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Article
Publication date: 1 July 2020

Iskandar Waini, Anuar Ishak and Ioan Pop

This paper aims to examine the effect of Dufour and Soret diffusions on Al2O3-water nanofluid flow over a moving thin needle by using the Tiwari and Das model.

Abstract

Purpose

This paper aims to examine the effect of Dufour and Soret diffusions on Al2O3-water nanofluid flow over a moving thin needle by using the Tiwari and Das model.

Design/methodology/approach

The governing equations are reduced to the similarity equations using similarity transformations. The resulting equations are programmed in Matlab software through the bvp4c solver to obtain their solutions. The features of the skin friction, heat transfer and mass transfer coefficients, as well as the velocity, temperature and concentration profiles for different values of the physical parameters, are analysed and discussed.

Findings

The non-uniqueness of the solutions is observed for a certain range of the physical parameters. The authors also notice that the bifurcation of the solutions occurs in which the needle moves toward the origin (λ < 0). It is discovered that the first branch solutions of the skin friction coefficient and the heat transfer coefficients increase, but the mass transfer coefficient decreases in the presence of nanoparticle. Additionally, the simultaneous effect of Dufour and Soret diffusions tends to enhance the heat transfer coefficient; however, dual behaviours are observed for the mass transfer coefficient. Further analysis shows that between the two solutions, only one of them is stable and thus physically reliable in the long run.

Originality/value

The problem of Al2O3-water nanofluid flow over a moving thin needle with Dufour and Soret effects are the important originality of the present study. Besides, the temporal stability of the dual solutions is examined for time.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 16 August 2022

Najiyah Safwa Khashi’ie, Iskandar Waini, Norihan Md Arifin and Ioan Pop

This paper aims to analyse numerically the unsteady stagnation-point flow of Cu-Al2O3/H2O hybrid nanofluid towards a radially shrinking Riga surface with thermal radiation.

Abstract

Purpose

This paper aims to analyse numerically the unsteady stagnation-point flow of Cu-Al2O3/H2O hybrid nanofluid towards a radially shrinking Riga surface with thermal radiation.

Design/methodology/approach

The governing partial differential equations are transformed into a set of ordinary (similar) differential equations by applying appropriate transformations. The numerical computation of these equations including the stability analysis is conducted using the bvp4c solver.

Findings

Two solutions are possible within the allocated interval: shrinking parameter, unsteadiness decelerating parameter, electro-magneto-hydrodynamics (EMHD) parameter, nanoparticles volumetric concentration, radiation parameter and width parameter, whereas the stability analysis certifies that the first (upper branch) solution, which fulfills the boundary conditions is the physical/real solution. The EMHD parameter generated from the application of Riga plate enhances the skin friction coefficient as well as the heat transfer process. The width parameter d is also one of the factors in the deterioration of the skin friction coefficient and heat transfer rate. It is crucial to control the width parameter of the magnets and electrodes to obtain the desired outcome. The radiation parameter is not affecting the boundary layer separation because the critical values are unchanged. However, the addition of radiation and unsteadiness decelerating parameters boosts the thermal rate.

Originality/value

The results are novel and contribute to the discovery of the flow and thermal performance of the hybrid nanofluid subjected to a radially shrinking Riga plate. Besides, this work is beneficial to the other researchers and general audience from industries regarding the factors which contribute to the thermal enhancement of the working fluid.

Details

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

Keywords

Article
Publication date: 8 February 2022

Iskandar Waini, Umair Khan, Aurang Zaib, Anuar Ishak and Ioan Pop

This study aims to investigate the micropolar fluid flow through a moving flat plate containing CoFe2O4-TiO2 hybrid nanoparticles with the substantial influence of…

Abstract

Purpose

This study aims to investigate the micropolar fluid flow through a moving flat plate containing CoFe2O4-TiO2 hybrid nanoparticles with the substantial influence of thermophoresis particle deposition and viscous dissipation.

Design/methodology/approach

The partial differential equations are converted to the similarity equations of a particular form through the similarity variables. Numerical outcomes are computed by applying the built-in program bvp4c in MATLAB. The process of flow, heat and mass transfers phenomena are examined for several physical aspects such as the hybrid nanoparticles, micropolar parameter, the thermophoresis particle deposition and the viscous dissipation.

