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Article
Publication date: 3 April 2017

Rohana Abdul Hamid, Roslinda Nazar and Ioan Pop

The purpose of this paper is to numerically study the boundary layer problem for the case of two-dimensional flow of dusty fluid over a shrinking surface in the presence…

Abstract

Purpose

The purpose of this paper is to numerically study the boundary layer problem for the case of two-dimensional flow of dusty fluid over a shrinking surface in the presence of the fluid suction at the surface.

Design/methodology/approach

The governing equations of the problem are reduced to the system of ordinary differential equations using the similarity transformation and then solved using the bvp4c method in the Matlab software.

Findings

The effects of the drag coefficient parameter L, the fluid–particle interaction parameter δ, the suction parameter s and the particle loading parameter ω on the flow of the permeable shrinking sheet are investigated. It is found that the aforementioned parameters have different effects in the shrinking sheet flow. This study has also succeeded in discovering the second solution, and through the stability analysis, it is suggested that the solution is unstable and not physically realizable in practice.

Practical implications

The current findings add to a growing body of literature on the boundary layer problem in the dusty fluid. The dusty fluid is significant in various practical applications such as in the transporting suspended powdered materials through pipes, propulsion and combustion in rockets, the flow of blood in arteries, wastewater treatment and as corrosive particles in engine oil flow.

Originality/value

Even though the dusty fluid problem has been extensively studied in the flow of the stretching sheet, limited findings can be found over a shrinking flow. In fact, this is the first study to discover the second solution in the dusty fluid problem.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 4
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 January 2017

Siti Hidayah Muhad Saleh, Norihan Md. Arifin, Roslinda Nazar and Ioan Pop

The purpose of this paper is to present the results of an analysis performed to study unsteady mixed convection at the stagnation point flow over a plate moving along the…

Abstract

Purpose

The purpose of this paper is to present the results of an analysis performed to study unsteady mixed convection at the stagnation point flow over a plate moving along the direction of flow impingement. The similarity transformations are used to transform the governing nonlinear partial differential equation to a system of an ordinary differential equation.

Design/methodology/approach

The transformed equations are then solved numerically by a shooting technique together with bvp4c function.

Findings

The numerical results are compared with the corresponding results from previous researchers. The effects of the unsteadiness Parameter A, Prandtl number Pr, mixed convection parameter λ for plane (m = 0) and axisymmetric (m = 1) flow on the shear stress or the skin friction and heat transfer coefficients, as well as the velocity and temperature profiles, are presented and discussed.

Originality/value

Dual solutions for the opposing flow and multiple solutions for the assisting flow are found.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 26 July 2018

Rohana Abdul Hamid, Roslinda Nazar and Ioan Pop

This present aims to present the numerical study of the unsteady stretching/shrinking flow of a fluid-particle suspension in the presence of the constant suction and dust…

Abstract

Purpose

This present aims to present the numerical study of the unsteady stretching/shrinking flow of a fluid-particle suspension in the presence of the constant suction and dust particle slip on the surface.

Design/methodology/approach

The governing partial differential equations for the two phases flows of the fluid and the dust particles are reduced to the pertinent ordinary differential equations using a similarity transformation. The numerical results are obtained using the bvp4c function in the Matlab software.

Findings

The results revealed that in the decelerating shrinking flow, the wall skin friction is higher in the dusty fluid when compared to the clean fluid. In addition, the effect of the fluid-particle interaction parameter to the fluid-phase can be seen more clearly in the shrinking flow. Other non-dimensional physical parameters such as the unsteadiness parameter, the mass suction parameter, the viscosity ratio parameter, the particle slip parameter and the particle loading parameter are also considered and presented in figures. Further, the second solution is discovered in this problem and the solution expanded with higher unsteadiness and suction values. Hence, the stability analysis is performed, and it is confirmed that the second solution is unstable.

Practical implications

In practice, the flow conditions are commonly varying with time; thus, the study of the unsteady flow is very crucial and useful. The problem of unsteady flow of a dusty fluid has a wide range of possible applications such as in the centrifugal separation of particles, sedimentation and underground disposable of radioactive waste materials.

Originality/value

Even though the problem of dusty fluid has been broadly investigated, limited discoveries can be found over an unsteady shrinking flow. Indeed, this paper managed to obtain the second (dual) solutions, and stability analysis is performed. Furthermore, the authors also considered the artificial particle-phase viscosity, which is an important term to study the particle-particle and particle-wall interactions. With the addition of this term, the effects of the particle slip and suction parameters can be investigated. Very few studies in the dusty fluid embedded this parameter in their problems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 29 July 2019

Fadzilah Md Ali, Kohilavani Naganthran, Roslinda Nazar and Ioan Pop

This study aims to perform a stability analysis on a steady magnetohydrodynamic (MHD) mixed convection boundary-layer stagnation-point flow of an incompressible, viscous…

Abstract

Purpose

This study aims to perform a stability analysis on a steady magnetohydrodynamic (MHD) mixed convection boundary-layer stagnation-point flow of an incompressible, viscous and electrically conducting fluid over a vertical flat plate. The effect of induced magnetic field is also considered.

