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Article
Publication date: 25 July 2019

Sajjad Haider, Imran Syed Muhammad, Yun-Zhang Li and Adnan Saeed Butt

This paper aims to incorporate a numerical investigation of unsteady flow of nano-fluid near the boundary wall and heat transmission over a flat sheet in porous media…

Abstract

Purpose

This paper aims to incorporate a numerical investigation of unsteady flow of nano-fluid near the boundary wall and heat transmission over a flat sheet in porous media under the assumption that sheet is continuously stretching. A comprehensive study is accomplished to probe the impacts of different physical parameters on heat transmission and fluid flow.

Design/methodology/approach

The problem is designed mathematically by using Navier–Stokes equations and corresponding equations are transmuted into non-dimensional form, which are reduced to local non-similarity equations. Implicit finite difference scheme is used to attain a non-similar solution for values of similarity variable ranging in [0,1]

Findings

The reduced Nusselt number is a decreasing function of each dimensionless number, while the reduced Sherwood number is an increasing function of each considered value of parameters Pr, Sc, Nb and Nt.

Originality value

Motivated by the industrial, technological and scientific importance, the objective of this study is to discuss the unsteady flow generated by linear stretching of the surface in Nano-fluid in a porous medium. However, the investigation of unsteady boundary layer flow and heat transfer of a Nano-fluid past a stretching surface immersed in a porous medium has not been discussed yet. Furthermore, finite difference scheme is used to solve the problem, and authenticate results are achieved which are in good agreement with published work.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 29 August 2019

Sajjad Haider, Adnan Saeed Butt, Imran Syed Muhammad, Asif Ali, Yun-Zhang Li, Syed Muhammad Ali Naqvi and Muhammad Adnan Qaiser

The purpose of this study is to theoretically probe the shape impacts of nano-particle on boundary layer flow of nano-fluid toward a stretching cylinder with…

Abstract

Purpose

The purpose of this study is to theoretically probe the shape impacts of nano-particle on boundary layer flow of nano-fluid toward a stretching cylinder with heat-transmission effects. The base fluid used for this study is pure water, and aluminum oxide nano-particles are suspended in it. Four different shapes of nano-particle, namely, cylindrical, brick, platelets and blades, are considered to carry out the study.

Design/methodology/approach

The problem is modelled mathematically and the nonlinear system of equations is attained by using appropriate transmutations. The solution of transmuted equations is achieved by utilizing a shooting technique with Fourth-Fifth order Runge–Kutta Fehlberg scheme. Numerically attained results are elucidated through graphs and tables which are further compared under limiting cases with existing literature to check the validity of the results.

Findings

It is observed that fluid velocity and temperature of cylindrical shaped water nano-fluids are more than the nano-fluid having brick-shaped nano-particles. Moreover, it is seen that the nano-fluids suspended with platelets-shaped nano-particles have higher velocity and temperature than the nano-fluids containing blade-shaped nano-particles. The curvature parameter and nano-particles volume fraction have increasing effects on flow velocity and temperature of nano-fluids containing all types of nano-particle shapes.

Originality/value

Numerous authors have examined the impacts of nano-particle shapes on characteristics of heat transfer and fluid flow. However, to the best of the authors’ knowledge, the shape impacts of nano-particles on boundary layer flow of nano-fluid toward a stretching cylinder with heat-transmission effects have not been discussed. So, to fulfill this gap, the present paper explicates the impacts of various nano-particle shapes on Al2O3–water-based nano-fluid flow past a stretching cylinder with heat-transfer effects.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 3 September 2019

Sajjad Haider, Nouman Ijaz, A. Zeeshan and Yun-Zhang Li

Numerous researchers have probed the peristaltic flows because of their immense usage in industrial engineering, biomedical engineering and biological sciences. However…

Abstract

Purpose

Numerous researchers have probed the peristaltic flows because of their immense usage in industrial engineering, biomedical engineering and biological sciences. However, the investigation of peristaltic flow in two-phase fluid of a rotating frame in the presence of a magnetic field has not been yet discussed. Therefore, to fulfill this gap in the existing literature, this paper will explicate the peristaltic flow of two-phase fluid across a rotating channel with the effect of wall properties in the presence of a magnetic field. The purpose of this study is to investigate the two-phase velocity distribution and rotation parameter when magneto-hydrodynamics is applied.