Findings

The friction factor, heat and mass transfer rates are higher with an increment of 1.4%, 2.2% and 1.4%, respectively, in the presence of the hybrid nanoparticles (with 2% volume fraction). However, they are declined because of the rise of the micropolar parameter. The imposition of viscous dissipation reduces the heat transfer rate, significantly. Meanwhile, thermophoresis particle deposition boosts the mass transfer. Multiple solutions are developed for a certain range of physical parameters. Lastly, the first solution is shown to be stable and reliable physically.

Originality/value

As far as the authors have concerned, no work on thermophoresis particle deposition of hybrid nanoparticles on micropolar flow through a moving flat plate with viscous dissipation effect has been reported in the literature. Most importantly, this current study reported the stability analysis of the non-unique solutions and, therefore, fills the gap of the study and contributes to new outcomes in this particular problem.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 32 no. 10
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 5 August 2021

Ioan Pop, Iskandar Waini and Anuar Ishak

This study aims to explore the stagnation flow over a shrinking surface in a hybrid nanofluid consists of Al2O3 and Cu nanoparticles. Here, the flow is subjected to the…

Abstract

Purpose

This study aims to explore the stagnation flow over a shrinking surface in a hybrid nanofluid consists of Al2O3 and Cu nanoparticles. Here, the flow is subjected to the magnetohydrodynamic (MHD) and the melting phenomenon effects.

Design/methodology/approach

The similarity variables are used to gain the similarity equations. These equations are solved via the bvp4c solver. The effects of several physical parameters on the flow and the thermal characteristics of the hybrid nanofluid are analysed and discussed. Later, the temporal stability analysis is used to determine the stability of the dual solutions obtained as time evolves.

Findings

Results show that two solutions are found for the limited range of the stretching/shrinking parameter λ, and then these solutions are terminated at λ=λc. The rise of the melting parameter Me from 0 to 2 contributes to enhance 109.63% of the local Nusselt number Rex-1/2Nux and 3.30% of the skin friction coefficient Rex1/2Cf. Contrarily, the values of Rex-1/2Nux and Rex1/2Cf decline by 25.04% and 5.58%, respectively, as the magnetic parameter Mg increases from 0 to 0.3. Additionally, Al2O3-Cu/water has the highest values of Rex1/2Cf and the lowest values of Rex-1/2Nux. Lastly, it is found that the first solution is physically stable as time evolves.

Originality/value

This paper considers the MHD stagnation point flow of a hybrid nanofluid over a shrinking surface with the melting phenomenon effects. Most importantly, it is shown that there exist dual solutions within a specific range of the physical parameters. Besides, the temporal stability of the solutions is also reported in this study. The finding can contribute to foresee the flow and thermal behaviours in industrial applications. Also, the suitable values of parameters can be determined to avoid misjudgement in flow and heat transfer analysis.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 32 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 17 August 2021

Iskandar Waini, Anuar Ishak, Ioan Pop and Roslinda Nazar

This paper aims to examine the Cu-Al2O3/water hybrid nanofluid flow over a shrinking sheet in the presence of the magnetic field and dust particles.

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Abstract

Purpose

This paper aims to examine the Cu-Al2O3/water hybrid nanofluid flow over a shrinking sheet in the presence of the magnetic field and dust particles.

Design/methodology/approach

The governing partial differential equations for the two-phase flow of the hybrid nanofluid and the dust particles are reduced to ordinary differential equations using a similarity transformation. Then, these equations are solved using bvp4c in MATLAB software. The bvp4c solver is a finite-difference code that implements the three-stage Lobatto IIIa formula. The numerical results are gained for several values of the physical parameters. The effects of these parameters on the flow and the thermal characteristics of the hybrid nanofluid and the dust particles are analyzed and discussed. Later, the temporal stability analysis is used to determine the stability of the dual solutions obtained as time evolves.

Findings

The outcome shows that the flow is unlikely to exist unless satisfactory suction strength is imposed on the shrinking sheet. Besides, the heat transfer rate on the shrinking sheet decreases with the increase of . However, the increase in and lead to enhance the heat transfer rate. Two solutions are found, where the domain of the solutions is expanded with the rising of, and. Consequently, the boundary layer separation on the surface is delayed in the presence of these parameters. Implementing the temporal stability analysis, it is found that only one of the solutions is stable as time evolves.