Design/methodology/approach

The governing boundary layer equations are transformed into a system of ordinary differential equations using the similarity transformations. The system is then solved numerically using the “bvp4c” function in MATLAB.

Findings

Dual solutions are found to exist for a certain range of the buoyancy parameter for both the assisting and opposing flows. The results from the stability analysis showed that the first solution (upper branch) is stable and valid physically, while the second solution (lower branch) is unstable.

Practical implications

This problem is important in many metallurgical processes, namely, drawing, annealing and tinning of copper wires. The results obtained are very useful for researchers to determine which solution is physically stable, whereby mathematically more than one solution exists for the skin friction coefficient and the heat transfer characteristics.

Originality/value

The present results of the stability analysis are original and new for the problem of MHD mixed convection stagnation-point flow of viscous conducting fluid over a vertical flat plate, with the effect of induced magnetic field.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 11
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 22 June 2018

Mohd Ezad Hafidz Hafidzuddin, Roslinda Nazar, Norihan M. Arifin and Ioan Pop

This study aims to investigate the unsteady two-dimensional viscous flow and heat transfer over an unsteady permeable stretching/shrinking sheet (surface) with generalized…

Abstract

Purpose

This study aims to investigate the unsteady two-dimensional viscous flow and heat transfer over an unsteady permeable stretching/shrinking sheet (surface) with generalized slip velocity condition.

Design/methodology/approach

Similarity transformation is used to reduce the system of partial differential equations into a system of nonlinear ordinary differential equations. The resulting equations are then solved numerically using “bvp4c” function in MATLAB software.

Findings

Dual solutions are found for a certain range of the unsteady, suction and stretching/shrinking parameters. Stability analysis is performed, and it is revealed that the first (upper branch) solution is stable and physically realizable, whereas the second (lower branch) solution is unstable.

Practical implications

The results obtained can be used to explain the characteristics and applications of the generalized slip in boundary layer flow. Such condition is applied for particulate fluids such as foams, emulsions, polymer solutions and suspensions. Furthermore, the phenomenon of stretching/shrinking sheet can be found on the manufacturing of polymer sheets, rising and shrinking balloon or moving and shrinking polymer film.

Originality/value

The present numerical results are original and new for the study of unsteady flow and heat transfer over a permeable stretching/shrinking sheet with generalized slip velocity.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 15 May 2020

Amin Noor, Roslinda Nazar, Kohilavani Naganthran and Ioan Pop

This paper aims to probe the problem of an unsteady mixed convection stagnation point flow and heat transfer past a stationary surface in an incompressible viscous fluid…

Abstract

Purpose

This paper aims to probe the problem of an unsteady mixed convection stagnation point flow and heat transfer past a stationary surface in an incompressible viscous fluid numerically.

Design/methodology/approach

The governing nonlinear partial differential equations are transformed into a system of ordinary differential equations by a similarity transformation, which is then solved numerically by a Runge – Kutta – Fehlberg method with shooting technique and a collocation method, namely, the bvp4c function.

Findings

The effects of the governing parameters on the fluid flow and heat transfer characteristics are illustrated in tables and figures. It is found that dual (upper and lower branch) solutions exist for both the cases of assisting and opposing flow situations. A stability analysis has also been conducted to determine the physical meaning and stability of the dual solutions.

Practical implications

This theoretical study is significantly relevant to the applications of the heat exchangers placed in a low-velocity environment and electronic devices cooled by fans.

Originality/value

The case of suction on unsteady mixed convection flow at a three-dimensional stagnation point has not been studied before; hence, all generated numerical results are claimed to be novel.

Details

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

Keywords

Article
Publication date: 1 April 2022

Nurul Amira Zainal, Roslinda Nazar, Kohilavani Naganthran and Ioan Pop

According to the previous research, bioconvection has been recognized as an important mechanism in current engineering and environmental systems. For example, researchers…

Abstract

Purpose

According to the previous research, bioconvection has been recognized as an important mechanism in current engineering and environmental systems. For example, researchers exploit this mechanism in modern green bioengineering to develop environmentally friendly fuels, fuel cells and photosynthetic microorganisms. This study aims to analyse how this type of convection affects the flow behaviour and heat transfer performance of mixed convection stagnation point flow in alumina-copper/water hybrid nanofluid. Also, the impact of a modified magnetic field on the boundary layer flow is considered.

