Radiative hybrid nanofluid flow past a rotating permeable stretching/shrinking sheet

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nur Syazana Anuar ◽  
Norfifah Bachok ◽  
Ioan Pop
Keyword(s):  
Nusselt Number ◽  
Stability Analysis ◽  
Differential Equations ◽  
Skin Friction ◽  
Local Nusselt Number ◽  
Current Work ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Local Skin ◽  
Content Type

Purpose This paper aims to discuss a stability analysis on Cu-Al2O3/water nanofluid having a radiation and suction impacts over a rotating stretching/shrinking sheet. Design/methodology/approach The partial differential equations are converted into nonlinear ordinary differential equations using similarity transformation and then being solved numerically using built in function in Matlab software (bvp4c). The effects of pertinent parameters on the temperature and velocity profiles together with local Nusselt number and skin friction are reported. Findings Compared to previously published studies, the current work is noticed to be in good deal. The analysis further shows that the non-unique solutions exist for certain shrinking parameter values. Hence, a stability analysis is executed using a linear temporal stability analysis and concluded that the second solution is unstable, while the first solution is stable. The effect of suction parameter is observed to be significant in obtaining the solutions. The improvement of the local skin friction and the decrease of the local Nusselt number on the shrinking surface are observed with the increment of the copper nanoparticle volume fractions. Originality/value The originality of current work is the numerical solutions and stability analysis of hybrid nanofluid in rotating flow. This work has also resulted in producing the non-unique solutions for the shrinking sheet, and a stability analysis has also been executed for this flow showing that the second solution is unstable, while the first solution is stable. This paper is therefore valuable for engineers and scientist to get acquainted with the properties of the flow, its behavior and the way to predict it. The authors admit that all the findings are original and were not published anywhere else.

Hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface

2019 ◽  
Vol 29 (9) ◽  
pp. 3110-3127 ◽  
Author(s):  
Iskandar Waini ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Local Nusselt Number ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Shrinking Surface

PurposeThis paper aims to investigate the steady flow and heat transfer of a Cu-Al2O3/water hybrid nanofluid over a nonlinear permeable stretching/shrinking surface with radiation effects. The surface velocity condition is assumed to be of the power-law form with an exponent of 1/3. The governing equations of the problem are converted into a system of similarity equations by using a similarity transformation.Design/methodology/approachThe problem is solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The results of the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are presented through graphs and tables for several values of the parameters. The effects of these parameters on the flow and heat transfer characteristics are examined and discussed.FindingsResults found that dual solutions exist for a certain range of the stretching/shrinking and suction parameters. The increment of the skin friction coefficient and reduction of the local Nusselt number on the shrinking sheet is observed with the increasing of copper (Cu) nanoparticle volume fractions for the upper branch. The skin friction coefficient and the local Nusselt number increase when suction parameter is increased for the upper branch. Meanwhile, the temperature increases in the presence of the radiation parameter for both branches.Originality/valueThe problem of Cu-Al2O3/water hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface with radiation effects is the important originality of the present study where the dual solutions for the flow reversals are obtained.

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 Magnetohydrodynamic Hybrid Nanofluid Flow Past an Exponentially Stretching Sheet with Slip Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3291
Author(s):  
Abdul Samad Khan ◽  
He-Yong Xu ◽  
Waris Khan
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Skin Friction ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Slip Parameter ◽  
Nanofluid Flow ◽  
Slip Conditions ◽  
Exponentially Stretching ◽  
The Impact

This study presents the magnetized hybrid nanofluid flow with heat source/sink over an exponentially stretching/shrinking sheet. Slip conditions are implemented to analyze the hybrid nanofluid flow for both slip and no-slip conditions. Additionally, the hybrid nanofluid of alumina and copper (hybrid nanoparticles) with blood (base fluid) has been considered and discussed with both suction and injection parameters. The appropriate similarity variables are used to convert partial differential equations (PDEs) into ordinary differential equations (ODEs) and solved analytically with the help of the homotopy analysis method (HAM). The impact of different embedded parameters has been shown in the form of graphs and tables. The numerical values of skin friction and Nusselt number are presented in the form of Tables for both slip and no-slip cases. It is summarized that the upsurge of the velocity slip parameter and magnetic parameter increases the skin friction, while the rising of the thermal slip parameter and heat generation parameter decreases the Nusselt number.

scholarly journals Stability Analysis on Magnetohydrodynamic Flow of Casson Fluid over a Shrinking Sheet with Homogeneous-Heterogeneous Reactions

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 652 ◽  
Author(s):  
Rusya Yahaya ◽  
Norihan Md Arifin ◽  
Siti Mohamed Isa
Keyword(s):  
Stability Analysis ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Skin Friction ◽  
Fluid Velocity ◽  
Casson Fluid ◽  
Skin Friction Coefficient ◽  
Heterogeneous Reactions ◽  
Shrinking Sheet ◽  
Local Skin