Originality/value

The dusty fluid problem has been widely studied for the flow over a stretching sheet, but only limited findings can be found for the shrinking counterpart. Therefore, this study considers the problem of the dusty fluid flow over a shrinking sheet containing Cu-Al2O3/water hybrid nanofluid with the effect of the magnetic field. In fact, this is the first study to discover the dual solutions of the dusty hybrid nanofluid flow over a shrinking sheet. Also, further analysis shows that only one of the solutions is stable as time evolves.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 32 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 3 July 2021

Iskandar Waini, Ioan Pop, Sakhinah Abu Bakar and Anuar Ishak

This paper aims to investigate the radiation and magnetohydrodynamic effect on the flow toward a stagnation point of an exponentially shrinking sheet in a hybrid nanofluid.

Abstract

Purpose

This paper aims to investigate the radiation and magnetohydrodynamic effect on the flow toward a stagnation point of an exponentially shrinking sheet in a hybrid nanofluid.

Design/methodology/approach

The governing partial differential equations are transformed into a set of similarity equations and are then solved numerically using the boundary value problem solver, bvp4c, available in MATLAB software. The effects of several physical parameters on the flow and the thermal characteristics of the hybrid nanofluid are analyzed and discussed.

Findings

Numerical results clarify that the dual solutions arise for the shrinking case (λ < 0). The critical values expand for the stronger magnetic field. Besides, the skin friction and the heat transfer coefficients enhance with the rise of the magnetic field and the hybrid nanoparticles. The heat transfer rate increases by 10.11% for the nanofluid and 28.69% for the hybrid nanofluid compared to the regular fluid. In addition, the presence of radiation gives a higher heat transfer rate. Using the stability analysis, it is found that the first solution is stable, and the second solution is unstable, over time.

Originality/value

The stagnation point flow problem has been widely studied for the flow over a stretching sheet, but only limited findings can be found for the flow over a shrinking sheet. Therefore, the present study considers the problem of the stagnation point flow over a shrinking sheet in a Cu-Al2O3/water hybrid nanofluid with the effects of magnetic field and thermal radiation. The dual solutions of the hybrid nanofluid flow over a shrinking sheet are obtained. Further analysis shows that only one of the solutions is stable and thus physically reliable as time evolves.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 32 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 4 February 2020

Iskandar Waini, Anuar Ishak and Ioan Pop

The purpose of this paper is to examine the axisymmetric flow and heat transfer of a hybrid nanofluid over a permeable biaxial stretching/shrinking sheet.

Abstract

Purpose

The purpose of this paper is to examine the axisymmetric flow and heat transfer of a hybrid nanofluid over a permeable biaxial stretching/shrinking sheet.

Design/methodology/approach

In this study, 0.1 solid volume fraction of alumina (Al2O3) is fixed, then consequently, various solid volume fractions of copper (Cu) are added into the mixture with water as the base fluid to form Cu-Al2O3/water hybrid nanofluid. The hybrid nanofluid equations are converted to the similarity equations by using the similarity transformation. The bvp4c solver, which is available in the Matlab software is used for solving the similarity equations numerically. The numerical results for selected values of the parameters are presented in tabular and graphical forms, and are discussed in detail.

Findings

It is found that dual solutions exist up to a certain value of the stretching/shrinking and suction parameters. The critical value λc < 0 for the existence of the dual solutions decreases as nanoparticle volume fractions for copper increase. The temporal stability analysis is performed to analyze the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable.

Originality/value

The present problem is new, original with many important results for practical problems in the modern industry.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 14 October 2020

Iskandar Waini, Anuar Ishak and Ioan Pop

This study aims to investigate the flow impinging on a stagnation point of a shrinking cylinder subjected to prescribed surface heat flux in Al2O3-Cu/water hybrid nanofluid.

Abstract

Purpose

This study aims to investigate the flow impinging on a stagnation point of a shrinking cylinder subjected to prescribed surface heat flux in Al2O3-Cu/water hybrid nanofluid.

Design/methodology/approach

Using similarity variables, the similarity equations are obtained and then solved using bvp4c in MATLAB. The effects of several physical parameters on the skin friction and heat transfer rate, as well as the velocity and temperature profiles are analysed and discussed.

