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1 – 10 of 285Siti 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.
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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.
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The purpose of this study is to analyze numerically the steady axisymmetric rotational stagnation point flow impinging on a radially permeable stretching/shrinking sheet in a…
Abstract
Purpose
The purpose of this study is to analyze numerically the steady axisymmetric rotational stagnation point flow impinging on a radially permeable stretching/shrinking sheet in a nanofluid.
Design/methodology/approach
Similarity transformation is used to convert the system of partial differential equations into a system of ordinary (similarity) differential equations. This system is then reduced to a system of first-order differential equations and solved numerically using the bvp4c function in MATLAB software.
Findings
Dual solutions exist when the surface is stretched, as well as when the surface is shrunk. For these solutions, a stability analysis is carried out revealing that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable and therefore not physically realizable.
Originality/value
The present results are original and new for the study of fluid flow and heat transfer over a stretching/shrinking surface, as they successfully extend the problem considered by Weidman (2016) to the case of nanofluids.
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Iskandar Waini, Farah Nadzirah Jamrus, Natalia C. Roșca, Alin V. Roșca and Ioan Pop
This study aims to investigate the dual solutions for axisymmetric flow and heat transfer due to a permeable radially shrinking disk in copper oxide (CuO) and silver (Ag) hybrid…
Abstract
Purpose
This study aims to investigate the dual solutions for axisymmetric flow and heat transfer due to a permeable radially shrinking disk in copper oxide (CuO) and silver (Ag) hybrid nanofluids with radiation effect.
Design/methodology/approach
The partial differential equations that governed the problem will undergo a transformation into a set of similarity equations. Following this transformation, a numerical solution will be obtained using the boundary value problem solver, bvp4c, built in the MATLAB software. Later, analysis and discussion are conducted to specifically examine how various physical parameters affect both the flow characteristics and the thermal properties of the hybrid nanofluid.
Findings
Dual solutions are discovered to occur for the case of shrinking disk (λ < 0). Stronger suction triggers the critical values’ expansion and delays the boundary layer separation. Through stability analysis, it is determined that one of the solutions is stable, whereas the other solution exhibits instability, over time. Moreover, volume fraction upsurge enhances skin friction and heat transfer in hybrid nanofluid. The hybrid nanofluid’s heat transfer also heightened with the influence of radiation.
Originality/value
Flow over a shrinking disk has received limited research focus, in contrast to the extensively studied axisymmetric flow problem over a diverse set of geometries such as flat surfaces, curved surfaces and cylinder. Hence, this study highlights the axisymmetric flow due to a shrinking disk under radiation influence, using hybrid nanofluids containing CuO and Ag. Upon additional analysis, it is evidently shows that only one of the solutions exhibits stability, making it a physically dependable choice in practical applications. The authors are very confident that the findings of this study are novel, with several practical uses of hybrid nanofluids in modern industry.
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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.
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Alin V. Roşca, Natalia C. Roşca and Ioan Pop
The purpose of this study is to investigate the influence of the second order slip velocity on the boundary layer stagnation point flow of a nanofluid past a non-aligned…
Abstract
Purpose
The purpose of this study is to investigate the influence of the second order slip velocity on the boundary layer stagnation point flow of a nanofluid past a non-aligned stretching/shrinking sheet.
Design/methodology/approach
Proper similarity variables are used to transform the system of partial differential equations into a system of ordinary (similarity) differential equations. This system is then solved numerically using the bvp4c solver in MATLAB software. As in the papers by Kuznetsov and Nield (2010, 2013) and Fang et al. (2009), the authors considered the stretching/shrinking parameter λ, the first-order (a1, a2) and second-order (b1) slip parameters and the Lewis number Le, Nb the Brownian parameter and Nt the thermophoresis parameter fixed at Le = 10, Nb = Nt = 0.5 when the Prandtl number Pr is fixed at Pr = 1.
Findings
Dual solutions are found as the sheet is shrunk in the horizontal direction. Stability analysis shows that the first solution is physically realizable, whereas the second solution is not practicable.
Originality/value
The present results are original and new for the study of fluid flow and heat transfer over a stretching/shrinking surface, as they successfully extend the problem considered by Wang (2008) and Lok et al. (2011) to the case of nanofluids.
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Khalid Mahmood, Muhammad Sajid, Nasir Ali and Tariq Javed
An attempt is made to study magnetohydrodynamic viscous fluid impinging orthogonally toward a stagnation point on a vertical surface lubricated with power law fluid. It has been…
Abstract
Purpose
An attempt is made to study magnetohydrodynamic viscous fluid impinging orthogonally toward a stagnation point on a vertical surface lubricated with power law fluid. It has been assumed that the surface temperature varies linearly with the distance from the stagnation point. The problem is governed by system of partial differential equations for both the base fluid and the lubricant. The continuity of velocity and shear stress is assumed at the interface layer between the base fluid and the lubricant. Dimensionless variables are introduced to transform original problem into ordinary differential equations. An implicit finite-difference scheme known as the Keller-Box method is implemented to obtain the numerical solutions. The influence of various important parameters is presented in the form of graphs and tables. The limiting cases for full and no-slip conditions are deduced from the present solutions. A comparison of the present results with the existing results in the special case validates the obtained numerical solutions. The purpose of this study is to see the behaviour of flow characteristics in the presence of lubrication.
Design/methodology/approach
The authors’ problem is governed by system of partial differential equations for both the base fluid and the lubricant. Dimensionless variables are introduced to transform original problem into ordinary differential equations. The obtained ordinary differential equation along with boundary conditions are highly nonlinear and coupled. An implicit finite-difference scheme known as the Keller-Box method is implemented to obtain the numerical solutions.
