuracy and convergence properties of our formulations by comparing numerical results with the analytical derivatives for the potential equation. For the 1.5D Maxwell’s system, we shall compare our numerical results based on the proposed adjoint-based formulation vs those obtained with a traditional finite difference approach. Numerical results shall show that our proposed adjoint-based technique produces enhanced accuracy solutions while its cost is negligible, as opposed to the finite difference approach that requires the solution of one additional problem per derivative.

Keywords: inverse problem, bed boundary positions, electromagnetism, potential equation

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Authors: Jyoti Sharma, Raj Kumar Arya

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The coatings of homogeneous ternary solution of Poly(styrene)(PS)-Poly(ethyleneglycol)-6000(PEG) Chlorobenzene (CLB) of two different concentrations (5.05%-4.98%-89.97% and 10.05%-5.12%-84.82%) were studied and dried under quiescent conditions. Residual solvent percentage and coatings thickness were calculated by gravimetric weight loss data. Residual solvent remained lower in case of the single thick layer as compared to layer-by-layer assembly technique. The Results suggests the effectiveness of the single thick layer for minimizing the residual solvent. A single thick layer had an initial coating thickness of 1098 µm and the final thickness of 106 µm which is lower as compared to the dried coatings of nearly the same final thickness by layer-by-layer assembly technique.

Keywords: films, layer-by-layer assembly, polymeric coatings, ternary system

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Authors: Bandari Shankar, Yohannes Yirga

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In this paper, the problem of heat and mass transfer in unsteady MHD boundary-layer flow of nanofluids over stretching sheet with a non uniform heat source/sink is considered. The unsteadiness in the flow and temperature is caused by the time-dependent stretching velocity and surface temperature. The unsteady boundary layer equations are transformed to a system of non-linear ordinary differential equations and solved numerically using Keller box method. The velocity, temperature, and concentration profiles were obtained and utilized to compute the skin-friction coefficient, local Nusselt number, and local Sherwood number for different values of the governing parameters viz. solid volume fraction parameter, unsteadiness parameter, magnetic field parameter, Schmidt number, space-dependent and temperature-dependent parameters for heat source/sink. A comparison of the numerical results of the present study with previously published data revealed an excellent agreement

Keywords: unsteady, heat and mass transfer, manetohydrodynamics, nanofluid, non-uniform heat source/sink, stretching sheet

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Authors: Sari F. Alkhatib, Chang Je Park, Gyuhong Roh, Daeseong Jo

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The iterative scheme which is used to treat buildup factors for stratified shields of three-layers or more is being investigated here using the layer-splitting technique. The second layer in a double-layer shield was split into two equivalent layers and the scheme was implemented on the new 'three-layer' shield configuration. The results of such manipulation for water-lead and water-iron shields combinations are presented here for 1 MeV photons. It was found that splitting the second layer introduces some deviation on the overall buildup factor. This expected deviation appeared to be higher in the case of low Z layer followed by high Z. However, the iterative scheme showed a great consistency and strong coherence with the introduced changes.

Keywords: build-up factor, iterative scheme, stratified shields, radiation protection

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Authors: Anna Bykalyuk, Frédéric Kuznik, Kévyn Johannes

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In this paper, the influence of a vertical plate’s thermal capacity is numerically investigated in order to evaluate the evolution of the thermal boundary layer structure, as well as the convective heat transfer coefficient and the velocity and temperature profiles. Whereas the heat flux of the heated vertical plate is evaluated under time depending boundary conditions. The main important feature of this problem is the unsteadiness of the physical phenomena. A 2D CFD model is developed with the Ansys Fluent 14.0 environment and is validated using unsteady data obtained for plasterboard studied under a dynamic temperature evolution. All the phenomena produced in the vicinity of the thermal conductive vertical plate (plasterboard) are analyzed and discussed. This work is the first stage of a holistic research on transient free convection that aims, in the future, to study the natural convection in the vicinity of a vertical plate containing Phase Change Materials (PCM).

