Search results for: boundary conditions

Authors: F. Rasi Marzabadi

Abstract:

A series of experiments were carried out to study unsteady behavior of the flow field as well as the boundary layer of an airfoil oscillating in plunging motion in a subsonic wind tunnel. The measurements involved surface pressure distribution complimented with surface-mounted hot-films. The effect of leadingedge roughness that simulates surface irregularities on the wind turbine blades was also studied on variations of aerodynamic loads and boundary layer behavior.

Keywords: Boundary layer transition, plunging, reduced frequency, wind turbine.

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Authors: M. K. Hasan, Y. H. Ng, J. Sulaiman

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This paper present the implementation of a new ordering strategy on Successive Overrelaxation scheme on two dimensional boundary value problems. The strategy involve two directions alternatingly; from top and bottom of the solution domain. The method shows to significantly reduce the iteration number to converge. Four numerical experiments were carried out to examine the performance of the new strategy.

Keywords: Two dimensional boundary value problems, Successive Overrelaxation scheme, Alternating Top-Bottom strategy, fast convergence

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Authors: Ezzah Liana Ahmad Fauzi, Syakila Ahmad, Ioan Pop

Abstract:

The steady mixed convection boundary layer flow from a vertical cone in a porous medium filled with a nanofluid is numerically investigated using different types of nanoparticles as Cu (copper), Al2O3 (alumina) and TiO2 (titania). The boundary value problem is solved by using the shooting technique by reducing it into an ordinary differential equation. Results of interest for the local Nusselt number with various values of the constant mixed convection parameter and nanoparticle volume fraction parameter are evaluated. It is found that dual solutions exist for a certain range of mixed convection parameter.

Keywords: boundary layer, mixed convection, nanofluid, porous medium, vertical cone.

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Authors: Benshi Zhu

Abstract:

In this paper, the existence of multiple positive solutions for a class of third-order three-point discrete boundary value problem is studied by applying algebraic topology method.

Keywords: Positive solutions, Discrete boundary value problem, Third-order, Three-point, Algebraic topology

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Authors: Gabriela R. Fernandes, Renato F. Denadai, Guido J. Denipotti

Abstract:

In this work, are discussed two formulations of the boundary element method - BEM to perform linear bending analysis of plates reinforced by beams. Both formulations are based on the Kirchhoff's hypothesis and they are obtained from the reciprocity theorem applied to zoned plates, where each sub-region defines a beam or a slab. In the first model the problem values are defined along the interfaces and the external boundary. Then, in order to reduce the number of degrees of freedom kinematics hypothesis are assumed along the beam cross section, leading to a second formulation where the collocation points are defined along the beam skeleton, instead of being placed on interfaces. On these formulations no approximation of the generalized forces along the interface is required. Moreover, compatibility and equilibrium conditions along the interface are automatically imposed by the integral equation. Thus, these formulations require less approximation and the total number of the degree s of freedom is reduced. In the numerical examples are discussed the differences between these two BEM formulations, comparing as well the results to a well-known finite element code.

Keywords: Boundary elements, Building floor structures, Platebending.

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Authors: A. Soltani, M. Karimi Demneh

Abstract:

In this paper, modeling of an acoustic enclosed vehicle cabin has been carried out by using boundary element method. Also, the second purpose of this study is analyzing of linear wave equation in an acoustic field. The resultants of this modeling consist of natural frequencies that have been compared with resultants derived from finite element method. By using numerical method (boundary element method) and after solution of wave equation inside an acoustic enclosed cabin, this method has been progressed to simulate noise inside a simple vehicle cabin.

Keywords: Boundary element method, natural frequency, noise, vehicle cabin.

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Authors: Md. Fazlul Karim, Esa Al-Islam

Abstract:

This paper describes the development of a boundary fitted nested grid (BFNG) model to compute tsunami propagation of 2004 Indonesian tsunami in Southern Thailand coastal waters. We develop a numerical model employing the shallow water nested model and an orthogonal boundary fitted grid to investigate the tsunami impact on the Southern Thailand due to the Indonesian tsunami of 2004. Comparisons of water surface elevation obtained from numerical simulations and field measurements are made.

