Stability analysis of Cu–H2O nanofluid over a curved stretching–shrinking sheet: existence of dual solutions

2019 ◽  
Vol 97 (8) ◽  
pp. 911-922 ◽  
Author(s):  
Usama ◽  
S. Nadeem ◽  
A.U. Khan
Keyword(s):  
Stability Analysis ◽  
Volume Fraction ◽  
Reverse Flow ◽  
Velocity Slip ◽  
Coupled System ◽  
Dual Solutions ◽  
Shrinking Sheet ◽  
Flow Situation ◽  
The Stability ◽  
Parameter Values

The effect of mass suction with temperature jump and velocity slip of viscous, unsteady nanofluid flow past a curved shrinking–stretching surface is analyzed in this work. Copper (Cu) and water are considered nanoparticles and base fluids, respectively. The complicated coupled system of differential equations is converted into non-dimensional form with some suitable similarity variables. The solution of the nonlinear problem is produced by use of numerical scheme available in the form of bvp4c package in MATLAB. In the case of shrinking towards the surface, a reverse flow situation is also developed and requires careful selection of solution by examining the stability of the solution. Detailed stability analysis is done and critical values are determined for the possible existence of dual solutions. Variation in parameters is analyzed by plotting graphs and tables. The numerical values are also calculated for the reduced Nusselt number and skin friction due to variation in values of different flow parameters. Results have shown that for the curved shrinking surfaces, one should expect multiple solutions for a set of parameter values such as mass suction, curvature, nanoparticles volume fraction, and unsteadiness.

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.

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

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 276 ◽  
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.

scholarly journals Dual Solutions of Casson nanofluid flow due to an Exponentially porous Stretching Surface with a Second-order Slip: Stability Analysis

2021 ◽  
Author(s):  
Debasish Dey ◽  
RUPJYOTI BORAH
Keyword(s):  
Stability Analysis ◽  
Velocity Slip ◽  
Casson Fluid ◽  
Second Order ◽  
Dual Solutions ◽  
Stretching Surface ◽  
Casson Nanofluid ◽  
Flow Parameters ◽  
Model Equations ◽  
The Stability

An analysis has been done to scrutinize the existence of dual solutions of the Casson nanofluid caused due to an exponential form of stretching surface which is situated in porous medium and second order velocity slip. An uniform magnetic field is considered in the transverse dirction of the flow. A suitable similarity transformation is employed to amend the model equations into solvable form and hence solved by adopting the MATLAB built-in bvp4c solver scheme. Results are discussed through both graphical mode and tabulations with respect to some novel flow parameters. The stability analysis has been studied and found two solutions, one is stable in nature and physically tractable. From the study, we have seen that the flow parameters associated with nanofluid enhance the heat transfer of the fluid. The Casson fluid parameter has also a power to increase temperature of the system.

Simulation of time-dependent radiative heat motion over a stretching/shrinking sheet of hybrid Nanofluid: Stability analysis for dual solutions

2022 ◽  
pp. 239779142110690
Author(s):  
Seema Tinker ◽  
SR Mishra ◽  
PK Pattnaik ◽  
Ram Prakash Sharma
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Dual Solutions ◽  
The Other ◽  
Time Dependent ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Heat Transfer Characteristics ◽  
Suction Parameter ◽  
Transfer Characteristics

The heat transfer characteristics for the flow of a time-dependent hybrid nanofluid with thermal radiation and source/sink over a stretching/shrinking sheet are examined in the current investigation. We have transformed the governing equations of the presented study into the similarity equations utilizing similarity variables. However, a numerical solution is obtained by using in-build MATLAB code bvp5c. The mass and energy profiles for diverse values of thermophysical parameters are studied together with their physical quantities. It is observed that dual solutions exist, that is, one is upper, and the other is lower branch solution for a definite choice of the unsteadiness parameter. Also, stability analysis is executed to determine the long-term stability of dual solutions, indicating that out of the two, only one is stable and the other is unstable. It is revealed that comparatively, the first solution shows stability, while the second solution shows instability. There is a considerable influence of second-order slip on the problem’s respective flow and heat transfer characteristics. Further, major outcomes also show the dimensionless frictional stress and the magnitude of conventional heat transfer enhancement with growing suction parameter values.

scholarly journals Effect of Velocity Slip Boundary Condition on the Flow and Heat Transfer of Cu-Water and TiO2-Water Nanofluids in the Presence of a Magnetic Field

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Abdelhalim Ebaid ◽  
Fahd Al Mutairi ◽  
S. M. Khaled
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Fluid Velocity ◽  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Dual Solutions ◽  
Slip Condition ◽  
Shrinking Sheet ◽  
Physical Parameters ◽  
Flow And Heat Transfer