Keywords: CFD modeling, natural convection, thermal conductive plate, time-depending boundary conditions

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Authors: Rezwana Rahman

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Various simulations have been conducted to understand the particle's macroscopic behavior in the solid-gas multiphase flow in rotating drums in the past. In these studies, the particle-wall no-slip boundary condition was usually adopted. However, the non-slip boundary condition is rarely encountered in real systems. A little effort has been made to investigate the particle behavior at slip boundary conditions. The paper represents a study of the gas-solid flow in a horizontal rotating drum at a slip boundary wall condition. Two different sizes of particles with the same density have been considered. The Eulerian–Eulerian multiphase model with the kinetic theory of granular flow was used in the simulations. The granular pressure at the rolling flow regime with specularity coefficient 1 was examined and compared with that obtained based on the no-slip boundary condition. The results reveal that the profiles of granular pressure distribution on the transverse plane of the drum are similar for both boundary conditions. But, overall, compared with those for the no-slip boundary condition, the values of granular pressure for specularity coefficient 1 are larger for the larger particle and smaller for the smaller particle.

Keywords: boundary condition, eulerian–eulerian, multiphase, specularity coefficient, transverse plane

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Authors: Gaokai Liu

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The distribution of material grain sizes reflects the strength, fracture, corrosion and other properties, and the grain size can be acquired via the grain boundary. In recent years, the automatic grain boundary detection is widely required instead of complex experimental operations. In this paper, an effective solution is applied to acquire the grain boundary of material images. First, the initial superpixel segmentation result is obtained via a superpixel approach. Then, a region merging method is employed to merge adjacent regions based on certain similarity criterions, the experimental results show that the merging strategy improves the superpixel segmentation result on material datasets.

Keywords: grain boundary detection, image segmentation, material images, region merging

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Authors: K. Jafar, R. Nazar, A. Ishak, I. Pop

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The present analysis considers the steady stagnation point flow and heat transfer towards a permeable sheet in an upper-convected Maxwell (UCM) electrically conducting fluid, with a constant magnetic field applied in the transverse direction to flow, and a local heat generation within the boundary layer with a heat generation rate proportional to (T-T_inf)^p. Using a similarity transformation, the governing system of partial differential equations is first transformed into a system of ordinary differential equations, which is then solved numerically using a finite-difference scheme known as the Keller-box method. Numerical results are obtained for the flow and thermal fields for various values of the shrinking/stretching parameter lambda, the magnetic parameter M, the elastic parameter K, the Prandtl number Pr, the suction parameter s, the heat generation parameter Q, and the exponent p. The results indicate the existence of dual solutions for the shrinking sheet up to a critical value lambda_c whose value depends on the value of M, K, and s. In the presence of internal heat absorbtion (Q<0), the surface heat transfer rate decreases with increasing p but increases with parameter Q and s, when the sheet is either stretched or shrunk.

Keywords: magnetohydrodynamic (MHD), boundary layer flow, UCM fluid, stagnation point, shrinking sheet

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Authors: Harshavardhan Reddy, Balaji Subramanian

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A systematic parametric study to find the optimum bellmouth profile by relating geometric and performance parameters to satisfy a set of specifications is reported. A careful aerodynamic design of bellmouth intake is critical to properly direct the flow with minimal losses and maximal flow uniformity into the honeycomb located inside the settling chamber of an indraft wind tunnel, thus improving the efficiency of the entire unit. Design charts for elliptically profiled bellmouths with two different contraction ratios (9 and 18) and three different test section speeds (25 m/s, 50 m/s, and 75 m/s) were presented. A significant performance improvement - especially in the Coefficient of discharge and in the flow angularity and boundary layer thickness at the honeycomb inlet - was observed when an entry corner radius (r/D = 0.08) was added to the bellmouth profile. The nonuniformity at the honeycomb inlet drops by about three times (~1% to 0.3%) when moving from square to regular octagonal cross-section. An octagonal cross-sectioned bellmouth intake with L/d = 0.55, D/d = 1.625, and r/D = 0.08 met all the four target performance specifications and is proposed as the best choice for a low-speed wind tunnel.

Keywords: bellmouth intake, low-speed wind tunnel, coefficient of discharge, nonuniformity, flow angularity, boundary layer thickness, CFD, aerodynamics

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Authors: Gary Miller, Andriy Didenko, David Allison

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The boundary of a region in the plane shrinks according to its curvature. A simple algorithm based upon this motion by curvature performed by a spreadsheet simulates the evaporation/dissipation behavior of oil spill boundaries.

