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Purpose: A finite element computational methodology on a curved boundary using an efficient subparametric point transformation is presented. The proposed collocation method uses one-side curved and two-side straight triangular elements to derive exact subparametric shape functions. Design/methodology/approach: Our proposed method builds upon the domain discretization into linear, quadratic and cubic-order elements using subparametric spaces and such a discretization greatly reduces the computational complexity. A unique subparametric transformation for each triangle is derived from the unique parabolic arcs via a one-of-a-kind relationship between the nodal points. Findings: The novel transformation derived in this paper is shown to increase the accuracy of the finite element approximation of the boundary value problem (BVP). Our overall strategy is shown to perform well for the BVP considered in this work. The accuracy of the finite element approximate solution increases with higher-order parabolic arcs. Originality/value: The proposed collocation method uses one-side curved and two-side straight triangular elements to derive exact subparametric shape functions. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to propose a new strong-form numerical method, called the free element method, for solving general boundary value problems governed by partial differential equations. The main idea of the method is to use a locally formed element for each point to set up the system of equations. The proposed method is used to solve the fluid mechanics problems. Design/methodology/approach: The proposed free element method adopts the isoparametric elements as used in the finite element method (FEM) to represent the variation of coordinates and physical variables and collocates equations node-by-node based on the newly derived element differential formulations by the authors. The distinct feature of the method is that only one independently formed individual element is used at each point. The final system of equations is directly formed by collocating the governing equations at internal points and the boundary conditions at boundary points. The method can effectively capture phenomena of sharply jumped variables and discontinuities (e.g. the shock waves). Findings: a) A new numerical method called the FEM is proposed; b) the proposed method is used to solve the compressible fluid mechanics problems for the first time, in which the shock wave can be naturally captured; and c) the method can directly set up the system of equations from the governing equations. Originality/value: This paper presents a completely new numerical method for solving compressible fluid mechanics problems, which has not been submitted anywhere else for publication. [ABSTRACT FROM AUTHOR]

Purpose This paper aims to address the management of people and their working behaviour successfully during workplace change – from a traditional way of working towards new ways of working. The study was based on the observation that during workplace change, organisations often fail to see the importance of managing (working) behaviour during the process of workplace change. The focus is mostly on the design of the new working environment and the information technology in it. However, these do not seem to be the determining aspects of the success of workplace change, merely necessary boundary conditions. This paper will elucidate how internal communication can make the greatest impact on shifting people’s working behaviour and attitudes and thus manage it effectively.Design/methodology/approach A literature study has been conducted to investigate the relation between the topics of new ways of working, workplace change and internal communication. This study surfaced the importance of the aspect of (working) behaviour within workplace change. Subsequently, a field study was performed, during which several interviews were held with the project team of the R&D department of a chemical multinational, who is on the brink of implementing a new workplace concept. Also, focus group interviews were held with their employees to research personal views on expected working behaviour.Findings The outcomes of the research, literature review and field study clarify the critical success factors for internal communication to manage the workplace change, so it lives up to the expectations. These are: face-to-face communication, assigning the manager the role of workplace change leader and use internal communication to inform employees and inspire them.Originality/value In this paper, the behavioural aspect has been identified as a key determinant of perceived success of a new workplace concept. Managing workplace change successfully should therefore merely focus on managing the working behaviour of the people involved, instead of managing the building and interior design or the technology in it. Internal communication was identified as a pivotal tool to reach this success. [ABSTRACT FROM AUTHOR]