Design/methodology/approach

The constituent equations are solved under the condition of low Reynolds number and long wavelength. The exact method is used to attain the subsequent equations and a comprehensive graphical study for fluid phase, particulate phase velocity and flow rates are furnished. The impacts of pertinent parameters, magnetic field and rotation are discussed in detail.

Findings

It is witnessed that the velocity profile of particulate phase gets higher values for the same parameters as compared to the fluid phase velocity. Moreover, the axial velocity increases with different values of particle volume fraction, but in case of magnetic field and rotation parameter, it shows the opposite behavior.

Practical implications

The outcomes of study have viable industrial implementations in systems comprising solid-liquid based flows of fluids involving peristaltic movement.

Originality/value

The investigation of peristaltic flow in two-phase fluid of a rotating frame in the presence of a magnetic field has not been yet discussed. Therefore, to fulfill this gap, the present study will explicate the peristaltic flow of two-phase fluid across a rotating channel with the effect of wall properties in the presence of magnetic field.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 30 October 2020

Maoyuan Li, Yun Zhang, Shi Zhang, Binkui Hou and Huamin Zhou

The orientation behavior of fiber is of great significance in improving the performance of fiber-reinforced polymer products. Generally, the Folgar–Tucker equation can…

Abstract

Purpose

The orientation behavior of fiber is of great significance in improving the performance of fiber-reinforced polymer products. Generally, the Folgar–Tucker equation can accurately describe the variation of orientation vector of fiber, whereas the stability of numerical algorithms was the major challenge. This paper aims to propose an accurate, stable algorithm to solve the Folgar–Tucker equation for the fiber orientation behavior.

Design/methodology/approach

First, the mismatch problem between the strain rate and the pressure field was solved by using the integral transformation method. Then, an accurate, stable algorithm to solve the Folgar–Tucker equation based on the invariant-based optimal fitting method was proposed. The equation was discretized by finite element/finite difference method, and the Lagrange multiplier method was applied to ensure stability.

Findings

The proposed algorithm is proven to accurately and steadily coincide with the experimental results for different cases, including the fiber orientation behaviors under combined flow field, rectangular sheet, three-dimensional computed tomography imaging of tensile specimen and box cases.

Originality/value

The fiber orientation behavior during the injection molding can be accurately predicted, which plays a significant role in determining the mechanical properties of products.

Details

Engineering Computations, vol. 38 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 5 June 2019

Xiang Liu, Fei Guo, Yun Zhang, Junjie Liang, Dequn Li and Huamin Zhou

The purpose of this paper is to develop a coupled approach to solve the pressure–velocity-coupled problem efficiently in the three-dimensional injection molding simulation.

Abstract

Purpose

The purpose of this paper is to develop a coupled approach to solve the pressure–velocity-coupled problem efficiently in the three-dimensional injection molding simulation.

Design/methodology/approach

A fully coupled pressure–velocity algorithm is developed to solve the coupled problem, by treating the pressure gradient term implicitly. And, the Schur complement preconditioned FGMRES is applied to decompose the resulting coupled pressure–velocity equation into pressure and velocity subsystems. Then, BoomerAMG is adopted to solve the pressure subsystem, and block Jacobi preconditioned FGMRES is applied to the velocity subsystem.

Findings

According to the several experiments, the fully coupled pressure–velocity algorithm was demonstrated to have faster convergence than the traditional SIMPLE algorithm, and the calculating time was reduced by up to 70 per cent. And, the Schur complement preconditioned FGMRES worked more efficiently than block Gauss–Seidel preconditioned FGMRES, block-selective AMG and AMG with block ILU(0) smoother and could take at least 47.4 per cent less time. The proposed solver had good scalability for different-size problems, including various cases with different numbers of elements. It also kept good speedup and efficiency in parallel performance.