Keywords: Boundary-fitted nested grid model, finite difference method, Indonesian tsunami of 2004, Southern Thailand.

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Authors: Chinsuk Hong

Abstract:

This paper investigates the characteristics of wall pressure fluctuations in naturally developing boundary layer flows on axisymmetric bodies experimentally. The axisymmetric body has a modified ellipsoidal blunt nose. Flush-mounted microphones are used to measure the wall pressure fluctuations in the boundary layer flow over the body. The measurements are performed in a low noise wind tunnel. It is found that the correlation between the flow regime and the characteristics of the pressure fluctuations is distinct. The process from small fluctuation in laminar flow to large fluctuation in turbulent flow is investigated. Tollmien-Schlichting wave (T-S wave) is found to generate and develop in transition. Because of the T-S wave, the wall pressure fluctuations in the transition region are higher than those in the turbulent boundary layer.

Keywords: Wall Pressure Fluctuation, Boundary Layer Flow, Transition, Turbulent Flow, Axisymmetric Body, Flow Noise.

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Authors: Tse-Yu Hsieh, Jyh-Jian Chen

Abstract:

Since polymerase chain reaction (PCR) has been invented, it has emerged as a powerful tool in genetic analysis. The PCR products are closely linked with thermal cycles. Therefore, to reduce the reaction time and make temperature distribution uniform in the reaction chamber, a novel oscillatory thermal cycler is designed. The sample is placed in a fixed chamber, and three constant isothermal zones are established and lined in the system. The sample is oscillated and contacted with three different isothermal zones to complete thermal cycles. This study presents the design of the geometric characteristics of the chamber. The commercial software CFD-ACE+TM is utilized to investigate the influences of various materials, heating times, chamber volumes, and moving speed of the chamber on the temperature distributions inside the chamber. The chamber moves at a specific velocity and the boundary conditions with time variations are related to the moving speed. Whereas the chamber moves, the boundary is specified at the conditions of the convection or the uniform temperature. The user subroutines compiled by the FORTRAN language are used to make the numerical results realistically. Results show that the reaction chamber with a rectangular prism is heated on six faces; the effects of various moving speeds of the chamber on the temperature distributions are examined. Regarding to the temperature profiles and the standard deviation of the temperature at the Y-cut cross section, the non-uniform temperature inside chamber is found as the moving speed is larger than 0.01 m/s. By reducing the heating faces to four, the standard deviation of the temperature of the reaction chamber is under 1.4×10-3K with the range of velocities between 0.0001 m/s and 1 m/s. The nature convective boundary conditions are set at all boundaries while the chamber moves between two heaters, the effects of various moving velocities of the chamber on the temperature distributions are negligible at the assigned time duration.

Keywords: Polymerase chain reaction, oscillatory thermal cycler, standard deviation of temperature, nature convective.

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Authors: M. Chumburidze, D. Lekveishvili

Abstract:

We have considered the harmonic oscillations and general dynamic (pseudo oscillations) systems of theory generalized Green-Lindsay of couple-stress thermo-elasticity for isotropic, homogeneous elastic media. Approximate solution of some mixed boundary value problems for finite domain, bounded by the some closed surface are constructed.

Keywords: The couple-stress thermo-elasticity, boundary value problems.

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Authors: Nur Nadiah Abd Hamid, Ahmad Abd. Majid, Ahmad Izani Md. Ismail

Abstract:

Linear two-point boundary value problem of order two is solved using extended cubic B-spline interpolation method. There is one free parameters, λ, that control the tension of the solution curve. For some λ, this method produced better results than cubic B-spline interpolation method.

Keywords: two-point boundary value problem, B-spline, extendedcubic B-spline.