Purpose Based on integrating learning, resource-based and social network theories, the purpose of this paper is to shed fresh light on the association between export experience and export performance by seeking to better understand the links between them, and assessing the boundary conditions, moderators, mediators, and non-linear relationships in greater depth.Design/methodology/approach This paper mobilizes a quantitative research design using a survey of Brazil-based exporters. The authors test the hypotheses proposed in this study by employing moderated mediation regression models.Findings The authors find support for a J-shape relationship between export experience and export market performance. In particular, the authors find that innovation and international marketing resources mediate the effect of export experience on export market performance, and the authors unveil that this mediation effect is contingent on the strength of international business network ties.Originality/value This study advances the export marketing literature by explaining how export experience drives export success in two ways: first, by clarifying the ambiguity in extant theoretical explanations and previous empirical findings regarding the shape of the relationship between export experience and export performance. Second, this study reconciles the disagreement as to whether superior export performance results from exporters’ existing resources or from their learning by exporting. Thus, the paper is valuable for scholars and export managers or policymakers alike by providing recommendations on how less experienced firms can overcome the initial period of weak export performance. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to propose an efficient computational technique, which uses Haar wavelets collocation approach coupled with the Newton-Raphson method and solves the following class of system of Lane–Emden equations: − (t k 1 y ′ (t)) ′ = t − ω 1 f 1 (t , y (t) , z (t)) , − (t k 2 z ′ (t)) ′ = t − ω 2 f 2 (t , y (t) , z (t)) , where t > 0, subject to the following initial values, boundary values and four-point boundary values: y (0) = γ 1 , y ′ (0) = 0 , z (0) = γ 2 , z ′ (0) = 0 , y ′ (0) = 0 , y (1) = δ 1 , z ′ (0) = 0 , z (1) = δ 2 , y (0) = 0 , y (1) = n 1 z (v 1) , z (0) = 0 , z (1) = n 2 y (v 2) , where n1,n2,v1,v2∈(0,1) and k1≥0, k2≥0, ω1<1, ω2<1 , γ1, γ2, δ1, δ2 are real constants. Design/methodology/approach: To deal with singularity, Haar wavelets are used, and to deal with the nonlinear system of equations that arise during computation, the Newton-Raphson method is used. The convergence of these methods is also established and the results are compared with existing techniques. Findings: The authors propose three methods based on uniform Haar wavelets approximation coupled with the Newton-Raphson method. The authors obtain quadratic convergence for the Haar wavelets collocation method. Test problems are solved to validate various computational aspects of the Haar wavelets approach. The authors observe that with only a few spatial divisions the authors can obtain highly accurate solutions for both initial value problems and boundary value problems. Originality/value: The results presented in this paper do not exist in the literature. The system of nonlinear singular differential equations is not easy to handle as they are singular, as well as nonlinear. To the best of the knowledge, these are the first results for a system of nonlinear singular differential equations, by using the Haar wavelets collocation approach coupled with the Newton-Raphson method. The results developed in this paper can be used to solve problems arising in different branches of science and engineering. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to introduce a novel algorithm to solve initial/boundary value problems of high-order ordinary differential equations (ODEs) and high-order system of ordinary differential equations (SODEs). Design/methodology/approach: The proposed method is based on Hermite polynomials and extreme learning machine (ELM) algorithm. The Hermite polynomials are chosen as basis function of hidden neurons. The approximate solution and its derivatives are expressed by utilizing Hermite network. The model function is designed to automatically meet the initial or boundary conditions. The network parameters are obtained by solving a system of linear equations using the ELM algorithm. Findings: To demonstrate the effectiveness of the proposed method, a variety of differential equations are selected and their numerical solutions are obtained by utilizing the Hermite extreme learning machine (H-ELM) algorithm. Experiments on the common and random data sets indicate that the H-ELM model achieves much higher accuracy, lower complexity but stronger generalization ability than existed methods. The proposed H-ELM algorithm could be a good tool to solve higher order linear ODEs and higher order linear SODEs. Originality/value: The H-ELM algorithm is developed for solving higher order linear ODEs and higher order linear SODEs; this method has higher numerical accuracy and stronger superiority compared with other existing methods. