Unsteady stagnation point flow past a permeable stretching/shrinking Riga plate in Al2O3-Cu/H2O hybrid nanofluid with thermal radiation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Riga Plate ◽  
Layer Flow

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.

Non-axisymmetric Homann stagnation point flow and heat transfer past a stretching/shrinking sheet using hybrid nanofluid

2020 ◽  
Vol 30 (10) ◽  
pp. 4583-4606 ◽  
Author(s):  
Najiyah Safwa Khashi’ie ◽  
Norihan Md Arifin ◽  
Ioan Pop ◽  
Roslinda Nazar ◽  
Ezad Hafidz Hafidzuddin ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Strain Rate ◽  
Stagnation Point ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Hybrid Nanofluid ◽  
Ambient Fluid ◽  
Content Type ◽  
Flow And Heat Transfer

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.

Off-centered stagnation point flow of an experimental-based hybrid nanofluid impinging to a spinning disk with low to high non-alignments

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Saeed Dinarvand ◽  
Alireza Mahdavi Nejad
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Thermophysical Properties ◽  
Transformation Method ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Spinning Disk

Purpose The purpose of this study is to model and solve numerically the three-dimensional off-centered stagnation point flow and heat transfer of magnesium oxide–silver/water hybrid nanofluid impinging to a spinning disk. Design/methodology/approach The applied effective thermophysical properties of hybrid nanofluid including thermal conductivity and dynamics viscosity are according to the reported experimental relations that would be expanded by a mass-based algorithm. The single phase formulations coupled with experimental-based hybrid nanofluid model is implemented to derive the governing partial differential equations which are then transferred to a set of dimensionless ordinary differential equations (ODEs) with the use of the similarity transformation method. Afterward, the reduced ODEs are solved numerically by bvp4c function from MATLAB that is a trustworthy and efficient code according to three-stage Lobatto IIIa formula. Findings The effect of spinning parameter and nanoparticles masses (mMgO, mAg) on the hydrodynamics and thermal boundary layers behavior and also the quantities of engineering interest are presented in tabular and graphical forms. The recent work demonstrates that the analysis of flow and heat transfer becomes more complicated when there is a non-alignment between the impinging flow and the disk axes. From computational results demonstrate that, the radial and azimuthal velocities are, respectively, the increasing and decreasing functions of the disk spinning parameter. Further, for the greater values of the spinning parameter, an overshoot of the radial velocity owing to the centrifugal forces of the spinning disk is observed. Besides, the quantities of engineering interest gently enhance with first and second nanoparticle masses, while comparing their absolute values illustrates the fact that the effect of second nanoparticle mass (mAg) is greater. Further, it is inferred that the second nanoparticle’s mass enhancement results in the amplification of the heat transfer; although, the high skin friction and the relevant shear stress should be controlled. Originality/value The combination of experimental thermophysical properties with theoretical modeling of the problem can be the novelty of the present work. It is evident that the experimental relations of effective thermophysical properties can be trustable and flexible in the theoretical/mathematical modeling of hybrid nanofluids flows. Besides, to the best of the authors’ knowledge, no one has ever attempted to study the present problem through a mass-based model for hybrid nanofluid.

Mixed convection and stability analysis of stagnation-point boundary layer flow and heat transfer of hybrid nanofluids over a vertical plate

2019 ◽  
Vol 30 (7) ◽  
pp. 3737-3754 ◽  
Author(s):  
Mohammad Ghalambaz ◽  
Natalia C. Roşca ◽  
Alin V. Roşca ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Stability Analysis ◽  
Mixed Convection ◽  
Boundary Layer Flow ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Hybrid Nanofluids ◽  
Layer Flow