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Authors: V. Ghadamyari, F. Samadi, F. Kowsary

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An inverse geometry problem is solved to predict an unknown irregular boundary profile. The aim is to minimize the objective function, which is the difference between real and computed temperatures, using three different versions of Conjugate Gradient Method. The gradient of the objective function, considered necessary in this method, obtained as a result of solving the adjoint equation. The abilities of three versions of Conjugate Gradient Method in predicting the boundary profile are compared using a numerical algorithm based on the method. The predicted shapes show that due to its convergence rate and accuracy of predicted values, the Powell-Beale version of the method is more effective than the Fletcher-Reeves and Polak –Ribiere versions.

Keywords: Boundary elements, Conjugate Gradient Method, Inverse Geometry Problem, Sensitivity equation.

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Authors: M.Pourmahmoud, M.Salmanzadeh, M.Mehrani, M.R.Isvandzibaei

Abstract:

In this paper a study on the vibration of thin cylindrical shells with ring supports and made of functionally graded materials (FGMs) composed of stainless steel and nickel is presented. Material properties vary along the thickness direction of the shell according to volume fraction power law. The cylindrical shells have ring supports which are arbitrarily placed along the shell and impose zero lateral deflections. The study is carried out based on third order shear deformation shell theory (T.S.D.T). The analysis is carried out using Hamilton-s principle. The governing equations of motion of FGM cylindrical shells are derived based on shear deformation theory. Results are presented on the frequency characteristics, influence of ring support position and the influence of boundary conditions. The present analysis is validated by comparing results with those available in the literature.

Keywords: Vibration, FGM, Cylindrical shell, Hamilton'sprinciple, Ring support.

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Authors: K. Vasudeva Karanth, N. Yagnesh Sharma

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Generally flow behavior in centrifugal fan is observed to be in a state of instability with flow separation zones on suction surface as well as near the front shroud. Overall performance of the diffusion process in a centrifugal fan could be enhanced by judiciously introducing the boundary layer suction slots. With easy accessibility of CFD as an analytical tool, an extensive numerical whole field analysis of the effect of boundary layer suction slots in discrete regions of suspected separation points is possible. This paper attempts to explore the effect of boundary layer suction slots corresponding to various geometrical locations on the impeller with converging configurations for the slots. The analysis shows that the converging suction slots located on the impeller blade about 25% from the trailing edge, significantly improves the static pressure recovery across the fan. Also it is found that Slots provided at a radial distance of about 12% from the leading and trailing edges marginally improve the static pressure recovery across the fan.

Keywords: Boundary layer suction converging slot, Flowseparation, Sliding mesh, Unsteady analysis, Recirculation zone, Jetsand wakes.

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Authors: Delfim Soares Jr., Webe J. Mansur

Abstract:

The Time-Domain Boundary Element Method (TDBEM) is a well known numerical technique that handles quite properly dynamic analyses considering infinite dimension media. However, when these analyses are also related to nonlinear behavior, very complex numerical procedures arise considering the TD-BEM, which may turn its application prohibitive. In order to avoid this drawback and model nonlinear infinite media, the present work couples two BEM formulations, aiming to achieve the best of two worlds. In this context, the regions expected to behave nonlinearly are discretized by the Domain Boundary Element Method (D-BEM), which has a simpler mathematical formulation but is unable to deal with infinite domain analyses; the TD-BEM is employed as in the sense of an effective non-reflexive boundary. An iterative procedure is considered for the coupling of the TD-BEM and D-BEM, which is based on a relaxed renew of the variables at the common interfaces. Elastoplastic models are focused and different time-steps are allowed to be considered by each BEM formulation in the coupled analysis.

Keywords: Boundary Element Method, Dynamic Elastoplastic Analysis, Iterative Coupling, Multiple Time-Steps.

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Authors: Dylan M. Copeland

Abstract:

We present new finite element methods for Helmholtz and Maxwell equations on general three-dimensional polyhedral meshes, based on domain decomposition with boundary elements on the surfaces of the polyhedral volume elements. The methods use the lowest-order polynomial spaces and produce sparse, symmetric linear systems despite the use of boundary elements. Moreover, piecewise constant coefficients are admissible. The resulting approximation on the element surfaces can be extended throughout the domain via representation formulas. Numerical experiments confirm that the convergence behavior on tetrahedral meshes is comparable to that of standard finite element methods, and equally good performance is attained on more general meshes.