Keywords: mathematical modeling, oil, evaporation, dissipation, boundary

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Authors: Saikat Datta

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Incompressible laminar time-varying flow is investigated over a rounded backward-facing step for a triangular piston motion at the inlet of a straight channel with very high acceleration, followed by a slow deceleration experimentally and through numerical simulation. The backward-facing step is an important test-case as it embodies important flow characteristics such as separation point, reattachment length, and recirculation of flow. A sliding piston imparts two successive triangular velocities at the inlet, constant acceleration from rest, 0≤t≤t0, and constant deceleration to rest, t0≤tKeywords: laminar boundary layer separation, rounded backward facing step, separation bubble, unsteady separation, unsteady vortex flows

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Authors: S. Zenhari, M. R. Hematiyan, A. Khosravifard, M. R. Feizi

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The boundary element method (BEM) and the method of fundamental solutions (MFS) are well-known fundamental solution-based methods for solving a variety of problems. Both methods are boundary-type techniques and can provide accurate results. In comparison to the finite element method (FEM), which is a domain-type method, the BEM and the MFS need less manual effort to solve a problem. The aim of this study is to compare the accuracy and reliability of the BEM and the MFS. This comparison is made for 2D potential and elasticity problems with different boundary and loading conditions. In the comparisons, both convex and concave domains are considered. Both linear and quadratic elements are employed for boundary element analysis of the examples. The discretization of the problem domain in the BEM, i.e., converting the boundary of the problem into boundary elements, is relatively simple; however, in the MFS, obtaining appropriate locations of collocation and source points needs more attention to obtain reliable solutions. The results obtained from the presented examples show that both methods lead to accurate solutions for convex domains, whereas the BEM is more suitable than the MFS for concave domains.

Keywords: boundary element method, method of fundamental solutions, elasticity, potential problem, convex domain, concave domain

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Authors: Omar S. Qaftan, T. T. Sabbagh

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This paper studies the free-field response by adopting a flexible membrane container as soil boundary for experimental shaking table tests. The influence of the soil container boundary on the soil behaviour and the dynamic soil properties under seismic effect were examined. A flexible container with 1/50 scale factor was adopted in the experimental tests, including construction, instrumentation, and determination of the results of dynamic tests on a shaking table. Horizontal face displacements and accelerations were analysed to determine the influence of the container boundary on the performance of the soil. The outputs results show that the flexible boundary container allows more displacement and larger accelerations. The soil in a rigid wall container cannot deform as similar as the soil in the real field does. Therefore, the response of flexible container tested is believed to be more reliable for soil boundary than that in the rigid container.

Keywords: soil, seismic, earthquake, interaction

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Authors: Indri Mahadiraka Rumamby, R. R. Dwinanti Rika Marthanty, Jessica Sjah

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Smoothed particle hydrodynamics (SPH) was originally created to simulate nonaxisymmetric phenomena in astrophysics. However, this method still has several shortcomings, namely the high computational cost required to model values with high resolution and problems with boundary conditions. The difficulty of modeling boundary conditions occurs because the SPH method is influenced by particle deficiency due to the integral of the kernel function being truncated by boundary conditions. This research aims to answer if SPH modeling with a focus on boundary layer interactions and continuous flow can produce quantifiably accurate values with low computational cost. This research will combine algorithms and coding in the main program of meandering river, continuous flow algorithm, and solid-fluid algorithm with the aim of obtaining quantitatively accurate results on solid-fluid interactions with the continuous flow on a meandering channel using the SPH method. This study uses the Fortran programming language for modeling the SPH (Smoothed Particle Hydrodynamics) numerical method; the model is conducted in the form of a U-shaped meandering open channel in 3D, where the channel walls are soil particles and uses a continuous flow with a limited number of particles.

Keywords: smoothed particle hydrodynamics, computational fluid dynamics, numerical simulation, fluid mechanics

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Authors: Anuar Ishak

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The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: dual solutions, heat transfer, mixed convection, stability analysis

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Authors: Vivek Mahadev, Manoj Kumar, Neelu Mathur, Brahm Dutt Pandey