Purpose This study aims to study the mixed convection flow and heat transfer of Al2O3-Cu/water hybrid nanofluid over a vertical plate. Governing equations for conservation of mass, momentum and energy for the hybrid nanofluid over a vertical flat plate are introduced. Design/methodology/approach The similarity transformation approach is used to transform the set of partial differential equations into a set of non-dimensional ordinary differential equations. Finite-deference with collocation method is used to integrate the governing equations for the velocity and temperature profiles. Findings The results show that dual solutions exist for the case of opposing flow over the plate. Linear stability analysis was performed to identify a stable solution. The stability analysis shows that the lower branch of the solution is always unstable, while the upper branch of the solution is always stable. The results of boundary layer analysis are reported for the various volume fractions of composite nanoparticles and mixed convection parameter. The outcomes show that the composition of nanoparticles can notably influence the boundary layer flow and heat transfer profiles. It is also found that the trend of the variation of surface skin friction and heat transfer for each of the dual solution branches can be different. The critical values of the mixed convection parameter, λ, where the dual solution branches joint together, are also under the influence of the composition of hybrid nanoparticles. For instance, assuming a total volume fraction of 5 per cent for the mixture of Al2O3 and Cu nanoparticles, the critical value of mixing parameter of λ changes from −3.1940 to −3.2561 by changing the composition of nanofluids from Al2O3 (5 per cent) + Cu (0%) to Al2O3 (2.5%) + Cu (2.5 per cent). Originality/value The mixed convection stability analysis and heat transfer study of hybrid nanofluids for a stagnation-point boundary layer flow are addressed for the first time. The introduced hybrid nanofluid model and similarity solution are new and of interest in both mathematical and physical points of view.

Unsteady stagnation-point flow and heat transfer of fractional Maxwell fluid towards a time dependent stretching plate with generalized Fourier’s law

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yu Bai ◽  
Lamei Huo ◽  
Yan Zhang
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Fractional Derivative ◽  
Stagnation Point ◽  
Maxwell Fluid ◽  
Stagnation Point Flow ◽  
Fourier’S Law ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Stretching Plate

Purpose The purpose of this study is to investigate the unsteady stagnation-point flow and heat transfer of fractional Maxwell fluid towards a time power-law-dependent stretching plate. Based on the characteristics of pressure in the boundary layer, the momentum equation with the fractional Maxwell model is firstly formulated to analyze unsteady stagnation-point flow. Furthermore, generalized Fourier’s law is considered in the energy equation and boundary condition of convective heat transfer. Design/methodology/approach The nonlinear fractional differential equations are solved by the newly developed finite difference scheme combined with L1-algorithm, whose convergence is verified by constructing a numerical example. Findings Some interesting results can be revealed. The larger fractional derivative parameter of velocity promotes the flow, while the smaller fractional derivative parameter of temperature accelerates the heat transfer. The temperature boundary layer is thicker than the velocity boundary layer, and the velocity enlarges as the stagnation parameter raises. This is because when Prandtl number < 1, the capacity of heat diffusion is greater than that of momentum diffusion. It is to be observed that all the temperature profiles first enhance a little and then reduce rapidly, which indicates the thermal retardation of Maxwell fluid. Originality/value The unsteady stagnation-point flow model of Maxwell fluid is extended from integral derivative to fractional derivative, which has more flexibility to describe viscoelastic fluid’s complex dynamic process and provide a theoretical basis for industrial processing.

Stagnation-point flow of an aqueous titania-copper hybrid nanofluid toward a wavy cylinder

2018 ◽  
Vol 28 (7) ◽  
pp. 1716-1735 ◽  
Author(s):  
Mohammad Yousefi ◽  
Saeed Dinarvand ◽  
Mohammad Eftekhari Yazdi ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Stagnation Point ◽  
Base Fluid ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Analytic Modeling ◽  
Flow And Heat Transfer ◽  
Special Cases ◽  
Hybrid Nanofluids

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.

Numerical solutions of non-alignment stagnation-point flow and heat transfer over a stretching/shrinking surface in a nanofluid

2016 ◽  
Vol 26 (6) ◽  
pp. 1747-1767 ◽  
Author(s):  
Ioan Pop ◽  
Kohi Naganthran ◽  
Roslinda Nazar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Content Type ◽  
Boundary Layer Equations ◽  
Flow And Heat Transfer ◽  
Shrinking Surface