Keywords: Boundary elements, finite elements, Helmholtz equation, Maxwell equations.

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Authors: Reza Sharifian, Vagharshak Belubekyan

Abstract:

This paper is concerned with an investigation into the localized non-stability of a thin elastic orthotropic semi-infinite plate. In this study, a semi-infinite plate, simply supported on two edges and different boundary conditions, clamped, hinged, sliding contact and free on the other edge, are considered. The mathematical model is used and a general solution is presented the conditions under which localized solutions exist are investigated.

Keywords: Localized, Non-stability, Orthotropic, Semi-infinite

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Authors: M.R.Isvandzibaei, P.J.Awasare

Abstract:

In this paper a study on the vibration of thin cylindrical shells with ring supports and made of functionally graded materials (FGMs) composed of stainless steel and nickel is presented. Material properties vary along the thickness direction of the shell according to volume fraction power law. The cylindrical shells have ring supports which are arbitrarily placed along the shell and impose zero lateral deflections. The study is carried out based on third order shear deformation shell theory (T.S.D.T). The analysis is carried out using Hamilton-s principle. The governing equations of motion of FGM cylindrical shells are derived based on shear deformation theory. Results are presented on the frequency characteristics, influence of ring support position and the influence of boundary conditions. The present analysis is validated by comparing results with those available in the literature.

Keywords: Vibration, FGM, Cylindrical shell, Hamilton'sprinciple, Ring support.

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Authors: Roslinda Nazar, Anuar Ishak, Ioan Pop

Abstract:

Unsteady boundary layer flow of an incompressible micropolar fluid over a stretching sheet when the sheet is stretched in its own plane is studied in this paper. The stretching velocity is assumed to vary linearly with the distance along the sheet. Two equal and opposite forces are impulsively applied along the x-axis so that the sheet is stretched, keeping the origin fixed in a micropolar fluid. The transformed unsteady boundary layer equations are solved numerically using the Keller-box method for the whole transient from the initial state to final steady-state flow. Numerical results are obtained for the velocity and microrotation distributions as well as the skin friction coefficient for various values of the material parameter K. It is found that there is a smooth transition from the small-time solution to the large-time solution.

Keywords: Boundary layer, micropolar fluid, stretching surface, unsteady flow.

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Authors: Stephen Kirkup

Abstract:

This paper discusses the implementation of the boundary element method (BEM) on an Excel spreadsheet and how it can be used in teaching vector calculus and simulation. There are two separate spreadheets, within which Laplace equation is solved by the BEM in two dimensions (LIBEM2) and axisymmetric three dimensions (LBEMA). The main algorithms are implemented in the associated programming language within Excel, Visual Basic for Applications (VBA). The BEM only requires a boundary mesh and hence it is a relatively accessible method. The BEM in the open spreadsheet environment is demonstrated as being useful as an aid to teaching and learning. The application of the BEM implemented on a spreadsheet for educational purposes in introductory vector calculus and simulation is explored. The development of assignment work is discussed, and sample results from student work are given. The spreadsheets were found to be useful tools in developing the students’ understanding of vector calculus and in simulating heat conduction.

Keywords: Boundary element method, laplace equation, vector calculus, simulation, education.

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Authors: A. Bumbová, J. Kellner, J. Navrátil, D. Pluskal, M. Kozubková, E. Kozubek

Abstract:

The paper deals with the possibilities of modelling vapour propagation of explosive substances in the FLUENT software. With regard to very low tensions of explosive substance vapours the experiment has been verified as exemplified by mononitrotoluene. Either constant or time variable meteorological conditions have been used for calculation. Further, it has been verified that the eluent source may be time-dependent and may reflect a real situation or the liberation rate may be constant. The execution of the experiment as well as evaluation were clear and it could also be used for modelling vapour and aerosol propagation of selected explosive substances in the atmospheric boundary layer.