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Perimeter guarding and protection of critical installations require prompt intrusion detection and assessment to take effective countermeasures. Currently, visual and electronic surveillance are the primary methods used for perimeter guarding. These methods can be costly and complicated, requiring careful planning according to the location and terrain. Moreover, these methods often struggle to detect stealthy and camouflaged insurgents. The object of the present work is to devise a surveillance technique using seismic sensors that overcomes the limitations of existing systems. The aim is to improve intrusion detection, assessment, and characterization by utilizing seismic sensors. Most of the similar systems have only two types of intrusion detection capability viz., human or vehicle. In our work we could even categorize further to identify types of intrusion activity such as walking, running, group walking, fence jumping, tunnel digging and vehicular movements. A virtual fence of 60 meters at GCNEP, Bahadurgarh, Haryana, India, was created by installing four underground geophones at a distance of 15 meters each. The signals received from these geophones are then processed to find unique seismic signatures called features. Various feature optimization and selection methodologies, such as LightGBM, Boruta, Random Forest, Logistics, Recursive Feature Elimination, Chi-2 and Pearson Ratio were used to identify the best features for training the machine learning models. The trained models were developed using algorithms such as supervised support vector machine (SVM) classifier, kNN, Decision Tree, Logistic Regression, Naïve Bayes, and Artificial Neural Networks. These models were then used to predict the category of events, employing weighted ensemble voting to analyze and combine their results. The models were trained with 1940 training events and results were evaluated with 831 test events. It was observed that using the weighted ensemble voting increased the efficiency of predictions. In this study we successfully developed and deployed the virtual fence using geophones. Since these sensors are passive, do not radiate any energy and are installed underground, it is impossible for intruders to locate and nullify them. Their flexibility, quick and easy installation, low costs, hidden deployment and unattended surveillance make such systems especially suitable for critical installations and remote facilities with difficult terrain. This work demonstrates the potential of utilizing seismic sensors for creating better perimeter guarding and protection systems using multiple machine learning models in weighted ensemble voting. In this study the virtual fence achieved an intruder detection efficiency of over 97%.

Keywords: geophone, seismic perimeter surveillance, machine learning, weighted ensemble method

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Authors: F. A. Hamad, S. He

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In this paper, the average heat transfer characteristics for a cross flow cylinder of 16 mm diameter in a vertical pipe has been studied for single-phase flow (water/oil) and multicomponent (non-boiling) flow (water-air, water-oil, oil-air and water-oil-air). The cylinder is uniformly heated by electrical heater placed at the centre of the element. The results show that the values of average heat transfer coefficients for water are around four times the values for oil flow. Introducing air as a second phase with water has very little effect on heat transfer rate, while the heat transfer increased by 70% in case of oil. For water–oil flow, the heat transfer coefficient values are reflecting the percentage of water up to 50%, but increasing the water more than 50% leads to a sharp increase in the heat transfer coefficients to become close to the values of pure water. The enhancement of heat transfer by mixing two phases may be attributed to the changes in flow structure near to cylinder surface which lead to thinner boundary layer and higher turbulence. For three-phase flow, the heat transfer coefficients for all cases fall within the limit of single-phase flow of water and oil and are very close to pure water values. The net effect of the turbulence augmentation due to the introduction of air and the attenuation due to the introduction of oil leads to a thinner boundary layer of oil over the cylinder surface covered by a mixture of water and air bubbles.

Keywords: circular cylinder, cross flow, hear transfer, multicomponent multiphase flow

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Authors: Parveen Kumar, J. K. Juneja, Chandra Prakash, K. K. Raina

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A series of polycrystalline ferroelectric ceramics with compositional formula Ba0.80-xSmxPb0.20Ti0.90Zr0.10O3 with x varying from 0 to 0.01 in the steps of 0.0025 has been prepared by solid state reaction method. The dielectric constant and tangent loss was measured as a function of frequency from 100Hz to 1MHz at different temperatures (200-500oC). The electrical behavior was then investigated using complex impedance spectroscopy (CIS) technique. From the CIS study, it has been found that there is a contribution of both grain and grain boundary in the electrical behavior of such ceramics. Grain and grain boundary resistivity and capacitance were calculated at different temperature using CIS technique. The present paper is about the discussion of grain and grain boundary contribution towards the electrical properties of Sm modified BaTiO3 based ceramics at high temperature.