Two-dimensional magnetohydrodynamic (MHD) stagnation point flow of incompressible Casson fluid over a shrinking sheet is studied. In the present study, homogeneous-heterogeneous reactions, suction and slip effects are considered. Similarity variables are introduced to transform the governing partial differential equations into non-linear ordinary differential equations. The transformed equations and boundary conditions are then solved using the bvp4c solver in MATLAB. The local skin friction coefficient is tabulated for different values of suction and shrinking parameters. The profiles for fluid velocity and concentration for various parameters are illustrated. It was found that two solutions were obtained at certain ranges of parameters. Then, the bvp4c solver was used to perform stability analysis on the dual solutions. Based on the results, the first solution was more stable and physically meaningful than the other solution. The skin friction coefficient increased when suction increased, but decreased when the magnitude of shrinking parameter increased. Meanwhile, the velocity and concentration profile increased in the presence of a magnetic field. It is also noted that the higher the strength of the homogeneous-heterogeneous reactions, the lower the concentration of reactants.

Analysis of Hiemenz flow of Reiner-Rivlin fluid over a stretching/shrinking sheet

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Golam Mortuja Sarkar ◽  
Suman Sarkar ◽  
Bikash Sahoo
Keyword(s):  
Nusselt Number ◽  
Stability Analysis ◽  
Friction Coefficient ◽  
Skin Friction Coefficient ◽  
Dual Solutions ◽  
Shrinking Sheet ◽  
Content Type ◽  
Hiemenz Flow ◽  
Self Similar ◽  
The Stability

Purpose This paper aims to theoretically and numerically investigate the steady two-dimensional (2D) Hiemenz flow with heat transfer of Reiner-Rivlin fluid over a linearly stretching/shrinking sheet. Design/methodology/approach The Navier–Stokes equations are transformed into self-similar equations using appropriate similarity transformations and then solved numerically by using shooting technique. A simple but effective mathematical analysis has been used to prove the existence of a solution for stretching case (λ> 0). Moreover, an attempt has been laid to carry the asymptotic solution behavior for large stretching. The obtained asymptotic solutions are compared with direct numerical solutions, and the comparison is quite remarkable. Findings It is observed that the self-similar equations exhibit dual solutions within the range [λc, −1] of shrinking parameter λ, where λc is the turning point from where the dual solutions bifurcate. Unique solution is found for all stretching case (λ > 0). It is noticed that the effects of cross-viscous parameter L and shrinking parameter λ on velocity and thermal fields show opposite character in the dual solution branches. Thus, a linear temporal stability analysis is performed to determine the basic feasible solution. The stability analysis is based on the sign of the smallest eigenvalue, where positive or negative sign leading to a stable or unstable solution. The stability analysis reveals that the first solution is stable that describes the main flow. Increase in cross-viscous parameter L resulting in a significant increment in skin friction coefficient, local Nusselt number and dual solutions domain. Originality/value This work’s originality is to examine the combined effects of cross-viscous parameter and stretching/shrinking parameter on skin friction coefficient, local Nusselt number, velocity and temperature profiles of Hiemenz flow over a stretching/shrinking sheet. Although many studies on viscous fluid and nanofluid have been investigated in this field, there are still limited discoveries on non-Newtonian fluids. The obtained results can be used as a benchmark for future studies of higher-grade non-Newtonian flows with several physical aspects. All the generated results are claimed to be novel and have not been published elsewhere.

Duality and stability of MHD Darcy–Forchheimer porous medium flow of rotating nanofluid on a linear shrinking/stretching sheet: Buongiorno model

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Jawad Raza ◽  
Sumera Dero ◽  
Liaquat Ali Lund ◽  
Zurni Omar
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Differential Equations ◽  
Shrinking Sheet ◽  
Dual Nature ◽  
Content Type ◽  
Great Achievement ◽  
Medium Flow ◽  
Buongiorno Model ◽  
Porous Medium Flow

Purpose The purpose of study is to examine the dual nature of the branches for the problem of Darcy–Forchheimer porous medium flow of rotating nanofluid on a linearly stretching/shrinking surface under the field of magnetic influence. The dual nature of the branches confronts the uniqueness and existence theorem, moreover, mathematically it is a great achievement. For engineering purposes, this study applied a linear stability test on the multiple branches to determine which solution is physically reliable (stable). Design/methodology/approach Nanofluid model has been developed with the help of Buongiorno model. The partial differential equations in space coordinates for the law of conservation of mass, momentum and energy have been transformed into ordinary differential equations by introducing the similarity variables. Two numerical techniques, namely, the shooting method in Maple software and the three-stage Lobatto IIIA method in Matlab software, have been used to find multiple branches and to accomplish stability analysis, respectively. Findings The parametric investigation has been executed to find the multiple branches and explore the effects on skin friction, Sherwood number, Nusselt number, concentration and temperature profiles. The findings exhibited the presence of dual branches only in the case of a shrinking sheet. Originality/value The originality of work is a determination of multiple branches and the performance of the stability analysis of the branches. It has also been confirmed that such a study has not yet been considered in the previous literature.

