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Article
Publication date: 7 November 2016

Ioan Pop, Siti Suzilliana Putri Mohamed Isa, Norihan M. Arifin, Roslinda Nazar, Norfifah Bachok and Fadzilah M. Ali

The purpose of this paper is to theoretically study the problem of the unsteady boundary layer flow past a permeable curved stretching/shrinking surface in the presence of a…

Abstract

Purpose

The purpose of this paper is to theoretically study the problem of the unsteady boundary layer flow past a permeable curved stretching/shrinking surface in the presence of a uniform magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically.

Design/methodology/approach

The transformed system of ordinary differential equations was solved using a fourth-order Runge-Kutta integration scheme. Results for the reduced skin friction coefficient and velocity profiles are presented through graphs and tables for several sets of values of the governing parameters. The effects of these parameters on the flow characteristics are thoroughly examined.

Findings

Results show that for the both cases of stretching and shrinking surfaces, multiple solutions exist for a certain range of the curvature, mass suction, unsteadiness, stretching/shrinking parameters and magnetic field parameter.

Originality/value

The paper describes how multiple (dual) solutions for the flow reversals are obtained. It is shown that the solutions exist up to a critical value of the shrinking parameter, beyond which the boundary layer separates from the surface and the solution based upon the boundary layer approximations is not possible.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 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 study aims…

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

Article
Publication date: 7 February 2020

Najiyah Safwa Khashi’ie, Norihan Md Arifin, Ioan Pop, Roslinda Nazar, Ezad Hafidz Hafidzuddin and Nadihah Wahi

This paper aims to scrutinize the analysis of non-axisymmetric Homann stagnation point flow and heat transfer of hybrid Cu-Al2O3/water nanofluid over a stretching/shrinking flat…

Abstract

Purpose

This paper aims to scrutinize the analysis of non-axisymmetric Homann stagnation point flow and heat transfer of hybrid Cu-Al2O3/water nanofluid over a stretching/shrinking flat plate.

Design/methodology/approach

The similarity transformation which fulfils the continuity equation is opted to transform the coupled momentum and energy equations into the nonlinear ordinary differential equations. Numerical solutions which are elucidated in the tables and graphs are obtained using the bvp4c solver.

Findings

Non-unique solutions (first and second) are feasible for both stretching and shrinking cases within the specific values of the parameters. First solution is the physical/real solution based on the execution of stability analysis. An upsurge of the ratio of the ambient fluid strain rate to the plate strain rate can delay the boundary layer separation, whereas a boost of the ratio of the ambient fluid shear rate to the plate strain rate only accelerates the separation of boundary layer. The heat transfer rate of hybrid nanofluid is greater for the stretching case than the shrinking case. However, for the shrinking case, the heat transfer rate intensifies with the increment of the copper (Cu) nanoparticles volume fraction, whereas a contrary result is found for the stretching case.

Originality/value

The present numerical results are original and new. It can contribute to other researchers on electing the relevant parameters to optimize the heat transfer process in the modern industry, and the right parameters to generate non-unique solution so that no misjudgment on flow and heat transfer features.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 10
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 July 2020

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

This paper aims to investigate the flow and heat transfer characteristics of a hybrid nanofluid (Cu-Al2O3/water) in the presence of magnetohydrodynamics and thermal radiation over…

Abstract

Purpose

This paper aims to investigate the flow and heat transfer characteristics of a hybrid nanofluid (Cu-Al2O3/water) in the presence of magnetohydrodynamics and thermal radiation over a permeable moving surface.

Design/methodology/approach

By choosing appropriate similarity variables, the partial differential equations are transformed into a system of linear equations which are solved by using the boundary value problem solver (bvp4c) in MATLAB. The implementation of stability analysis verifies the achievable result of the first solution which is considered stable while the second solution is unstable.

Findings

The findings revealed that the presence of a magnetic field and suction slows down the fluid motion because of the synchronism of the magnetic and electric field occurred from the formation of the Lorentz force. Also, the enhancement of the thermal radiation parameter escalates the heat transfer rate of the current study.