Keywords: grain, grain boundary, impedance, dielectric

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Authors: Meisam Akbari, Seyed Hossein Elahi, Mohammad Mashadgarmeh

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In this study, the effect of nickel-electrode as a stainless steel buffer layer is considered. Then, the effect of dilution of the last layer of welding on two samples of steel plate A516 Gr70 (C-Mn-Si) with SMAW welding process was investigated. Then, in a sample, the ENI-cl nickel electrode was welded as the buffer layer and the E316L-16 electrode as the last layer of welding and another sample with an E316L-16 electrode in two layers. The chemical composition of the latter layer was determined by spectrophotometry method. The results indicate that the chemical composition of the latter layer is different and the lowest dilution rate is obtained using the nickel electrode.

Keywords: degree of dilution, C-Mn-Si, spectrometry, nickel electrode, stainless steel

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Authors: Pankhuri Bansal, Sanjeev Kumar

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We examined the exotic role of electrical poling of layered BCZT-NZFO bulk composite for sustainable advancement of magnetoelectric (ME) technology. Practically, it seems quite difficult to access the full potential of ME composites due to their weak ME coupling performances. Using a standard poling protocol, we successfully deployed the coupling performance of laminated ME composite, comprised of a ferroelectric (FE) layer of BCZT and a ferrite layer of NZFO. However, the ME coupling constant of laminated composite is optimized by lowering the volume fraction of the FE component to strengthen the mechanical strain in the piezoelectric layer while fixing the thickness of the magnetostrictive ferrite layer. Here, we employed systematic zero field cooled (ZFC) and field cooled (FC) electrical poling protocol on morphotropic phase boundary (MPB) based BCZT composition, well-appreciated for it’s remarkable electromechanical activity. We report a record augmentation in magnetoelectric coupling as a consequence of a prudent field-cooled poling mechanism. On the basis of our findings, we emphasize that the degree of magnetoelectricity may be significantly improved for the miniaturization of efficient devices via proper execution of the poling technique.

Keywords: magnetoelectric, lead-free, ferroelctric, ferromagnetic, energy harvesting

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Authors: Theddeus T. Akano, Omotayo A. Fakinlede

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The modelling of physical phenomena, such as the earth’s free oscillations, the vibration of strings, the interaction of atomic particles, or the steady state flow in a bar give rise to Sturm-Liouville (SL) eigenvalue problems. The boundary applications of some systems like the convection-diffusion equation, electromagnetic and heat transfer problems requires the combination of Dirichlet and Neumann boundary conditions. Hence, the incorporation of Robin boundary condition in the analyses of Sturm-Liouville problem. This paper deals with the computation of the eigenvalues and eigenfunction of generalized Sturm-Liouville problems with Robin boundary condition using the finite element method. Numerical solutions of classical Sturm–Liouville problems are presented. The results show an agreement with the exact solution. High results precision is achieved with higher number of elements.

Keywords: Sturm-Liouville problem, Robin boundary condition, finite element method, eigenvalue problems

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Authors: X. Li, Y. Liu, H. Wong, B. Pardoen, A. Fabbri, F. McGregor, E. Liu

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The target of this paper is to investigate how saturated poroelastic soils subject to freezing temperatures behave and how different boundary conditions can intervene and affect the thermo-hydro-mechanical (THM) responses, based on a particular but classical configuration of a finite homogeneous soil layer studied by Terzaghi. The essential relations on the constitutive behavior of a freezing soil are firstly recalled: ice crystal - liquid water thermodynamic equilibrium, hydromechanical constitutive equations, momentum balance, water mass balance, and the thermal diffusion equation, in general, non-linear case where material parameters are state-dependent. The system of equations is firstly linearized, assuming all material parameters to be constants, particularly the permeability of liquid water, which should depend on the ice content. Two analytical solutions solved by the classic Laplace transform are then developed, accounting for two different sets of boundary conditions. Afterward, the general non-linear equations with state-dependent parameters are solved using a commercial code COMSOL based on finite elements method to obtain numerical results. The validity of this numerical modeling is partially verified using the analytical solution in the limiting case of state-independent parameters. Comparison between the results given by the linearized analytical solutions and the non-linear numerical model reveals that the above-mentioned linear computation will always underestimate the liquid pore pressure and displacement, whatever the hydraulic boundary conditions are. In the nonlinear model, the faster growth of ice crystals, accompanying the subsequent reduction of permeability of freezing soil layer, makes a longer duration for the depressurization of water liquid and slower settlement in the case where the ground surface is swiftly covered by a thin layer of ice, as well as a bigger global liquid pressure and swelling in the case of the impermeable ground surface. Nonetheless, the analytical solutions based on linearized equations give a correct order-of-magnitude estimate, especially at moderate temperature variations, and remain a useful tool for preliminary design checks.