In nanofluid mechanics, it has been proven recently that the no slip condition at the boundary is no longer valid which is the reason that we consider the effect of such slip condition on the flow and heat transfer of two types of nanofluids. The present paper considers the effect of the velocity slip condition on the flow and heat transfer of the Cu-water and the TiO2-water nanofluids over stretching/shrinking sheets in the presence of a magnetic field. The exact expression for the fluid velocity is obtained in terms of the exponential function, while an effective analytical procedure is suggested and successfully applied to obtain the exact temperature in terms of the generalized incomplete gamma function. It is found in this paper that the Cu-water nanofluid is slower than the TiO2-water nanofluid for both cases of the stretching/shrinking sheets. However, the temperature of the Cu-water nanofluid is always higher than the temperature of the TiO2-water nanofluid. In the case of shrinking sheet the dual solutions have been obtained at particular values of the physical parameters. In addition, the effect of various physical parameters on such dual solutions is discussed through the graphs.

Effects of Second-Order Slip and Magnetic Field on Mixed Convection Stagnation-Point Flow of a Maxwellian Fluid: Multiple Solutions

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
M. M. Rahman
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Reverse Flow ◽  
Second Order ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Variable Surface

In this paper, we investigate the effects of second-order slip and magnetic field on the nonlinear mixed convection stagnation-point flow toward a vertical permeable stretching/shrinking sheet in an upper convected Maxwell (UCM) fluid with variable surface temperature. Numerical results are obtained using the bvp4c function from matlab for the reduced skin-friction coefficient, the rate of heat transfer, the velocity, and the temperature profiles. The results indicate that multiple (dual) solutions exist for a buoyancy opposing flow for certain values of the parameter space irrespective to the types of surfaces whether it is stretched or shrinked. It is found that an applied magnetic field compensates the suction velocity for the existence of the dual solutions. Depending on the parametric conditions; elastic parameter, magnetic field parameter, first- and second-order slip parameters significantly controls the flow and heat transfer characteristics. The illustrated streamlines show that for upper branch solutions, the effects of stretching and suction are direct and obvious as the flow near the surface is seen to suck through the permeable sheet and drag away from the origin of the sheet. However, aligned but reverse flow occurs for the case of lower branch solutions when the mixed convection effect is less significant.

Nonlinear Effects on Coexistence Phenomenon in Parametric Excitation

2002 ◽  
Author(s):  
Leslie Ng ◽  
Richard Rand
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Stability Analysis ◽  
Linear Stability Analysis ◽  
Perturbation Methods ◽  
Nonlinear Effects ◽  
Free Vibrations ◽  
The Stability ◽  
Parameter Values ◽  
Two Degree Of Freedom

We investigate the effect of nonlinearites on a parametrically excited ordinary differential equation whose linearization exhibits the phenomena of coexistence. The differential equation studied governs the stability mode of vibration in an unforced conservative two degree of freedom system used to model the free vibrations of a thin elastica. Using perturbation methods, we show that at parameter values corresponding to coexistence, nonlinear terms can cause the origin to become nonlinearly unstable, even though linear stability analysis predicts the origin to be stable. We also investigate the bifurcations associated with this instability.

Unsteady forced bioconvection slip flow of a micropolar nanofluid from a stretching/shrinking sheet

2016 ◽  
Vol 230 (4) ◽  
pp. 177-187 ◽  
Author(s):  
Nur Amalina Abdul Latiff ◽  
Md Jashim Uddin ◽  
O Anwar Bég ◽  
Ahmad Izani Ismail
Keyword(s):  
Skin Friction ◽  
Microbial Fuel Cells ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Slip Flow ◽  
Velocity Slip ◽  
Shrinking Sheet ◽  
Local Skin ◽  
Linear Ordinary Differential Equations ◽  
Micropolar Nanofluid

The unsteady forced bioconvection boundary layer flow of a viscous incompressible micropolar nanofluid containing microorganisms over a stretching/shrinking sheet is studied numerically. A mathematical model, with the aid of appropriate transformations, is presented. The transformed non-linear ordinary differential equations are solved numerically by the Runge–Kutta–Fehlberg fourth- to fifth-order numerical method. The effect of the governing parameters on the dimensionless velocity, micro-rotation, temperature, nanoparticle volume fraction and microorganism as well as the local skin friction coefficient, the heat transfer rate and microorganisms transfer rate is thoroughly examined. The findings show that the value of skin friction and Nusselt number are decreased and microorganism number is increased as velocity slip, thermal slip and microorganism slip parameter are increased, respectively. Results from this investigation were compared with previous investigations demonstrating very good correlation. The present results are relevant to improving the performance of microbial fuel cells deploying nanofluids.

Sign in / Sign up

Export Citation Format

Share Document