Findings

The outcomes show that dual solutions are possible for the shrinking case, in the range λc<λ<1, where λc is the bifurcation point of the solutions. Meanwhile, the solution is unique for λ1. Besides, the boundary layer is detached on the surface at λc, where the value of λc is affected by the hybrid nanoparticle φhnf and the curvature parameter γ. Moreover, the friction and the heat transfer on the surface increase with the rising values φhnf and γ. Finally, the temporal stability analysis shows that the first solution is stable in the long run, whereas the second solution is not.

Originality/value

The present work considers the problem of stagnation point flow impinging on a shrinking cylinder containing Al2O3-Cu/water hybrid nanofluid, with prescribed surface heat flux. This paper shows that two solutions are obtained for the shrinking case. Further analysis shows that only one of the solutions is stable as time evolves.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 13 May 2020

Iskandar Waini, Anuar Ishak and Ioan Pop

This paper aims to examine the hybrid nanofluid flow towards a stagnation point on an exponentially stretching/shrinking vertical sheet with buoyancy effects.

Abstract

Purpose

This paper aims to examine the hybrid nanofluid flow towards a stagnation point on an exponentially stretching/shrinking vertical sheet with buoyancy effects.

Design/methodology/approach

Here, the authors consider copper (Cu) and alumina (Al2O3) as hybrid nanoparticles while water as the base fluid. The governing equations are reduced to the similarity equations using similarity transformations. The resulting equations are programmed in Matlab software through the bvp4c solver to obtain their solutions.

Findings

The authors found that the heat transfer rate is greater for Al2O3-Cu/water hybrid nanofluid if compared to Cu/water nanofluid. Besides, the non-uniqueness of the solutions is observed for certain physical parameters. The authors also notice that the bifurcation of the solutions occurs in the downward buoyant force and the shrinking regions. In addition, the first solution of the skin friction and heat transfer coefficients increase with the added hybrid nanoparticles and the mixed convection parameter. The temporal stability analysis shows that one of the solutions is stable as time evolves.

Originality/value

The present work is dealing with the problem of a mixed convection flow of a hybrid nanofluid towards a stagnation point on an exponentially stretching/shrinking vertical sheet, with the buoyancy effects is taken into consideration. The authors show that two solutions are obtained for a single value of parameter for both stretching and shrinking cases, as well as for both buoyancy aiding and opposing flows. A temporal stability analysis then shows that only one of the solutions is stable and physically reliable as time evolves.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 8 February 2022

Umair Khan, Aurang Zaib, Ioan Pop, Iskandar Waini and Anuar Ishak

Nanofluid research has piqued the interest of scientists due to its intriguing applications in nanoscience, biomedical and electrical engineering, medication delivery…

Abstract

Purpose

Nanofluid research has piqued the interest of scientists due to its intriguing applications in nanoscience, biomedical and electrical engineering, medication delivery, biotechnology, food processing, chemotherapy and other fields. This paper aims to inspect the behavior of the mixed convection magnetohydrodynamic flow and heat transfer induced by a nonlinear stretching/shrinking sheet in a nanofluid with a convective boundary condition. Tiwari and Das mathematical nanofluid model is incorporated in the analysis.

Design/methodology/approach

The mathematical model is initially transformed to a nondimensional form by using dimensionless variables. Then the nondimensional partial differential equations are further transformed to a set of similarity equations by using the similarity technique. These equations are solved numerically by the bvp4c function in MATLAB software.

Findings

For a certain range of the stretching/shrinking parameter, two solutions are obtained. The friction factor and the heat transfer rate escalate due to suction parameter with adding nanoparticles volume fraction by almost 27.15% and 0.153% for the upper branch solution, while the friction factor declines by almost 30.10% but the heat transfer rate augments by 0.145% for the lower branch solution. Furthermore, the behavior of the nanoparticle volume fractions on the heat transfer rate behaves differently in the presence of the mixed convection effect. The temperature of fluid augments with increasing Biot number for both solutions.

Originality/value

The present work considers the flow and heat transfer induced by a stretching/shrinking sheet in a nanofluid using the Tiwari–Das nanofluid model with a convective boundary condition, where the effect of the buoyancy force is taken into consideration. It is shown that two solutions are found for a certain range of the shrinking strength, while the solution is unique for the stretching case. This study is important for scientists working in the growing field of nanofluids to become familiar with the flow properties and behaviors of such nanofluids.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 32 no. 10
Type: Research Article
ISSN: 0961-5539

Keywords

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