Hybrid (Au-TiO2) nanofluid flow over a thin needle with magnetic field and thermal radiation: dual solutions and stability analysis

2021 ◽  
Vol 26 (1) ◽  
Author(s):  
Tayyaba Nazar ◽  
M. M. Bhatti ◽  
Efstathios E. Michaelides
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Thermal Radiation ◽  
Dual Solutions ◽  
Nanofluid Flow

scholarly journals Dual Solutions and Stability Analysis of Micropolar Nanofluid Flow with Slip Effect on Stretching/Shrinking Surfaces

Energies ◽  
2019 ◽  
Vol 12 (23) ◽  
pp. 4529 ◽  
Author(s):  
Sumera Dero ◽  
Azizah Mohd Rohni ◽  
Azizan Saaban ◽  
Ilyas Khan ◽  
Asiful H. Seikh ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Angular Velocity ◽  
Thermal Radiation ◽  
Velocity Slip ◽  
Dual Solutions ◽  
Nanofluid Flow ◽  
Linear Ordinary Differential Equations ◽  
Stretching Surfaces ◽  
Slip Effects ◽  
Micropolar Nanofluid

The purpose of the present paper is to investigate the micropolar nanofluid flow on permeable stretching and shrinking surfaces with the velocity, thermal and concentration slip effects. Furthermore, the thermal radiation effect has also been considered. Boundary layer momentum, angular velocity, heat and mass transfer equations are converted to non-linear ordinary differential equations (ODEs). Then, the obtained ODEs are solved by applying the shooting method and in the results, the dual solutions are obtained in the certain ranges of pertinent parameters in both cases of shrinking and stretching surfaces. Due to the presence of the dual solutions, stability analysis is done and it was found that the first solution is stable and physically feasible. The results are also compared with previously published literature and found to be in excellent agreement. Moreover, the obtained results reveal the angular velocity increases in the first solution when the value of micropolar parameter increases. The velocity of nanofluid flow decreases in the first solution as the velocity slip parameter increases, whereas the temperature profiles increase in both solutions when thermal radiation, Brownian motion and the thermophoresis parameters are increased. Concentration profile increases by increasing N t and decreases by increasing N b .

scholarly journals Effect of Viscous Dissipation in Heat Transfer of MHD Flow of Micropolar Fluid Partial Slip Conditions: Dual Solutions and Stability Analysis

Energies ◽  
2019 ◽  
Vol 12 (24) ◽  
pp. 4617 ◽  
Author(s):  
Liaquat Ali Lund ◽  
Zurni Omar ◽  
Ilyas Khan ◽  
Seifedine Kadry ◽  
Seungmin Rho ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Viscous Dissipation ◽  
Micropolar Fluid ◽  
Fluid Velocity ◽  
Dual Solutions ◽  
Critical Values ◽  
Partial Slip ◽  
Shrinking Sheet

In this study, first-order slip effect with viscous dissipation and thermal radiation in micropolar fluid on a linear shrinking sheet is considered. Mathematical formulations of the governing equations of the problem have been derived by employing the fundamental laws of conservations which then converted into highly non-linear coupled partial differential equations (PDEs) of boundary layers. Linear transformations are employed to change PDEs into non-dimensional ordinary differential equations (ODEs). The solutions of the resultant ODEs have been obtained by using of numerical method which is presented in the form of shootlib package in MAPLE 2018. The results reveal that there is more than one solution depending upon the values of suction and material parameters. The ranges of dual solutions are S ≥ S c i , i = 0 , 1 , 2 and no solution is S < S c i where S c i is the critical values of S . Critical values have been obtained in the presence of dual solutions and the stability analysis is carried out to identify more stable solutions. Variations of numerous parameters have been also examined by giving tables and graphs. The numerical values have been obtained for the skin friction and local Nusselt number and presented graphically. Further, it is observed that the temperature and thickness of the thermal boundary layer increase when thermal radiation parameter is increased in both solutions. In addition, it is also noticed that the fluid velocity increases in the case of strong magnetic field effect in the second solution.

Stability analysis on the kerosene nanofluid flow with hybrid zinc/aluminum-oxide (ZnO-Al2O3) nanoparticles under Lorentz force

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
LiJun Zhang ◽  
Tayyaba Nazar ◽  
M.M. Bhatti ◽  
Efstathios E. Michaelides
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Aluminum Oxide ◽  
Dual Solutions ◽  
Graphical Form ◽  
Al2o3 Nanoparticles ◽  
Lower Branch ◽  
Suction Parameter ◽  
Content Type ◽  
Zinc Aluminum Oxide

Purpose The flow and heat transfer of a hybrid nanofluid composed of kerosene and ZnO-Al2O3 nanoparticles (NPs) is investigated. The flow occurs over complex surfaces with stretching and shrinking features. The base fluid is electrically conducting, and an external magnetic field is added so that the nanofluid and the electric field are in equilibrium. Irrotational flow with viscous dissipation effects is considered. Design/methodology/approach The governing equations of the system are formulated, and a similarity transformation is used to convert the system of equations into ordinary differential equations, which are solved numerically. The friction coefficient of the flow and the Nusselt number are calculated for a wide range of parameters, and the results are presented in graphical form. In addition, dual solutions of the problem were noticed to occur for a certain range of the unsteadiness parameter. A stability analysis has been performed and presented to elucidate the behavior of these dual solutions. Findings For the solution of the upper branch, the velocity and temperature profiles of the nanofluid are enhanced by increasing the magnetic field parameter M, but the same variables decrease in the solution of the lower branch. The same trend is detected for the velocity of the fluid with the suction parameter. The temperature of the nanofluid decreases in both branches of the solution by increasing the Prandtl number. Similarly, they decrease with the suction parameter. The temperature of the nanofluid slightly increases in both branches of the solution by increasing the Eckert number. With the stability analysis the authors performed, it was determined that the solution is stable in the upper branch, but unstable in the lower branch. Originality/value The kerosene nanofluid with hybrid Zinc/Aluminum-oxide is presented for the first time in the literature.

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