scholarly journals Unsteady Three-Dimensional MHD Non-Axisymmetric Homann Stagnation Point Flow of a Hybrid Nanofluid with Stability Analysis

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 784 ◽  
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Stability Analysis ◽  
Differential Equations ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Industrial Sector ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid

The hybrid nanofluid under the influence of magnetohydrodynamics (MHD) is a new interest in the industrial sector due to its applications, such as in solar water heating and scraped surface heat exchangers. Thus, the present study accentuates the analysis of an unsteady three-dimensional MHD non-axisymmetric Homann stagnation point flow of a hybrid Al2O3-Cu/H2O nanofluid with stability analysis. By employing suitable similarity transformations, the governing mathematical model in the form of the partial differential equations are simplified into a system of ordinary differential equations. The simplified mathematical model is then solved numerically by the Matlab solver bvp4c function. This solving approach was proficient in generating more than one solution when good initial guesses were provided. The numerical results presented significant influences on the rate of heat transfer and fluid flow characteristics of a hybrid nanofluid. The rate of heat transfer and the trend of the skin friction coefficient improve with the increment of the nanoparticles’ concentration and the magnetic parameter; however, they deteriorate when the unsteadiness parameter increases. In contrast, the ratio of the escalation of the ambient fluid strain rate to the plate was able to adjourn the boundary layer separation. The dual solutions (first and second solutions) are obtainable when the surface of the sheet shrunk. A stability analysis is carried out to justify the stability of the dual solutions, and hence the first solution is seen as physically reliable and stable, while the second solution is unstable.

scholarly journals Unsteady MHD Mixed Convection Flow in Hybrid Nanofluid at Three-Dimensional Stagnation Point

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 549
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Mixed Convection ◽  
Skin Friction ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Skin Friction Coefficient ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid

There has been significant interest in exploring a stagnation point flow due to its numerous potential uses in engineering applications such as cooling of nuclear reactors. Hence, this study proposed a numerical analysis on the unsteady magnetohydrodynamic (MHD) mixed convection at three-dimensional stagnation point flow in Al2O3–Cu/H2O hybrid nanofluid over a permeable sheet. The ordinary differential equations are accomplished by simplifying the governing partial differential equations through suitable similarity transformation. The numerical computation is established by the MATLAB system software using the bvp4c technique. The bvp4c procedure is excellent in providing more than one solution once sufficient predictions are visible. The influence of certain functioning parameters is inspected, and notable results exposed that the rate of heat transfer is exaggerated along with the skin friction coefficient while the suction/injection and magnetic parameters are intensified. The results also signified that the rise in the volume fraction of the nanoparticle and the decline of the unsteadiness parameter demonstrates a downward attribution towards the heat transfer performance and skin friction coefficient. Conclusively, the observations are confirmed to have multiple solutions, which eventually contribute to an investigation of the analysis of the solution stability, thereby justifying the viability of the first solution.

scholarly journals Stability Analysis of Unsteady MHD Rear Stagnation Point Flow of Hybrid Nanofluid

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2428
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Differential Equations ◽  
Stagnation Point ◽  
Heat Generation ◽  
Heat Transfer Performance ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid ◽  
Transfer Performance ◽  
Distribution Profile

Previous studies have reported that investigating the stagnation point flow is relevant in a variety of industrial and technological processes, including extrusion and the polymer industries. Hence, the present work aims to analyse the heat transfer performance of unsteady magnetohydrodynamics (MHD) in hybrid nanofluid and heat generation/absorption impact. The multivariable differential equations with partial derivatives are converted into a specific type of ordinary differential equations by using valid similarity transformations. The resulting mathematical model is clarified utilising the bvp4c function. The results of various control parameters were analysed, and it was discovered that increasing the nanoparticle concentration and magnetic field increases the coefficient of skin friction along the stretching/shrinking surface. The inclusion of the heat generation parameter displays an upward trend in the temperature distribution profile, consequently degrading the heat transfer performance. The findings are confirmed to have more than one solution, and this invariably leads to a stability analysis, which confirms the first solution’s feasibility.

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.

scholarly journals MHD stagnation-point flow and heat transfer past a stretching/shrinking sheet in a hybrid nanofluid with induced magnetic field

2019 ◽  
Vol 30 (3) ◽  
pp. 1345-1364 ◽  
Author(s):  
Mohamad Mustaqim Junoh ◽  
Fadzilah Md Ali ◽  
Norihan Md Arifin ◽  
Norfifah Bachok ◽  
Ioan Pop
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Nonlinear Partial Differential Equations ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Induced Magnetic Field ◽  
Content Type

Purpose The purpose of this paper is to investigate the steady magnetohydrodynamics (MHD) boundary layer stagnation-point flow of an incompressible, viscous and electrically conducting fluid past a stretching/shrinking sheet with the effect of induced magnetic field. Design/methodology/approach The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations via the similarity transformations before they are solved numerically using the “bvp4c” function in MATLAB. Findings It is found that there exist non-unique solutions, namely, dual solutions for a certain range of the stretching/shrinking parameters. 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 the heat transfer field such as electronic cooling, engine cooling, generator cooling, welding, nuclear system cooling, lubrication, thermal storage, solar heating, cooling and heating in buildings, biomedical, drug reduction, heat pipe, space aircrafts and ships with better efficiency than that of nanofluids applicability. The results obtained are very useful for researchers to determine which solution is physically stable, whereby, mathematically more than one solution exist. Originality/value The present results are new and original for the problem of MHD stagnation-point flow over a stretching/shrinking sheet in a hybrid nanofluid, with the effect of induced magnetic field.