Keywords: atmospheric boundary layer, explosive substances, FLUENT software, modelling of propagation

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Authors: Saeed Sarabadan, Kamal Rashedi

Abstract:

This article presents a numerical method to find the heat flux in an inhomogeneous inverse heat conduction problem with linear boundary conditions and an extra specification at the terminal. The method is based upon applying the satisfier function along with the Ritz-Galerkin technique to reduce the approximate solution of the inverse problem to the solution of a system of algebraic equations. The instability of the problem is resolved by taking advantage of the Landweber’s iterations as an admissible regularization strategy. In computations, we find the stable and low-cost results which demonstrate the efficiency of the technique.

Keywords: Inverse problem, parabolic equations, heat equation, Ritz-Galerkin method, Landweber iterations.

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Authors: V. V. Zozulya

Abstract:

New theory for functionally graded (FG) shell based on expansion of the equations of elasticity for functionally graded materials (GFMs) into Legendre polynomials series has been developed. Stress and strain tensors, vectors of displacements, traction and body forces have been expanded into Legendre polynomials series in a thickness coordinate. In the same way functions that describe functionally graded relations has been also expanded. Thereby all equations of elasticity including Hook-s law have been transformed to corresponding equations for Fourier coefficients. Then system of differential equations in term of displacements and boundary conditions for Fourier coefficients has been obtained. Cases of the first and second approximations have been considered in more details. For obtained boundary-value problems solution finite element (FE) has been used of Numerical calculations have been done with Comsol Multiphysics and Matlab.

Keywords: Shell, FEM, FGM, legendre polynomial.

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Authors: Benshi Zhu

Abstract:

In this paper, the existence, multiplicity and noexistence of positive solutions for a class of semipositone discrete boundary value problems with two parameters is studied by applying nonsmooth critical point theory and sub-super solutions method.

Keywords: Discrete boundary value problems, nonsmoothcritical point theory, positive solutions, semipositone, sub-super solutions method

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Authors: M. Ghalambaz, A.R. Noghrehabadi, M.A. Behrang, E. Assareh, A. Ghanbarzadeh, N.Hedayat

Abstract:

This study presents a hybrid neural network and Gravitational Search Algorithm (HNGSA) method to solve well known Wessinger's equation. To aim this purpose, gravitational search algorithm (GSA) technique is applied to train a multi-layer perceptron neural network, which is used as approximation solution of the Wessinger's equation. A trial solution of the differential equation is written as sum of two parts. The first part satisfies the initial/ boundary conditions and does not contain any adjustable parameters and the second part which is constructed so as not to affect the initial/boundary conditions. The second part involves adjustable parameters (the weights and biases) for a multi-layer perceptron neural network. In order to demonstrate the presented method, the obtained results of the proposed method are compared with some known numerical methods. The given results show that presented method can introduce a closer form to the analytic solution than other numerical methods. Present method can be easily extended to solve a wide range of problems.

Keywords: Neural Networks, Gravitational Search Algorithm (GSR), Wessinger's Equation.

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Authors: F. M. Hady, A. Mahdy, R. A. Mohamed, Omima A. Abo Zaid

Abstract:

A numerical approach of the effectiveness of numerous parameters on magnetohydrodynamic (MHD) natural convection heat and mass transfer problem of a dusty micropolar fluid in a non-Darcy porous regime is prepared in the current paper. In addition, a convective boundary condition is scrutinized into the micropolar dusty fluid model. The governing boundary layer equations are converted utilizing similarity transformations to a system of dimensionless equations to be convenient for numerical treatment. The resulting equations for fluid phase and dust phases of momentum, angular momentum, energy, and concentration with the appropriate boundary conditions are solved numerically applying the Runge-Kutta method of fourth-order. In accordance with the numerical study, it is obtained that the magnitude of the velocity of both fluid phase and particle phase reduces with an increasing magnetic parameter, the mass concentration of the dust particles, and Forchheimer number. While rises due to an increment in convective parameter and Darcy number. Also, the results refer that high values of the magnetic parameter, convective parameter, and Forchheimer number support the temperature distributions. However, deterioration occurs as the mass concentration of the dust particles and Darcy number increases. The angular velocity behavior is described by progress when studying the effect of the magnetic parameter and microrotation parameter.