Originality/value

The present study is addressing the problem of MHD flow and heat transfer analysis of a hybrid nanofluid towards a permeable moving surface, with the consideration of the thermal radiation effect. The authors show that in both cases of assisting and opposing flow, there exist dual solutions within a specific range of the moving parameters. A stability analysis approved that only one of the solutions are physically relevant.

Details

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

Keywords

Article
Publication date: 26 September 2019

Rusya Iryanti Yahaya, Norihan M. Arifin, Roslinda Nazar and Ioan Pop

The purpose of this paper is to study the flow and heat transfer of a hybrid nanofluid, Cu–Al2O3/water, past a permeable stretching/shrinking sheet. The effects of Brownian motion…

Abstract

Purpose

The purpose of this paper is to study the flow and heat transfer of a hybrid nanofluid, Cu–Al2O3/water, past a permeable stretching/shrinking sheet. The effects of Brownian motion and thermophoresis are considered here.

Design/methodology/approach

Similarity transformations are used to reduce the governing partial differential equations to a system of ordinary (similarity) differential equations. A MATLAB solver called the bvp4c is then used to compute the numerical solutions of equations (12) to (14) subject to the boundary conditions of equation (15). Then, the effects of various physical parameters on the flow and thermal fields of the hybrid nanofluid are analyzed.

Findings

Multiple (dual) solutions are found for the basic boundary layer equations. A stability analysis is performed to see which solutions are stable and, therefore, applicable in practice and which are not stable. Besides that, a comparison is made between the hybrid nanofluid and a traditional nanofluid, Cu/water. The skin friction coefficient and Nusselt number of the hybrid nanofluid are found to be greater than that of the other nanofluid. Thus, the hybrid nanofluid has a higher heat transfer rate than the other nanofluid. However, the increase in the shrinking parameter reduces the velocity of the hybrid nanofluid.

Originality/value

The present results are original and new for the study of the flow and heat transfer past a permeable stretching/shrinking sheet in Cu–Al2O3/water hybrid nanofluid.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 8 August 2020

Najiyah Safwa Khashi'ie, Norihan M. Arifin, Ioan Pop, Roslinda Nazar and Ezad Hafidz Hafidzuddin

The purpose of this study is to implement a new class of similarity transformation in analyzing the three-dimensional boundary layer flow of hybrid nanofluid. The Cu-Al2O3/water…

Abstract

Purpose

The purpose of this study is to implement a new class of similarity transformation in analyzing the three-dimensional boundary layer flow of hybrid nanofluid. The Cu-Al2O3/water hybrid nanofluid is formulated using the single-phase nanofluid model with modified thermophysical properties.

Design/methodology/approach

The governing partial differential equations are reduced to the ordinary (similarity) differential equations using the proposed similarity transformation. The resulting equations are programmed in Matlab software through the bvp4c solver to obtain their solutions. The features of the reduced skin frictions and the velocity profiles for different values of the physical parameters are analyzed and discussed.

Findings

The non-uniqueness of the solutions is observed for certain physical parameters. The dual solutions are perceived for both permeable and impermeable cases and being the main agenda of the work. The execution of stability analysis proves that the first solution is undoubtedly stable than the second solution. An increase in the mass transpiration parameter leads to the uniqueness of the solution. Oppositely, as the injection parameter increase, the two solutions remain. However, no separation point is detected in this problem within the considered parameter values. The present results are decisive to the pair of alumina and copper only.

Originality/value

The present findings are original and can benefit other researchers particularly in the field of fluid dynamics. This study can provide a different insight of the transformation that is applicable to reduce the complexity of the boundary layer equations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 3
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 study…

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: 31 July 2019

Rahimah Jusoh, Roslinda Nazar and Ioan Pop

The purpose of this study is to describe the unsteady three-dimensional magnetohydrodynamic stagnation point flow of nanofluids with heat generation/absorption.

Abstract

Purpose

The purpose of this study is to describe the unsteady three-dimensional magnetohydrodynamic stagnation point flow of nanofluids with heat generation/absorption.

Design/methodology/approach

The comprehensive numerical simulations in this study accommodate a physical insight into the heat transfer and flow problem. The use of finite difference method through the bvp4c function in Matlab provides the numerical results and graphical illustrations for the heat transfer rate and shear stress.