scholarly journals Unsteady Stagnation Point Flow of Hybrid Nanofluid Past a Convectively Heated Stretching/Shrinking Sheet with Velocity Slip

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1649
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Skin Friction ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Velocity Slip ◽  
Slip Condition ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid

Unsteady stagnation point flow in hybrid nanofluid (Al2O3-Cu/H2O) past a convectively heated stretching/shrinking sheet is examined. Apart from the conventional surface of the no-slip condition, the velocity slip condition is considered in this study. By incorporating verified similarity transformations, the differential equations together with their partial derivatives are changed into ordinary differential equations. Throughout the MATLAB operating system, the simplified mathematical model is clarified by employing the bvp4c procedure. The above-proposed approach is capable of producing non-uniqueness solutions when adequate initial assumptions are provided. The findings revealed that the skin friction coefficient intensifies in conjunction with the local Nusselt number by adding up the nanoparticles volume fraction. The occurrence of velocity slip at the boundary reduces the coefficient of skin friction; however, an upward trend is exemplified in the rate of heat transfer. The results also signified that, unlike the parameter of velocity slip, the increment in the unsteady parameter conclusively increases the coefficient of skin friction, and an upsurge attribution in the heat transfer rate is observed resulting from the increment of Biot number. The findings are evidenced to have dual solutions, which inevitably contribute to stability analysis, hence validating the feasibility of the first solution.

scholarly journals Numerical Solution of Stagnation Point Flow and Heat Transfer over a Nonlinear Stretching/Shrinking Sheet in Hybrid Nanofluid: Stability Analysis

2020 ◽  
Vol 76 (2) ◽  
pp. 85-98
Author(s):  
Nur Syazana Anuar ◽  
Norfifah Bachok ◽  
Norihan Md Arifin ◽  
Haliza Rosali
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Pure Water ◽  
Nonlinear Parameter ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Local Skin

The steady, laminar, stagnation point flow of hybrid nanofluid past a nonlinearly stretching and shrinking sheet is studied. Hybrid nanofluid is regarded by disseminated two distinct nano-sized particles, silver (Ag) and copper oxide (CuO) in pure water. Similarity technique was used for the transformation of partial differential equations (PDEs) into an ordinary differential equations (ODEs). Obtained ODEs were solved using Matlab’s built in function (bvp4c). The results of important governing parameters which are nonlinear parameter, stretching/shrinking parameter and nanoparticle volume fraction are evaluated and discussed in graphical and tabular form for the velocity and temperature profiles, along with local skin friction, local Nusselt number. Nonunique solutions (first and second branch) are visible for some limit of shrinking parameter. It is noticed that nonlinear parameter hastens flow separations. Hence, a stability analysis is executed to identify which solutions are stable and physically feasible.

scholarly journals Stability analysis of heat transfer in nanomaterial flow of boundary layer towards a shrinking surface: Hybrid nanofluid versus nanofluid

2021 ◽  
Author(s):  
Aqeel ur Rehman ◽  
Zaheer Abbas
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Differential Equations ◽  
Stable Solution ◽  
Mhd Flow ◽  
Least Square Method ◽  
Dual Solutions ◽  
Least Square ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid

Many boundary value problems (BVPs) have dual solutions in some cases containing one stable solution (upper branch) while other unstable (lower branch). In this paper, MHD flow and heat transfer past a shrinking sheet is studied for three distinct fluids: kerosene hybrid nanofluid, kerosene nanofluid, and kerosene nanofluid. The partial differential equations (PDEs) are turned into ordinary differential equations (ODEs) using an appropriate transformation and then dual solutions are obtained analytically by employing the Least Square method (LSM). Moreover, stability analysis is implemented on the time-dependent case by calculating the least eigenvalues using Matlab routine bvp4c. It is noticed that negative eigenvalue is related to unstable solution i.e., it provides initial progress of disturbance and positive eigenvalue is related to stable solution i.e., the disturbance in solution decline initially. The impacts of various parameters, skin friction coefficient, and local Nusselt number for dual solutions are presented graphically. It is also noted that the results obtained for hybrid nanofluids are better than ordinary nanofluids.

Unsteady MHD Rear Stagnation-Point Flow of a Hybrid Nanofluid with Heat Generation/Absorption Effect

2021 ◽  
Vol 87 (1) ◽  
pp. 41-51
Author(s):  
Nurul Amira Zainal ◽  
Kohilavani Naganthran ◽  
Roslinda Nazar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Heat Generation ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid ◽  
Absorption Effect ◽  
Suction Parameter ◽  
The Impact ◽  
Rear Stagnation Point

The study of unsteady flow is essential in various engineering systems, for instance, the periodic fluid motion and start-up process. Therefore, this numerical study focuses on examining the unsteady magnetohydrodynamics (MHD) rear stagnation-point flow in Al2O3-Cu/H2O hybrid nanofluid past a permeable stretching/shrinking surface with the impact of heat generation/absorption. By choosing a suitable similarity transformation, partial differential equations are transformed into a system of nonlinear ordinary differential equations and solved using the bvp4c function in the MATLAB package. The effects of the solution domain’s operating parameters are analysed, and dual solutions are observable as the sheet shrinks. It is found that the addition of the suction parameter escalates the heat transfer efficiency. Eventually, the existence of the unsteadiness parameter and the heat generation/absorption effect significantly encourage heat transfer deterioration.

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.

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