Findings
Some findings of this study are that the lubricant increases the velocity of the base fluid inside the boundary layer. In the case of full slip, the effects of viscosity are suppressed by the lubricant. The temperature of the base fluid decreases by increase in lubrication on the surface. By increasing the slip on the surface, the skin friction decreases and local Nusselt number increases, but the rate of increase or decrease is less in magnitude for the case of opposing flow. The similarity solutions only exist for n = 1/2. A non-similar solution is obtained for the other values of the power-law index n.
Originality/value
The study of flow phenomenon over a lubricated surface has important applications in machinery components such as fluid bearings and mechanical seals. Coating is another major application of lubrication including the preparation of thin films, printing, painting, etc. The authors hope that the current study will provide the roadmap for the future studies in this direction.
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M. Nawaz, A Zeeshan, R Ellahi, S Abbasbandy and Saman Rashidi
The purpose of this paper is to study the Joules heating effects on stagnation point flow of Newtonian and non-Newtonian fluids over a stretching cylinder by means of genetic…
Abstract
Purpose
The purpose of this paper is to study the Joules heating effects on stagnation point flow of Newtonian and non-Newtonian fluids over a stretching cylinder by means of genetic algorithm (GA). The main emphasis is to find the analytical and numerical solutions for the said mathematical model. The work undertaken is a blend of numerical and analytical studies. Effects of active parameters such as: Hartmann number, Prandtl number, Eckert number, Nusselt number, Skin friction and dimensionless fluids parameters on the flow and heat transfer characteristics have been examined by graphs and tables. Compression is also made with the existing benchmark results.
Design/methodology/approach
Analytical solutions of non-linear coupled equations are developed by optimal homotopy analysis method (OHAM). A very effective and higher order numerical scheme hybrid GA and Nelder-Mead optimization Algorithms are used for numerical investigations.
Findings
An excellent agreement with the existing results in limiting sense is noted. It is observed that the radial velocity is an increasing function of dimensionless material parameters α 1, α 2 and β. Temperature increases by increasing the values of M, Pr, Ec and γ. Non-Newtonian parameter β has similar effects on skin friction coefficient and Nusselt number. The wall heat transfer rate is a decreasing function of A and ß whereas it increases by increasing conjugate parameter γ.
Originality/value
The problem under consideration has been widely studied by many investigators due to its importance and engineering applications. But most of the studies as the authors have documented are for Newtonian or viscous fluids. But no such analysis is available in the literature which can describe the Joules heating effects on stagnation point flow of Newtonian and non-Newtonian fluids over a stretching cylinder by means of GA.
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Mohammad Yousefi, Saeed Dinarvand, Mohammad Eftekhari Yazdi and Ioan Pop
The purpose of this paper is to investigate analytically the steady general three-dimensional stagnation-point flow of an aqueous titania-copper hybrid nanofluid past a circular…
Abstract
Purpose
The purpose of this paper is to investigate analytically the steady general three-dimensional stagnation-point flow of an aqueous titania-copper hybrid nanofluid past a circular cylinder that has a sinusoidal radius variation.
Design/methodology/approach
First, the analytic modeling of hybrid nanofluid is presented, and using appropriate similarity variables, the governing equations are transformed into nonlinear ordinary differential equations in the dimensionless stream function, which is solved by the well-known function bvp4c from MATLAB.
Findings
The current solution demonstrates good agreement with those of the previously published studies in the special cases of regular fluid and nanofluids. Graphical results are presented to investigate the influences of the titania and copper nanoparticle volume fractions and also the nodal/saddle indicative parameter on flow and heat transfer characteristics. Here, the thermal characteristics of hybrid nanofluid are found to be higher in comparison to the base fluid and fluid containing single nanoparticles. An important point to note is that the developed model can be used with great confidence to study the flow and heat transfer of hybrid nanofluids.
Originality/value
Analytic modeling of hybrid nanofluid is the important originality of present study. Hybrid nanofluids are potential fluids that offer better heat transfer performance and thermophysical properties than convectional heat transfer fluids (oil, water and ethylene glycol) and nanofluids with single nanoparticles. In this investigation, titania (TiO2, 50 nm), copper (Cu, 20 nm) and the hybrid of these two are separately dispersed into the water as the base fluid and analyzed.
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S. Sivasankaran, H. Niranjan and M. Bhuvaneswari
The purpose of this paper is to investigate the Newtonian heating and slip effect on mixed convective flow near a stagnation point in a porous medium with thermal radiation in the…
Abstract
Purpose
The purpose of this paper is to investigate the Newtonian heating and slip effect on mixed convective flow near a stagnation point in a porous medium with thermal radiation in the presence of magnetohydrodynamic (MHD), heat generation/absorption and chemical reaction.
Design/methodology/approach
The governing nonlinear coupled equations are converted into ordinary differential equations by similarity transformation. These equations are solved numerically using a Runge–Kutta–Fehlberg method with shooting technique and analytically using the homotopy analysis method (HAM).
Findings
The effects of different parameters on the fluid flow and heat transfer are investigated. It is found that the velocity and temperature profiles increase on an increase in the Biot number. The velocity and concentration profiles increase on decreasing the chemical reaction parameter.
Practical implications
This paper is helpful to the engineers and scientists in the field of thermal and manufacturing engineering.
Originality/value
The two-dimensional boundary layer flow over a vertical plate with slip and convective boundary conditions near the stagnation-point is analysed in the presence of magnetic field, radiation and heat generation/absorption. This paper is helpful to the engineers and scientists in the field of thermal and manufacturing engineering.
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