Findings

Dual solutions are discovered in this study. Thus, stability analysis is implemented and the first solution complies the stability behavior. Silver nanoparticles dominate the highest thermal conductivity. Accretion of the rate of heat transfer is obtained with an increment in the magnitude of heat absorption, suction parameter and nanoparticle volume fraction. A stronger magnetic field and larger unsteadiness parameter contribute to the increase of the surface shear stress.

Practical implications

Many practical fluid mechanics problems involve the time-dependent element. Practically, an unsteady flow of nanofluid can be implemented in the micro-manufacturing, periodic heat exchanges process, nano drug delivery system and nuclear reactors.

Originality/value

In spite of numerous studies on the unsteady flow, none of the researchers combined the effect of heat generation/absorption and magnetic field in the nanofluid model. The behavior of the flow and heat transfer have been analyzed thoroughly with the variations in the unsteadiness parameter, heat source/sink and nanoparticle volume fraction. Moreover, the discovery of dual solutions in this model strengthens the novelty of this study. Subsequently, the implementation of stability analysis leads to a remarkable revelation where the first solution is found to be stable.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 8 June 2012

Leony Tham, Roslinda Nazar and Ioan Pop

The purpose of this paper is to study the steady mixed convection boundary layer flow of a nanofluid past a horizontal circular cylinder in a stream flowing vertically upwards for…

Abstract

Purpose

The purpose of this paper is to study the steady mixed convection boundary layer flow of a nanofluid past a horizontal circular cylinder in a stream flowing vertically upwards for both cases of a heated and cooled cylinder.

Design/methodology/approach

The resulting system of nonlinear partial differential equations is solved numerically using an implicit finite‐difference scheme known as the Keller‐box method. This method is very efficient for solving boundary layer problems.

Findings

The solutions for the flow and heat transfer characteristics are evaluated numerically for various values of the parameters, namely the nanoparticle volume fraction φ and the mixed convection parameter λ at Prandtl number Pr=1 and 6.2. Three different types of nanoparticles considered are Cu, Al2O3 and TiO2 by using water‐based fluid with Pr=6.2. It is found that for each particular nanoparticle, as the nanoparticle volume fraction φ increases, the skin friction coefficient and heat transfer rate at the surface also increase, and it also leads to the increment of the value of mixed convection parameter λ which first gives no separation.

Research limitations/implications

The results of this paper are valid only up to the value of λ=λ0 (<0) below which a boundary layer solution does not exist.

Practical implications

The results obtained can be used to explain the characteristics and applications of nanofluids, which are widely used as coolants, lubricants, heat exchangers and micro‐channel heat sinks. Nanofluids usually contain the nanoparticles such as metals, oxides, or carbon nanotubes, whereby these nanoparticles have unique chemical and physical properties.

Originality/value

The results of this paper are important for the researchers working in the area of nanofluids. The paper is well prepared and presented. The results are original, new and important from both theoretical and application point of views.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 22 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 February 2003

Roslinda Nazar, Norsarahaida Amin and Ioan Pop

The laminar mixed convection boundary‐layer flow of a micropolar fluid past a horizontal circular cylinder in a stream flowing vertically upwards has been studied in both cases of…

1185

Abstract

The laminar mixed convection boundary‐layer flow of a micropolar fluid past a horizontal circular cylinder in a stream flowing vertically upwards has been studied in both cases of a heated and cooled cylinder. The solutions for the flow and heat transfer characteristics are evaluated numerically for different parameters, such as the mixed convection parameter λ, the material parameter K (vortex viscosity parameter) and the Prandtl number Pr=1 and 6.8, respectively. It is found, as for the case of a Newtonian fluid considered for Pr=1, that heating the cylinder delays separation and can, if the cylinder is warm enough, suppress it completely. Cooling the cylinder, on the other side, brings the separation point nearer to the lower stagnation point and for sufficiently cold cylinder there will not be a boundary‐layer on the cylinder. This model problem may solve industrial problems with processing of polymeric liquids, lubricants and molten plastics.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 13 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

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