Keywords: Micropolar dusty fluid, convective heating, natural convection, MHD, porous media.

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Authors: Xiguang Li

Abstract:

In this paper, by constructing a special set and utilizing fixed point theory in coin, we study the existence of solution of singular two point’s boundary value problem for second-order differential equation, which improved and generalize the result of related paper.

Keywords: Singular differential equation, boundary value problem, coin, fixed point theory.

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Authors: Masamitsu Chikaraishi, Mutsuto Kawahara

Abstract:

This paper focuses on a technique for identifying the geological boundary of the ground strata in front of a tunnel excavation site using the first order adjoint method based on the optimal control theory. The geological boundary is defined as the boundary which is different layers of elastic modulus. At tunnel excavations, it is important to presume the ground situation ahead of the cutting face beforehand. Excavating into weak strata or fault fracture zones may cause extension of the construction work and human suffering. A theory for determining the geological boundary of the ground in a numerical manner is investigated, employing excavating blasts and its vibration waves as the observation references. According to the optimal control theory, the performance function described by the square sum of the residuals between computed and observed velocities is minimized. The boundary layer is determined by minimizing the performance function. The elastic analysis governed by the Navier equation is carried out, assuming the ground as an elastic body with linear viscous damping. To identify the boundary, the gradient of the performance function with respect to the geological boundary can be calculated using the adjoint equation. The weighed gradient method is effectively applied to the minimization algorithm. To solve the governing and adjoint equations, the Galerkin finite element method and the average acceleration method are employed for the spatial and temporal discretizations, respectively. Based on the method presented in this paper, the different boundary of three strata can be identified. For the numerical studies, the Suemune tunnel excavation site is employed. At first, the blasting force is identified in order to perform the accuracy improvement of analysis. We identify the geological boundary after the estimation of blasting force. With this identification procedure, the numerical analysis results which almost correspond with the observation data were provided.

Keywords: Parameter identification, finite element method, average acceleration method, first order adjoint equation method, weighted gradient method, geological boundary, navier equation, optimal control theory.

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Authors: Sameh E. Ahmed, Ramadan A. Mohamed, Abd Elraheem M. Aly, Mahmoud S. Soliman

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In this paper, an enhancement of the heat transfer using non-Newtonian nanofluids by magnetohydrodynamic (MHD) mixed convection along stretching sheets embedded in an isotropic porous medium is investigated. Case of the Maxwell nanofluids is studied using the two phase mathematical model of nanofluids and the Darcy model is applied for the porous medium. Important effects are taken into account, namely, non-linear thermal radiation, convective boundary conditions, electromagnetic force and presence of the heat source/sink. Suitable similarity transformations are used to convert the governing equations to a system of ordinary differential equations then it is solved numerically using a fourth order Runge-Kutta method with shooting technique. The main results of the study revealed that the velocity profiles are decreasing functions of the Darcy number, the Deborah number and the magnetic field parameter. Also, the increase in the non-linear radiation parameters causes an enhancement in the local Nusselt number.

Keywords: MHD, nanofluids, stretching surface, non-linear thermal radiation, convective condition.

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Authors: Jieer Wu, Zheshu Ma

Abstract:

Nondestructive testing in engineering is an inverse Cauchy problem for Laplace equation. In this paper the problem of nondestructive testing is expressed by a Laplace-s equation with third-kind boundary conditions. In order to find unknown values on the boundary, the method of fundamental solution is introduced and realized. Because of the ill-posedness of studied problems, the TSVD regularization technique in combination with L-curve criteria and Generalized Cross Validation criteria is employed. Numerical results are shown that the TSVD method combined with L-curve criteria is more efficient than the TSVD method combined with GCV criteria. The abstract goes here.

Keywords: ill-posed, TSVD, Laplace's equation, inverse problem, L-curve, Generalized Cross Validation.

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