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to apply an iterative numerical method to find the numerical solution of the nonlinear non-self-adjoint singular boundary value problems that arises in the theory of epitaxial growth. Design/methodology/approach: The proposed problem has multiple solutions and it is singular too; so not every technique can capture all the solutions. This study proposes to use variational iterative numerical method and compute both the solutions. The computed solutions are very close to the exact result. Findings: It turns out that the existence or nonexistence of numerical solutions fully depends on the value of a parameter. The authors show that numerical solutions exist for small positive values of this parameter. For large positive values of the parameter, they find nonexistence of solutions. They also observe existence of solutions for negative values of the parameter and determine the range of parameter values which separates existence and nonexistence of solutions. This parameter has a clear physical meaning, as it describes the rate at which new material is deposited onto the system. This fact allows interpreting the physical significance of the results. Originality/value: The authors could capture both the solutions and got accurate estimation of the parameter. This method will be a great tool to handle such types of nonlinear non-self-adjoint equations that have multiple solutions in engineering and mathematical sciences. The results in this paper will have an impact on the understanding of theoretical models of epitaxial growth in near future. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to present a novel scheme for imposing periodic boundary conditions with downscaled macroscopic strain measures of gradient Cosserat continuum on the representative volume element (RVE) of discrete particle assembly in the frame of the second-order computational homogenization methods for granular materials. Design/methodology/approach: The proposed scheme is based on the generalized Hill's lemma of gradient Cosserat continuum and the incremental non-linear constitutive relation condensed to the peripheral particles of the RVE of discrete particle assembly. The generalized Hill's lemma conducts to downscale the macroscopic strain or stress measures and to impose the periodic boundary conditions on the RVE boundary so that the Hill-Mandel energy equivalence condition is ensured. Because of the incremental non-linear constitutive relation condensed to the peripheral particles of the RVE, the periodic boundary displacement and traction constraints together with the downscaled macroscopic strains and strain gradients, micro-rotations and curvatures are imposed in the point-wise sense without the need of introducing the Lagrange multipliers for enforcing the periodic boundary displacement and traction constraints in a weak sense. Findings: Numerical results demonstrate that the applicability and effectiveness of the proposed scheme in imposing the periodic boundary conditions on the RVE. The results of the RVE subjected to the periodic boundary conditions together with the displacement boundary conditions in the second-order computational homogenization for granular materials provide the desired estimations, which lie between the upper and the lower bounds provided by the displacement and the traction boundary conditions imposed on the RVE respectively. Research limitations/implications: Each grain in the particulate system under consideration is assumed to be rigid and circular. Practical implications: The proposed scheme for imposing periodic boundary conditions on the RVE can be adopted solely for estimating the effective mechanical properties of granular materials and/or integrated into the frame of the second-order computational homogenization method with a nested finite element method-discrete element method solution procedure for granular materials. It will tend to provide, at least theoretically, more reasonable results for effective material properties and solutions of a macroscopic boundary value problem simulated by the computational homogenization method. Originality/value: This paper presents a novel scheme for imposing periodic boundary conditions with downscaled macroscopic strain measures of gradient Cosserat continuum on the RVE of discrete particle assembly for granular materials without need of introducing Lagrange multipliers for enforcing periodic boundary conditions in a weak (integration) sense. [ABSTRACT FROM AUTHOR]

Purpose: Empathy is a core characteristic of helping and caring interactions and thus is fundamental to service. Yet, to date, service marketing literature has focused on a restricted view of the value of empathy as it leads to improved service quality perceptions and successful sales outcomes. The aim of this paper is to provide a review of the empathy literature and the dispositional and situational factors affecting it, so as to further explore its potential benefits and limitations for service. Design/methodology/approach: A summative review of the empathy literature uncovers cause–effect relationships and their potential boundary conditions. Theoretical propositions set an agenda for future research on empathy for service that breaks new ground. Findings: Empathy can reduce anti-social, revenge, discrimination and unethical behaviors in service settings. It can also improve value-in-context experiences for users of service innovations. Notwithstanding its potential benefits, empathy can diminish the objectivity and performance of service providers when experienced at extreme levels. Empathy can also serve as an ingratiation influence tactic and can be detrimental to the target in embarrassing service contexts. Originality/value: This paper suggests propositions for future research to advance theory and managerial practice on the use of empathy to improve service outcomes for interacting actors. It also alludes to the potential dark side of empathy when experienced at excessive levels or when used to manipulate. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to assess different five variables shear deformation plate theories for the buckling analysis of FGM plates.Design/methodology/approach Governing differential equations (GDEs) of the theories are derived by employing the Hamilton Principle. A polynomial radial basis function (RBF)-based Meshless method is used to discretize the GDEs, and a MATLAB code is developed to solve these discretize equations.Findings Numerical results are obtained for buckling loads. The results are compared with other available results for validation purpose. The effect of the span-to-thickness ratio and grading index is observed. It is observed that some theories underpredict the deflection for thick plates, while at the same time they seem to be in good agreement with other theories for thin plates.Originality/value This paper assesses the different theories with the same method to determine their applicability. [ABSTRACT FROM AUTHOR]

Purpose - The paper aims to focus on the semiconductor temperature prediction in the multichip modules by using a simplified 1D model, easy to implement in the electronic simulation tools. Design/methodology/approach - Accurate prediction of temperature variation of power semiconductor devices in power electronic circuits is important for obtaining optimum designs and estimating reliability levels. Temperature estimation of power electronic devices has generally been performed using transient thermal equivalent circuits. This paper has studied the thermal behaviour of the power modules. The study leads to correcting the junction temperature values estimated from the transient thermal impedance of each component operating alone. The corrections depend on multidimensional thermal phenomena in the structure. Findings - The classic analysis of thermal phenomena in the multichip structures, independently of powers' dissipated magnitude and boundary conditions, is not correct. An advanced 1D thermal model based on the finite element method is proposed. It takes into account the effect of the heat-spreading angle of the different devices in the module. Originality/value - The paper focuses on mathematical model of the thermal behaviour in the power module. The study leads to a correction of the junction temperature values estimated from the transient thermal impedance of each component given by manufacturers. The proposed model gives a good trade-off between accuracy, efficiency and simulation cost. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to propose a hybrid optimization approach with high level of solving precision and efficiency for endo-atmospheric ascent trajectory planning of launch vehicles.Design/methodology/approach Based on the indirect method of optimal control problems, the optimal endo-atmospheric ascent problem with path constraints and final condition constraints is transformed into a Hamiltonian two point boundary value problem (TPBVP). An advanced Gauss pseudo-spectral method is applied to change the Hamiltonian TPBVP into a system of nonlinear algebraic equations, which is solved by a modified Newton method. To guarantee the convergence of the solution, analytical initial guess technology and homotopy technology are also introduced. At last, simulation tests are made.Findings The hybrid approach for optimal endo-atmospheric ascent trajectory planning has both fast convergence rate and high solution precision. The simulation results indicate that not only the proposed method is feasible but also it is better than the indirect method, which is a most popular approach for solving the optimal endo-atmospheric ascent problem. Given the same degree of solution accuracy, the new method consumes quite less time on the CPU than that of the indirect method.Practical implications The new optimization approach has high level of both solution accuracy and efficiency. It can be used in rapid trajectory designing, on-line trajectory planning and closed-loop guidance of launch vehicles. Also, the proposed Gauss pseudo-spectral method in this paper is a new and efficient method for solving general TPBVPs.Originality/value The paper provides a new hybrid optimization method for rapid endo-atmospheric ascent trajectory planning of launch vehicles. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this study is to provide a robust numerical method for a two parameter singularly perturbed delay parabolic initial boundary value problem (IBVP). Design/methodology/approach: To solve the problem, the authors have used a hybrid scheme combining the midpoint scheme, the upwind scheme and the second-order central difference scheme for the spatial derivatives. The backward Euler scheme on a uniform mesh is used to approximate the time derivative. Here, the authors have used Shishkin type meshes for spatial discretization. Findings: It is observed that the proposed method converges uniformly with almost second-order spatial accuracy with respect to the discrete maximum norm. Originality/value: This paper deals with the numerical study of a two parameter singularly perturbed delay parabolic IBVP. To solve the problem, the authors have used a hybrid scheme combining the midpoint scheme, the upwind scheme and the second-order central difference scheme for the spatial derivatives. The backward Euler scheme on a uniform mesh is used to approximate the time derivative. The convergence analysis is carried out. It is observed that the proposed method converges uniformly with almost second-order spatial accuracy with respect to the discrete maximum norm. Numerical experiments illustrate the efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to study the wave propagation in a generalized piezothermoelastic rotating bar of circular cross-section using three-dimensional linear theory of elasticity. Design/methodology/approach – A mathematical model is developed to study the wave propagation in a generalized piezothermelastic rotating bar of circular cross-section by using Lord-Shulman (LS) and Green-Lindsay (GL) theory of thermoelasticity. After developing the formal solution of the mathematical model consisting of partial differential equations, the frequency equations have been derived by using the thermally insulated/isothermal and electrically shorted/charge free boundary conditions prevailing at the surface of the circular cross-sectional bar. The roots of the frequency equation are obtained by using the secant method, applicable for complex roots. Findings – In order to include the time requirement for the acceleration of the heat flow and the coupling between the temperature and strain fields, the analytical terms have been derived for the non-classical thermo-elastic theories, LS and GL theory. The computed physical quantities such as thermo-mechanical coupling, electro-mechanical coupling, frequency shift, specific loss and frequency have been presented in the form of dispersion curves. From the graphical patterns of the structure, the effect of thermal relaxation times and the rotational speed as well as the anisotropy of the of the material on the various considered wave characteristics is more significant and dominant in the flexural modes of vibration. The effect of such physical quantities provides the foundation for the construction of temperature sensors, acoustic sensor and rotating gyroscope. Originality/value – In this paper, the influence of thermal relaxation times and rotational speed on the wave number with thermo-mechanical coupling, electro-mechanical coupling, frequency shift, specific loss and frequency has been observed and are presented as dispersion curves. The effect of thermal relaxation time and rotational speed on wave number for the case of generalized piezothermoelastic material of circular cross-section was never reported in the literature. These results are new and original. [ABSTRACT FROM AUTHOR]

Purpose This paper aims to test the influence of external information search (EIS) on knowledge elaboration and group cognitive complexity (GCC) under the moderating effect of absorptive capacity (AC is indicated by prior knowledge base and gender diversity).Design/methodology/approach The results of three studies (one field study and two experimental studies) are reported. The first study tests the interaction between EIS and the two dimensions of AC on group knowledge elaboration in a sample of 65 organizational groups. In the second study, EIS was directly manipulated and the interaction with AC in a sample of 65 groups was tested. In the last experimental study, the AC of the boundary spanner (highest level of expertise versus lowest level of expertise) was manipulated and the effects of EIS in a sample of 37 groups were tested.Findings The first study reveals a significant interaction between EIS and prior knowledge base on knowledge elaboration and points toward a compensatory interplay of EIS and AC on GCC. The results of the second study indicate that EIS increases the time spent on task, as well as the efficiency of knowledge integration (GCC per unit of time). Furthermore, EIS has the strongest positive effect on GCC in groups in which at least one of the AC dimensions is average or high. The results of the last study show that the AC of the boundary spanner compensates for the lack of absorptive capacity of the group and also show that the cognitive distance between the boundary spanner and the rest of the group has a negative influence on the efficiency of knowledge integration in groups.Research limitations/implications The limitations of Study 1, common to non-experimental research (related to causality), are dealt with in the second and third studies that establish causality