Originality/value

A coupled solver has been proposed to effectively solve the coupled problem in the three-dimensional injection molding simulation, which is more robust and efficient than existing methods.

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Article
Publication date: 20 April 2015

Shi Zhang, Yun Zhang, Songxin Shi, Zhigao Huang and Huamin Zhou

– The purpose of this paper is to propose a new surface model combining the eccentric shell with multi-point constraint (MPC) for warpage prediction of injection molded plastics.

Abstract

Purpose

The purpose of this paper is to propose a new surface model combining the eccentric shell with multi-point constraint (MPC) for warpage prediction of injection molded plastics.

Design/methodology/approach

In this paper, three benchmark tests and a practical example are implemented to evaluate the performance of the new surface model and existing models.

Findings

The results demonstrate that the proposed model could give satisfactory solutions and has advantages over the existing models.

Practical implications

More precisely predicted warpage field for injection molded plastics can be achieved with the purposed model, such as that in the practical case.

Originality/value

The surface models are efficient and still popular for practical injection molding analysis. However, the existing models for warpage prediction cannot properly represent the true strain energy and obey material continuity assumption, and also they have not been assessed rigorously by benchmark tests. To overcome above-mentioned difficulty, a new surface model is proposed, which employs the eccentric shell without shear factor and MPC equation that ensuring material continuity. The results from experiment illustrate that the new model is superior to existing models.

Details

Engineering Computations, vol. 32 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 5 October 2015

Shi Zhang, Yun Zhang, Zhigao Huang, Huamin Zhou and Jianhui Li

– The purpose of this paper is to study the inter-element coupling effect of membrane and plate components between two adjacent shells occurring on the common boundary.

Abstract

Purpose

The purpose of this paper is to study the inter-element coupling effect of membrane and plate components between two adjacent shells occurring on the common boundary.

Design/methodology/approach

In this paper, three triangular flat shells developed by combining an excellent membrane element (OPT) with three outstanding plate bending elements (DKT, RDKTM and DST-BK), respectively, are used to study this phenomenon. Benchmark tests are implemented to evaluate the performance of three selected plate elements and the formulated flat shells.

Findings

The inter-element coupling effect of membrane and plate components belonging, respectively, to two adjacent shells deteriorate the performance of shells. Therefore, a shell’s performance cannot be guaranteed certainly by the superimposed membrane and plate behaviors.

Practical implications

The “order matching” criterion is proposed to explain this phenomenon and it is concluded that the flat shell that follows this criterion explicitly may alleviate or even overcome the inter-element coupling effect.

Originality/value

Previous studies mainly focus on formulation of high-performance membrane and plate elements. However, the inter-element coupling effect of membrane and plate components between two adjacent shells occurring on the common boundary, has attracted less attention. Thorough benchmark tests for three flat shells are implemented to investigate the phenomenon. The results shows that the inter-element coupling effect deteriorates the performance of shells. And the “order matching” criterion is proposed to explain this phenomenon and it is concluded that the flat shell that follows this criterion explicitly may alleviate or even overcome the inter-element coupling effect.

Details

Engineering Computations, vol. 32 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 30 September 2014

Zixiang Hu, Shi Zhang, Yun Zhang, Huamin Zhou and Dequn Li

The purpose of this paper is to propose an efficient iterative method for large-scale finite element equations of bad numerical stability arising from deformation analysis…

Abstract

Purpose

The purpose of this paper is to propose an efficient iterative method for large-scale finite element equations of bad numerical stability arising from deformation analysis with multi-point constraint using Lagrange multiplier method.

Design/methodology/approach

In this paper, taking warpage analysis of polymer injection molding based on surface model as an example, the performance of several popular Krylov subspace methods, including conjugate gradient, BiCGSTAB and generalized minimal residual (GMRES), with diffident Incomplete LU (ILU)-type preconditions is investigated and compared. For controlling memory usage, GMRES(m) is also considered. And the ordering technique, commonly used in the direct method, is introduced into the presented iterative method to improve the preconditioner.