Purpose – The purpose of this paper is to analyse numerically the steady stagnation-point flow of a viscous and incompressible fluid over continuously non-aligned stretching or shrinking surface in its own plane in a water-based nanofluid which contains three different types of nanoparticles, namely, Cu, Al2O3 and TiO2. Design/methodology/approach – Similarity transformation is used to convert the system of boundary layer equations which are in the form of partial differential equations into a system of ordinary differential equations. The system of similarity governing equations is then reduced to a system of first-order differential equations and solved numerically using the bvp4c function in Matlab software. Findings – Unique solution exists when the surface is stretched and dual solutions exist as the surface shrunk. For the dual solutions, stability analysis has revealed that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable. The effect of non-alignment is huge for the shrinking surface which is in contrast with the stretching surface. 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. This problem also applies to some situations such as materials which are manufactured by extrusion, production of glass-fibre and shrinking balloon. In this kind of circumstance, the rate of cooling and the stretching/shrinking process play an important role in moulding the final product according to preferable features. Originality/value – The present results are original and new for the study of fluid flow and heat transfer over a stretching/shrinking surface for the problem considered by Wang (2008) in a viscous fluid and extends to nanofluid by using the Tiwari and Das (2007) model.

Stability analysis on the stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet with heat source effect

2018 ◽  
Vol 28 (11) ◽  
pp. 2650-2663 ◽  
Author(s):  
Fatinnabila Kamal ◽  
Khairy Zaimi ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Heat Source ◽  
Skin Friction ◽  
Stagnation Point ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Content Type ◽  
Source Effect ◽  
Flow And Heat Transfer

PurposeThis paper aims to analyze the behavior of the stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet in the presence of the viscous dissipation and heat source effects.Design/methodology/approachThe governing partial differential equations are converted into ordinary differential equations by similarity transformations before being solved numerically using the bvp4c function built in Matlab software. Effects of suction/injection parameter and heat source parameter on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented in the forms of tables and graphs. A temporal stability analysis will be conducted to verify which solution is stable for the dual solutions exist for the shrinking case.FindingsThe analysis indicates that the skin friction coefficient and the local Nusselt number as well as the velocity and temperature were influenced by suction/injection parameter. In contrast, only the local Nusselt number, which represents heat transfer rate at the surface, was affected by heat source effect. Further, numerical results showed that dual solutions were found to exist for the certain range of shrinking case. Then, the stability analysis is performed, and it is confirmed that the first solution is linearly stable and has real physical implication, while the second solution is not.Practical implicationsIn practice, the study of the steady two-dimensional stagnation-point flow and heat transfer past a permeable stretching/shrinking sheet in the presence of heat source effect is very crucial and useful. The problems involving fluid flow over stretching or shrinking surfaces can be found in many industrial manufacturing processes such as hot rolling, paper production and spinning of fibers. Owing to the numerous applications, the study of stretching/shrinking sheet was subsequently extended by many authors to explore various aspects of skin friction coefficient and heat transfer in a fluid. Besides that, the study of suction/injection on the boundary layer flow also has important applications in the field of aerodynamics and space science.Originality/valueAlthough many studies on viscous fluid has been investigated, there is still limited discoveries found on the heat source and suction/injection effects. Indeed, this paper managed to obtain the second (dual) solutions and stability analysis is performed. The authors believe that all the results are original and have not been published elsewhere.

Unsteady Flow and Heat Transfer of a MHD Micropolar Fluid Over a Porous Stretching Sheet in the Presence of Thermal Radiation

2013 ◽  
Vol 29 (3) ◽  
pp. 559-568 ◽  
Author(s):  
G. C. Shit ◽  
R. Haldar ◽  
A. Sinha
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Boundary Layer Flow ◽  
Micropolar Fluid ◽  
Stretching Sheet ◽  
Flow And Heat Transfer ◽  
Non Linear ◽  
Layer Flow

AbstractA non-linear analysis has been made to study the unsteady hydromagnetic boundary layer flow and heat transfer of a micropolar fluid over a stretching sheet embedded in a porous medium. The effects of thermal radiation in the boundary layer flow over a stretching sheet have also been investigated. The system of governing partial differential equations in the boundary layer have reduced to a system of non-linear ordinary differential equations using a suitable similarity transformation. The resulting non-linear coupled ordinary differential equations are solved numerically by using an implicit finite difference scheme. The numerical results concern with the axial velocity, micro-rotation component and temperature profiles as well as local skin-friction coefficient and the rate of heat transfer at the sheet. The study reveals that the unsteady parameter S has an increasing effect on the flow and heat transfer characteristics.

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