between EIS and GCC.Practical implications The paper has important implications for the management of information search effort in organizational groups, in particular the groups are advised to: engage in EIS to increase their cognitive repertoire and cognitive complexity, delegate, when possible, their most competent members to engage in boundary spanning activities as they will maximize the cognitive benefits of EIS and finally minimize the cognitive dissimilarity between the boundary spanner and the rest of the group to facilitate the effective integration of novel insights into the group cognition.Originality/value This study is among the first empirical attempts to uncover the causal effect of EIS on knowledge elaboration and GCC in groups and to uncover the role of the boundary spanner in the EIS efforts. [ABSTRACT FROM AUTHOR]

Purpose This paper aims to enrich knowledge management theory and practice by investigating how boundary spanners’ willingness to share their knowledge contributes to innovation success and by examining the contingent role of market turbulence.Design/methodology/approach Cross-sectional survey data were collected from 296 top income Hungarian firms. Structural equation modelling with bootstrap procedures was used to test the hypotheses.Findings Boundary spanners’ willingness to share their knowledge has a dual effect on innovation success, which is captured by new product development innovativeness and performance. It has a direct effect on both new product development innovativeness and performance, and it has a mediated effect on new product development performance, where new product development innovativeness serves as a mediator. The study’s results indicate that these effects are robust and not contingent on the turbulence of the firm’s marketplace.Research limitations/implications This study’s respondents were managers in boundary-spanning positions charged with the task of linking the organisation with its external environment. Owing to their proximity to the external environment, their evaluation of market turbulence may be distorted.Practical implications Maintaining the willingness of managers in boundary-spanning positions to share what they know is essential to the continuous creation of superior new product development performance. Hence, firms should develop organisational cultures where employees’ knowledge-sharing willingness is presented as an important asset. While turbulent markets may be unpredictable and hostile, firms should not adjust their knowledge management practices.Originality/value Building on the research on knowledge sharing, boundary spanning theory and contingency theory, this paper increases the understanding of the salient factors that are often implicitly assumed in mechanisms involved in transforming knowledge into new product performance. This is the first empirical study to focus on boundary spanners’ knowledge behaviour and to consider the contingent role of market turbulence in knowledge management. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to predict the mechanical behavior of a piezoelectric nanoplate under shear stability by taking electric voltage into account in thermal environment.Design/methodology/approach Simplified first-order shear deformation theory has been used as a displacement field. Modified couple stress theory has been applied for considering small-size effects. An analytical solution has been taken into account for various boundary conditions.Findings The length scale impact on the results of any boundary conditions increases with an increase in l parameter. The effect of external electric voltage on the critical shear load is more than room temperature effects. With increasing aspect ratio the critical shear load decreases and external electric voltage becomes more impressive. By considering piezoelectric nanoplates, it is proved that the temperature rise cannot become a sensitive factor on the buckling behavior. The length scale parameter has more effect for more flexible boundary conditions than others. By considering nanosize, the consideration has led to much bigger critical load vs macro plate.Originality/value In the current paper for the first time the simplified first-order shear deformation theory is used for obtaining governing equations by using nonlinear strains for shear buckling of a piezoelectric nanoplate. The couple stress theory for the first time is applied on the nonlinear first-order shear deformation theory. For the first time, the thermal environment effects are considered on shear stability of a piezoelectric nanoplate. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to investigate airfoil self-noise generation and propagation by using a hybrid method based on the large-eddy simulation (LES) approach and Curle’s acoustic analogy as implemented in OpenFOAM.Design/methodology/approach Large-eddy simulation of near-field flow over a NACA6512-63 airfoil at zero angle of attack with a boundary layer trip at Rec = 1.9 × 105 has been carried out using the OpenFOAM® computational fluid dynamics (CFD) code. Calculated flow results are compared with published experimental data. The LES includes the wind tunnel installation effects by using appropriate inflow boundary conditions obtained from a RANS κ – ω SST model computation of the whole wind tunnel domain. Far-field noise prediction was achieved by an integral method based on Curle’s acoustic analogy. The predicted sound pressure levels are validated against the experimental data at various frequency ranges.Findings The numerical results presented in this paper show that the flow features around a NACA6512-63 airfoil have been correctly captured in OpenFOAM LES calculations. The mean surface pressure distributions and the local pressure peaks for the step trip setup agree very well with the experimental measurements. Aeroacoustic prediction using Curle’s analogy shows an overall agreement with the experimental data. The sound pressure level-frequency spectral analysis produces very similar data at low to medium frequency, whereas the experimentally observed levels are slightly over predicted at a higher frequency range.Practical implications This study has achieved and evaluated an alternative aeroacoustic simulation method based on the combination of LES with a simple Smagorinsky SGS model and Curle’s analogy, as implemented in the OpenFOAM CFD code. The unsteady velocity/pressure source data produced can be used for any simpler analytically based far-field noise prediction scheme.Originality/value A complete integration of the LES and Curle’s acoustic analogy for aeroacoustic simulations has been achieved in OpenFOAM. The capability and accuracy of the hybrid method are fully evaluated for high-camber airfoil self-noise predictions. Wind tunnel installation effects have been incorporated properly into the LES. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to present a numerically adaptive finite element (FE) method for accurate, efficient and reliable eigensolutions of regular second- and fourth-order Sturm–Liouville (SL) problems with variable coefficients.Design/methodology/approach After the conventional FE solution for an eigenpair (i.e. eigenvalue and eigenfunction) of a particular order has been obtained on a given mesh, a novel strategy is introduced, in which the FE solution of the eigenproblem is equivalently viewed as the FE solution of an associated linear problem. This strategy allows the element energy projection (EEP) technique for linear problems to calculate the super-convergent FE solutions for eigenfunctions anywhere on any element. These EEP super-convergent solutions are used to estimate the FE solution errors and to guide mesh refinements, until the accuracy matches user-preset error tolerance on both eigenvalues and eigenfunctions.Findings Numerical results for a number of representative and challenging SL problems are presented to demonstrate the effectiveness, efficiency, accuracy and reliability of the proposed method.Research limitations/implications The method is limited to regular SL problems, but it can also solve some singular SL problems in an indirect way.Originality/value Comprehensive utilization of the EEP technique yields a simple, efficient and reliable adaptive FE procedure that finds sufficiently fine meshes for preset error tolerances on eigenvalues and eigenfunctions to be achieved, even on problems which proved troublesome to competing methods. The method can readily be extended to vector SL problems. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to solve the second-order nonlinear boundary value problem with nonlinear boundary conditions by an iterative numerical method. Design/methodology/approach: The authors introduce eigenfunctions as test functions, such that a weak-form integral equation is derived. By expanding the numerical solution in terms of the weighted eigenfunctions and using the orthogonality of eigenfunctions with respect to a weight function, and together with the non-separated/mixed boundary conditions, one can obtain the closed-form expansion coefficients with the aid of Drazin inversion formula. Findings: When the authors develop the iterative algorithm, removing the time-varying terms as well as the nonlinear terms to the right-hand sides, to solve the nonlinear boundary value problem, it is convergent very fast and also provides very accurate numerical solutions. Research limitations/implications: Basically, the authors' strategy for the iterative numerical algorithm is putting the time-varying terms as well as the nonlinear terms on the right-hand sides. Practical implications: Starting from an initial guess with zero value, the authors used the closed-form formula to quickly generate the new solution, until the convergence is satisfied. Originality/value: Through the tests by six numerical experiments, the authors have demonstrated that the proposed iterative algorithm is applicable to the highly complex nonlinear boundary value problems with nonlinear boundary conditions. Because the coefficient matrix is set up outside the iterative loop, and due to the property of closed-form expansion coefficients, the presented iterative algorithm is very time saving and converges very fast. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to present thermal and mechanical stresses in solid and hollow thick-walled cylinders and spheres made of functionally graded materials (FGMs) under the effect of heat generation. Design/methodology/approach: Constant internal temperature and convective external conditions in hollow bodies along with internal heat generation with a combination of outer convective conditions in solid bodies are investigated individually. The effect of the heat convection coefficient on solid bodies is additionally discussed. The variation of the FGM properties in the radial direction is adapted to the Mori–Tanaka homogenization schemes, which produces irregular and two-point linear boundary value problems that are numerically solved by the pseudospectral Chebyshev method. Findings: It has been shown that the selection of the mixtures of FGMs has to be made correctly to keep the thermal and mechanical loads acting on objects at low levels. Originality/value: In this study, both solid and hollow functionally graded cylinders and spheres for different boundary conditions that are as their engineering applications are examined with the proposed method. The results have demonstrated that the pseudospectral Chebyshev method has high accuracy, low calculation costs and ease of application and can be easily adapted to such engineering problems. [ABSTRACT FROM AUTHOR]

Purpose The time of tightly coupled transient calculation and the accuracy of conventional loosely coupled algorithm make it difficult to meet the engineering design requirements for long-term conjugate heat transfer (CHT) problems. The purpose of this paper is to propose a new loosely coupled algorithm with sufficient accuracy and less calculation time on the basis of the quasi-steady flow field. Through this algorithm, it will be possible to reduce the update frequency of the flow field and devise a strategy by which to reasonably determine the update steps.Design/methodology/approach In this paper, the new algorithm updates the flow field by solving the steady governing equations in the fluid region and by calculating the transient temperature distribution until the next update of the fluid flow, by means of solving the transient energy equations in the entire computational domain. The authors propose a strategy by which to determine the update step, by using the engineering empirical formula of the Nusselt number, on the basis of the changes of the inlet and outlet boundary conditions.Findings Taking a duct heated by an inner forced air flow heating process as an example, the comparison results for the tightly coupled transient calculation by Fluent software shows that the new algorithm is able to significantly reduce the calculation time of the transient temperature distribution with reasonable accuracy. For example, the respective computing times are reduced to 22.8 and 40 per cent, while the duct wall temperature deviations are 7 and 5 per cent, using the two flow update time steps of 100 and 50 s on the variable inlet-flow rate conditions.Originality/value The new algorithm outlined in this paper further improves the calculated performance and meets the engineering design requirements for long-term CHT problems. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to study numerically the influence of a magnetic field on the transient free convective boundary layer flow of a nanofluid over a moving semi-infinite vertical cylinder with heat transferDesign/methodology/approach The problem is governed by the coupled non-linear partial differential equations with appropriate boundary conditions. The fluid is a water-based nanofluid containing nanoparticles of copper. The Brinkman model for dynamic viscosity and Maxwell–Garnett model for thermal conductivity are used. The governing boundary layer equations are written according to The Tiwari–Das nanofluid model. A robust, well-tested, implicit finite difference method of Crank–Nicolson type, which is unconditionally stable and convergent, is used to find the numerical solutions of the problem. The velocity and temperature profiles are studied for significant physical parameters such as the magnetic parameter, nanoparticles volume fraction and the thermal Grashof number Gr. The local skin-friction coefficient and the Nusselt number are also analysed and presented graphically.Findings The present computations have shown that an increase in the values of either magnetic parameter M or nanoparticle volume fraction decreases the local skin-friction coefficient, whereas the opposite effect is observed for thermal Grashof number Gr. The local Nusselt number increases with a rise in Gr and ϕ values. But an increase in M reduces the local Nusselt number.Originality/value This paper is relatively original and presents numerical investigation of transient two-dimensional laminar boundary layer free convective flow of a nanofluid over a moving semi-infinite vertical cylinder in the presence of an applied magnetic field. The present study is of immediate application to all those processes which are highly affected by heat enhancement concept and a magnetic field. Further the present study is relevant to nanofluid materials processing, chemical engineering coating operations exploiting nanomaterials and others. [ABSTRACT FROM AUTHOR]