Dual similarity solutions because of mixed convective flow of a double-nanoparticles hybrid nanofluid: critical points and stability analysis

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ioan Pop ◽  
Mohammadreza Nademi Rostami ◽  
Saeed Dinarvand
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Flow Regime ◽  
Magnetic Parameter ◽  
Volume Fraction ◽  
Similarity Solutions ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Buoyancy Parameter ◽  
Mixed Convective Flow

Purpose The purpose of this article is to study the steady laminar magnetohydrodynamics mixed convection stagnation-point flow of an alumina-graphene/water hybrid nanofluid with spherical nanoparticles over a vertical permeable plate with focus on dual similarity solutions. Design/methodology/approach The single-phase hybrid nanofluid modeling is based on nanoparticles and base fluid masses instead of volume fraction of first and second nanoparticles as inputs. After substituting pertinent similarity variables into the basic partial differential equations governing on the problem, the authors obtain a complicated system of nondimensional ordinary differential equations, which has non-unique solution in a certain range of the buoyancy parameter. It is worth mentioning that, the stability analysis of the solutions is also presented and it is shown that always the first solutions are stable and physically realizable. Findings It is proved that the magnetic parameter and the wall permeability parameter widen the range of the buoyancy parameter for which the solution exists; however, the opposite trend is valid for second nanoparticle mass. Besides, mass suction at the surface of the plate as well as magnetic parameter leads to reduce both hydrodynamic and thermal boundary layer thicknesses. Moreover, the assisting flow regime always has higher values of similarity skin friction and Nusselt number relative to opposing flow regime. Originality/value A novel mass-based model of the hybridity in nanofluids has been used to study the foregoing problem with focus on dual similarity solutions. The results of this paper are completely original and, to the best of the authors’ knowledge, the numerical results of the present paper were never published by any researcher.

Darcy-Forchheimer porous medium effect on rotating hybrid nanofluid on a linear shrinking/stretching sheet

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Liaquat Ali Lund ◽  
Zurni Omar ◽  
Ilyas Khan
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Differential Equations ◽  
Three Dimensional ◽  
Spherical Particles ◽  
Medium Effect ◽  
Hybrid Nanofluid ◽  
Three Dimensional Flow ◽  
Content Type ◽  
Dimensional Flow

Purpose The purpose of this study is to find the multiple branches of the three-dimensional flow of Cu-Al2 O3/water rotating hybrid nanofluid perfusing a porous medium over the stretching/shrinking surface. The extended model of Darcy due to Forchheimer and Brinkman has been considered to make the hybrid nanofluid model over the pores by considering the porosity and permeability effects. Design/methodology/approach The Tiwari and Das model with the thermophysical properties of spherical particles for efficient dynamic viscosity of the nanoparticle is used. The linear similarity transformations are applied to convert the partial differential equations into ordinary differential equations (ODEs). The system of governing ODEs is solved by using the three-stage Lobatto IIIa scheme in MATLAB for evolving parameters. Findings The system of governing ODEs produces dual branches. A unique stable branch is identified with help of stability analysis. The reduced heat transfer rate has been shown to increase with the reduced ϕ2 in both branches. Further, results revealed that the presence of multiple branches depends on the ranges of porosity, suction and stretching/shrinking parameters for the particular value of the rotating parameter. Originality/value Dual branches of the three-dimensional flow of Cu-Al2 O3/water rotating hybrid nanofluid have been found. Therefore, stability analysis of the branches is also conducted to know which branch is appropriate for the practical applications. To the best of the authors’ knowledge, this research is novel and there is no previously published work relevant to the present study.

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.

scholarly journals Magnetohydrodynamic Flow and Heat Transfer Induced by a Shrinking Sheet

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1175
Author(s):  
Nor Ain Azeany Mohd Nasir ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Differential Equations ◽  
Prandtl Number ◽  
Heat Generation ◽  
Local Nusselt Number ◽  
Magnetic Parameter ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer

The magnetohydrodynamic (MHD) stagnation point flow over a shrinking or stretching flat sheet is investigated. The governing partial differential equations (PDEs) are reduced into a set of ordinary differential equations (ODEs) by a similarity transformation and are solved numerically with the help of MATLAB software. The numerical results obtained are for different values of the magnetic parameter M, heat generation parameter Q, Prandtl number Pr and reciprocal of magnetic Prandtl number ε. The influences of these parameters on the flow and heat transfer characteristics are investigated and shown in tables and graphs. Two solutions are found for a certain rate of the shrinking strength. The stability of the solutions in the long run is determined, and shows that only one of them is stable. It is found that the skin friction coefficient f ″ ( 0 ) and the local Nusselt number − θ ′ ( 0 ) decrease as the magnetic parameter M increases. Further, the local Nusselt number increases as the heat generation increases.

Sign in / Sign up

Export Citation Format

Share Document