Design/methodology/approach

By applying appropriate transformations, the multivariable differential equations are transformed into a specific sort of ordinary differential equations. Using the bvp4c procedure, the adjusted mathematical model is revealed. Once sufficient assumptions are provided, multiple solutions are able to be produced.

Findings

The skin friction coefficient is declined when the nanoparticle concentration is increased in the opposing flow. In contrast, the inclusion of aligned angles displays an upward trend in heat transfer performance. The presence of several solutions is established, which simply leads to a stability analysis, hence verifies the viability of the initial solution.

Originality/value

The current findings are unique and novel for the investigation of mixed bioconvection flow towards a vertical flat plate in a base fluid with the presence of hybrid nanoparticles.

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: 17 December 2021

Nurul Amira Zainal, Roslinda Nazar, Kohilavani Naganthran and Ioan Pop

The investigation of fluid flow and heat transfer is incredibly significant in the present era, particularly in the engineering and manufacturing industries. Hence, this…

Abstract

Purpose

The investigation of fluid flow and heat transfer is incredibly significant in the present era, particularly in the engineering and manufacturing industries. Hence, this study aims to concern with analysing the unsteady stagnation point flow towards a permeable stretching/shrinking Riga plate of Al2O3-Cu/H2O. The effect of thermal radiation on the boundary layer flow is also taken into account.

Design/methodology/approach

The multi-variable differential equations with partial derivatives are transformed into third-order and second-order differential equations by applying appropriate transformations. The reduced mathematical model is solved in the MATLAB system by using the bvp4c procedure. This solution approach is capable of producing multiple solutions once the necessary assumptions are provided.

Findings

The results of various control parameters were analysed, and it has been observed that raising the solution viscosity from 0% to 0.5% and 1% improves the coefficient of skin friction and thermal conductivity by almost 1.0% and 1.9%. Similar response and observation can be witnessed in the addition of modified Hartmann number where the highest values dominate about 10.7% improvement. There is a substantial enhancement in the heat transfer rate, approximately 1.8% when the unsteadiness parameter leads around 30% in the boundary layer flow. In contrast, the increment in thermal radiation promotes heat transfer deterioration. Further, more than one solution is proven, which invariably leads to a stability analysis, which validates the first solution’s feasibility.

Originality/value

The present results are new and original for the study of flow and heat transfer on unsteady stagnation point flow past a permeable stretching/shrinking Riga plate in Al2O3-Cu/H2O hybrid nanofluid with thermal radiation.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 32 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 3 August 2021

Nurul Amira Zainal, Roslinda Nazar, Kohilavani Naganthran and Ioan Pop

The analysis of boundary layers is needed to reflect the behaviour of fluid flows in current industrial processes and to improve the efficacy of products. Hence, this…

Abstract

Purpose

The analysis of boundary layers is needed to reflect the behaviour of fluid flows in current industrial processes and to improve the efficacy of products. Hence, this study aims to analyse the flow and heat transfer performance of hybrid alumina-copper/water (Al2O3-Cu/H2O) nanofluid with the inclusion of activation energy and binary chemical reaction effect towards a moving wedge.

Design/methodology/approach

The multivariable differential equations with partial derivatives are converted into a specific type of ordinary differential equations by using valid similarity transformations. The reduced mathematical model is elucidated in the MATLAB system by using the bvp4c procedure. This solution method is competent in delivering multiple solutions once appropriate assumptions are supplied.

Findings

The results of multiple control parameters have been studied, and the findings are verified to provide more than one solution. The coefficient of skin friction was discovered to be increased by adding nanoparticles volume fraction from 0% to 0.5% and 1%, by almost 1.6% and 3.2%. Besides, increasing the nanoparticles volume fraction improves heat transfer efficiency gradually. The inclusion of the activation energy factor displays a downward trend in the mass transfer rates, consequently reducing the concentration profile. In contrast, the increment of the binary reaction rate greatly facilitates the augmentation of mass transfer rates. There is a significant enhancement in the heat transfer rate, approximately 13.2%, when the suction effect dominates about 10% in the boundary layer flow. Additionally, the results revealed that as the activation energy rises, the temperature and concentration profiles rise as well. It is proved that the activation energy parameter boosts the concentration of chemical species in the boundary layer. A similar pattern emerges as the wedge angle parameter increases. The current effort aims to improve the thermal analysis process, particularly in real-world applications such as geothermal reservoirs, chemical engineering and food processing, which often encountered mass transfer phenomenon followed by chemical reactions with activation energy.

Originality/value

The present results are original and new for the study of flow and heat transfer over a permeable moving wedge in a hybrid nanofluid with activation energy and binary chemical reaction.

Details

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

Keywords

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