MHD flow past a nonlinear stretching/shrinking sheet in carbon nanotubes: Stability analysis

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.

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Carbon nanotubes based fluid flow past a moving thin needle examine through dual solutions: Stability analysis

Journal of Energy Storage ◽

10.1016/j.est.2021.103913 ◽

2022 ◽

Vol 48 ◽

pp. 103913

Author(s):

Muhammad Yasir ◽

Awais Ahmed ◽

Masood Khan

Keyword(s):

Carbon Nanotubes ◽

Fluid Flow ◽

Stability Analysis ◽

Dual Solutions ◽

Flow Past

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Stagnation Point Flow and Heat Transfer over an Exponentially Stretching/Shrinking Sheet in CNT with Homogeneous–Heterogeneous Reaction: Stability Analysis

Symmetry ◽

10.3390/sym11040522 ◽

2019 ◽

Vol 11 (4) ◽

pp. 522 ◽

Cited By ~ 10

Author(s):

Nur Syazana Anuar ◽

Norfifah Bachok ◽

Norihan Md Arifin ◽

Haliza Rosali

Keyword(s):

Heat Transfer ◽

Carbon Nanotubes ◽

Stability Analysis ◽

Differential Equations ◽

Skin Friction ◽

Heterogeneous Reaction ◽

Shrinking Sheet ◽

Multi Wall Carbon Nanotubes ◽

Exponentially Stretching ◽

The Impact

This study focuses on the flow of stagnation region and heat transfer of carbon nanotubes (CNTs) over an exponentially stretching/shrinked sheet in the presence of homogeneous–heterogeneous reactions. Kerosene and water are considered base fluids in both single-wall and multi-wall carbon nanotubes. After employing the appropriate similarity variables, the system of partial differential equations is transformed to a system of nonlinear ordinary differential equations. Solution of the problems is obtained numerically using the bvp4c solver in MATLAB software. The impact of physical parameters, such as solid volume fraction, stretching/shrinking parameter, homogeneous and heterogeneous reaction rate, Schmidt number on the velocity, temperature and concentration profiles, skin friction, and heat transfer rate are discussed graphically and interpreted physically. The results indicate that for an exponentially shrinking sheet, dual solutions exist for a certain range. It is clear from figures that the concentration profile increases for increasing values of heterogeneous parameter and decreasing values of homogeneous parameter. Heat transfer and skin friction were observed to have a greater impact for single-wall carbon nanotubes (SWCNTs) compared to multi-wall carbon nanotubes (MWCNTs). A stability analysis has been performed to show which solutions are linearly stable.

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Steady incompressible magnetohydrodynamics Casson boundary layer flow past a permeable vertical and exponentially shrinking sheet: A stability analysis

Heat Transfer-Asian Research ◽

10.1002/htj.21554 ◽

2019 ◽

Vol 48 (8) ◽

pp. 3538-3556 ◽

Cited By ~ 12

Author(s):

Liaquat Ali Lund ◽

Zurni Omar ◽

Ilyas Khan

Keyword(s):

Boundary Layer ◽

Stability Analysis ◽

Boundary Layer Flow ◽

Shrinking Sheet ◽

Flow Past ◽

Exponentially Shrinking Sheet ◽

Layer Flow ◽

Incompressible Magnetohydrodynamics

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Dual Solutions and Stability Analysis of a Hybrid Nanofluid over a Stretching/Shrinking Sheet Executing MHD Flow

Symmetry ◽

10.3390/sym12020276 ◽

2020 ◽

Vol 12 (2) ◽

pp. 276 ◽

Cited By ~ 11

Author(s):

Liaquat Ali Lund ◽

Zurni Omar ◽

Ilyas Khan ◽

El-Sayed M. Sherif

Keyword(s):

Stability Analysis ◽

Differential Equations ◽

Volume Fraction ◽

Solid Volume Fraction ◽

Temporal Stability ◽

Mhd Flow ◽

Numerical Results ◽

Dual Solutions ◽

Shrinking Sheet ◽

Hybrid Nanofluid

In this paper, the unsteady magnetohydrodynamic (MHD) flow of hybrid nanofluid (HNF) composed of C u − A l 2 O 3 /water in the presence of a thermal radiation effect over the stretching/shrinking sheet is investigated. Using similarity transformation, the governing partial differential equations (PDEs) are transformed into a system of ordinary differential equations (ODEs), which are then solved by using a shooting method. In order to validate the obtained numerical results, the comparison of the results with the published literature is made numerically as well as graphically and is found in good agreements. In addition, the effects of many emerging physical governing parameters on the profiles of velocity, temperature, skin friction coefficient, and heat transfer rate are demonstrated graphically and are elucidated theoretically. Based on the numerical results, dual solutions exist in a specific range of magnetic, suction, and unsteadiness parameters. It was also found that the values of f ″ ( 0 ) rise in the first solution and reduce in the second solution when the solid volume fraction ϕ C u is increased. Finally, the temporal stability analysis of the solutions is conducted, and it is concluded that only the first solution is stable.

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Magnetohydrodynamic (MHD) Flow of Micropolar Fluid with Effects of Viscous Dissipation and Joule Heating Over an Exponential Shrinking Sheet: Triple Solutions and Stability Analysis

Symmetry ◽

10.3390/sym12010142 ◽

2020 ◽

Vol 12 (1) ◽

pp. 142 ◽

Cited By ~ 6

Author(s):

Liaquat Ali Lund ◽

Zurni Omar ◽

Ilyas Khan ◽

Jawad Raza ◽

El-Sayed M. Sherif ◽

...

Keyword(s):

Stability Analysis ◽

Differential Equations ◽

Viscous Dissipation ◽

Joule Heating ◽

Micropolar Fluid ◽

Numerical Study ◽

Mhd Flow ◽

Shrinking Sheet ◽

Linear Ordinary Differential Equations ◽

All Solutions

A numerical study was carried out to examine the magnetohydrodynamic (MHD) flow of micropolar fluid on a shrinking surface in the presence of both Joule heating and viscous dissipation effects. The governing system of non-linear ordinary differential equations (ODEs) was obtained from the system of partial differential equations (PDEs) by employing exponential transformations. The resultant equations were transformed into initial value problems (IVPs) by shooting technique and then solved by the Runge–Kutta (RK) method. The effects of different parameters on velocity, angular velocity, temperature profiles, skin friction coefficient, and Nusselt number were obtained and demonstrated graphically. We observed that multiple solutions occurred in certain assortments of the parameters for suction on a surface. The stability analysis of solutions was performed, and we noted that the first solution was stable while the remaining two solutions were not. The results also showed that the velocity of the fluid increased as the non-Newtonian parameter rose in all solutions. Furthermore, it was detected that the temperature of fluid rose at higher values of the Eckert number in all solutions.

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