Findings

It is found that the proposed preconditioned GMRES method is robust and effective for solving problems considered in this paper, and approximate minimum degree (AMD) ordering is most beneficial for the reduction of fill-ins in the ILU preconditioner and acceleration of the convergence, especially for relatively accurate ILU-type preconditioning. And because of concerns about memory usage, GMRES(m) is a good choice if necessary.

Originality/value

In this paper, for overcoming difficulties of bad numerical stability resulting from Lagrange multiplier method, together with increasing scale of problems in engineering applications and limited hardware conditions of computer, a stable and efficient preconditioned iterative method is proposed for practical purpose. Before the preconditioning, AMD reordering, commonly used in the direct method, is introduced to improve the preconditioner. The numerical experiments show the good performance of the proposed iterative method for practical cases, which is implemented in in-house and commercial codes on PC.

Details

Engineering Computations, vol. 31 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 2 October 2017

Dan Chen, Fen Liu, Yi Zhang, Yun Zhang and Huamin Zhou

The numerical simulation of dispersed-phase evolution in injection molding process of polymer blends is of great significance in both adjusting material microstructure and…

Abstract

Purpose

The numerical simulation of dispersed-phase evolution in injection molding process of polymer blends is of great significance in both adjusting material microstructure and improving performances of the final products. This paper aims to present a numerical strategy for the simulation of dispersed-phase evolution for immiscible polymer blends in injection molding.

Design/methodology/approach

First, the dispersed-phase modeling is discussed in detail. Then the Maffettone–Minale model, affine deformation model, breakup model and coalescence statistical model are chosen for the dispersed-phase evolution. A general coupled model of microscopic morphological evolution and macroscopic flow field is constructed. Besides, a stable finite element simulation strategy based on pressure-stabilizing/Petrov–Galerkin/streamline-upwind/Petrov–Galerkin method is adopted for both scales.

Findings

Finally, the simulation results are compared and evaluated with the experimental data, suggesting the reliability of the presented numerical strategy.

Originality/value

The coupled modeling of dispersed-phase and complex flow field during injection molding and the tracing and simulation of droplet evolution during the whole process can be achieved.

Details

Engineering Computations, vol. 34 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 18 April 2017

Lin Deng, Junjie Liang, Yun Zhang, Huamin Zhou and Zhigao Huang

Lattice Boltzmann method (LBM) has made great success in computational fluid dynamics, and this paper aims to establish an efficient simulation model for the polymer…

Abstract

Purpose

Lattice Boltzmann method (LBM) has made great success in computational fluid dynamics, and this paper aims to establish an efficient simulation model for the polymer injection molding process using the LBM. The study aims to validate the capacity of the model for accurately predicting the injection molding process, to demonstrate the superior numerical efficiency in comparison with the current model based on the finite volume method (FVM).

Design/methodology/approach

The study adopts the stable multi-relaxation-time scheme of LBM to model the non-Newtonian polymer flow during the filling process. The volume of fluid method is naturally integrated to track the movement of the melt front. Additionally, a novel fractional-step thermal LBM is used to solve the convection-diffusion equation of the temperature field evolution, which is of high Peclet number. Through various simulation cases, the accuracy and stability of the present model are validated, and the higher numerical efficiency verified in comparison with the current FVM-based model.

Findings

The paper provides an efficient alternative to the current models in the simulation of polymer injection molding. Through the test cases, the model presented in this paper accurately predicts the filling process and successfully reproduces several characteristic phenomena of injection molding. Moreover, compared with the popular FVM-based models, the present model shows superior numerical efficiency, more fit for the future trend of parallel computing.

Research limitations/implications

Limited by the authors’ hardware resources, the programs of the present model and the FVM-based model are run on parallel up to 12 threads, which is adequate for most simulations of polymer injection molding. Through the tests, the present model has demonstrated the better numerical efficiency, and it is recommended for the researcher to investigate the parallel performance on even larger-scale parallel computing, with more threads.

Originality/value

To the authors’ knowledge, it is for the first time that the lattice Boltzmann method is applied in the simulation of injection molding, and the proposed model does obviously better in numerical efficiency than the current popular FVM-based models.

Details

Engineering Computations, vol. 34 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

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