Keywords: chemical potential, cryosuction, Laplace transform, multiphysics coupling, phase transformation, thermodynamic equilibrium

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Authors: H. Barati, M. Wu, A. Kharicha, A. Ludwig

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A transient model for nozzle clogging has been developed and successfully validated against a laboratory experiment. Key steps of clogging are considered: transport of particles by turbulent flow towards the nozzle wall; interactions between fluid flow and nozzle wall, and the adhesion of the particle on the wall; the growth of the clog layer and its interaction with the flow. The current paper is to investigate the mesh (size and type) sensitivity of the model in both two and three dimensions. It is found that the algorithm for clog growth alone excluding the flow effect is insensitive to the mesh type and size, but the calculation including flow becomes sensitive to the mesh quality. The use of 2D meshes leads to overestimation of the clog growth because the 3D nature of flow in the boundary layer cannot be properly solved by 2D calculation. 3D simulation with tetrahedron mesh can also lead to an error estimation of the clog growth. A mesh-independent result can be achieved with hexahedral mesh, or at least with triangular prism (inflation layer) for near-wall regions.

Keywords: clogging, continuous casting, inclusion, simulation, submerged entry nozzle

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Authors: Suleiman Bashir Adamu, Lawan Sani Taura

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We study the role of boundary conditions via -symmetric quantum mechanics, where denotes parity operator and denotes time reversal operator. Using the one-dimensional Schrödinger Hamiltonian for a free particle in an infinite square well, we introduce symmetric boundary conditions. We find solutions of the 1D Klein-Gordon equation for a free particle in an infinite square well with Hermitian boundary and symmetry boundary conditions, where in both cases the energy eigenvalues and eigenfunction, respectively, are obtained.

Keywords: Eigenvalues, Eigenfunction, Hamiltonian, Klein- Gordon equation, PT-symmetric quantum mechanics

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Authors: Seong-Ho Ha, Young-Ok Yoon, Shae K. Kim

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Oxide layer of normal Al-Mg alloy can be characterized by upper MgO and lower MgAl2O4 spinel. The formation of the MgO outmost layer occurs by the surface segregation of Mg in the initial oxidation. After then, the oxidation is proceeded with the formation of MgA12O4 spinel beneath the MgO. Growth of the oxide layer is accelerated by constant formation of MgA12O4 spinel. On the other hand, the oxidation resistance of Al-Mg alloys can be significantly improved simply by Mg+Al2Ca master alloy use as the Mg alloying element and such an improvement is attributed to the CaO/MgO mixed layer. Al-Mg alloy containing Al2Ca shows CaO as the upper layer and MgO as the lower one without MgA12O4 spinel. Such a dense oxide film acts as a protective layer. However, the CaO/MgO scale has the outmost MgO, partly, after a long time exposure to a harsh oxidation condition. The aim of this study is to investigate the inter-filling behaviour of CaO and MgO mixed layer in oxidation resistance mechanism of Al-Mg alloys containing Al2Ca. The process of outmost MgO layer formation will be clarified.

Keywords: Al-Mg alloy, Al2Ca, oxidation, MgO

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Authors: W. K. Zahra, M. A. El-Beltagy, R. R. Elkhadrawy

Abstract:

So many practical problems in science and technology developed over the past decays. For instance, the mathematical boundary layer theory or the approximation of solution for different problems described by differential equations. When such problems consider large or small parameters, they become increasingly complex and therefore require the use of asymptotic methods. In this work, we consider the singularly perturbed boundary value problems which contain very small parameters. Moreover, we will consider these perturbation parameters as random variables. We propose a numerical method to solve this kind of problems. The proposed method is based on an exponential spline, Shishkin mesh discretization, and polynomial chaos expansion. The polynomial chaos expansion is used to handle the randomness exist in the perturbation parameter. Furthermore, the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Numerical results are provided to show the applicability and efficiency of the proposed method, which maintains a very remarkable high accuracy and it is ε-uniform convergence of almost second order.

Keywords: singular perturbation problem, polynomial chaos expansion, Shishkin mesh, two small parameters, exponential spline

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