Stability Analysis of Stagnation-Point Flow in a Nanofluid over a Stretching/Shrinking Sheet with Second-Order Slip, Soret and Dufour Effects: A Revised Model

Najib, Najwa; Bachok, Norfifah; Arifin, Norihan Md; Ali, Fadzilah Md

doi:10.3390/app8040642

Cited by 35 publications

(23 citation statements)

References 50 publications

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“…Figure 15 illustrated the smallest eigenvalue σ 1 of both solutions towards ε where σ 1 act as a determinant of the stability solutions. Positive σ 1 implies that the flow is stable whereas negative σ 1 indicates an initial growth of disturbances which resulting that the flow is unstable [55][56][57][58][59][60][61][62][63][64][65]. It is validated from Figure 15 that the first and second solutions have positive and negative σ 1 , respectively which indicates that the first solution is the real solution.…”

Section: Resultsmentioning

confidence: 88%

“…The execution of the stability analysis is mathematically performed to verify the physical or real solution among all the solutions. There has been much current literature that discussed the importance, formulation and execution of the stability analysis (see Ismail et al [55][56][57], Bakar et al [58,59], Anuar et al [60], Salleh et al [61,62], Najib et al [63], Jamaludin et al [64] and Yahaya et al [65]).…”

Section: Stability Analysismentioning

confidence: 99%

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Dual Stratified Nanofluid Flow Past a Permeable Shrinking/Stretching Sheet Using a Non-Fourier Energy Model

et al. 2019

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The present study emphasizes the combined effects of double stratification and buoyancy forces on nanofluid flow past a shrinking/stretching surface. A permeable sheet is used to give way for possible wall fluid suction while the magnetic field is imposed normal to the sheet. The governing boundary layer with non-Fourier energy equations (partial differential equations (PDEs)) are converted into a set of nonlinear ordinary differential equations (ODEs) using similarity transformations. The approximate relative error between present results (using the boundary value problem with fourth order accuracy (bvp4c) function) and previous studies in few limiting cases is sufficiently small (0% to 0.3694%). Numerical solutions are graphically displayed for several physical parameters namely suction, magnetic, thermal relaxation, thermal and solutal stratifications on the velocity, temperature and nanoparticles volume fraction profiles. The non-Fourier energy equation gives a different estimation of heat and mass transfer rates as compared to the classical energy equation. The heat transfer rate approximately elevates 5.83% to 12.13% when the thermal relaxation parameter is added for both shrinking and stretching cases. Adversely, the mass transfer rate declines within the range of 1.02% to 2.42%. It is also evident in the present work that the augmentation of suitable wall mass suction will generate dual solutions. The existence of two solutions (first and second) are noticed in all the profiles as well as the local skin friction, Nusselt number and Sherwood number graphs within the considerable range of parameters. The implementation of stability analysis asserts that the first solution is the real solution.

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Section: Resultsmentioning

confidence: 88%

Section: Stability Analysismentioning

confidence: 99%

Dual Stratified Nanofluid Flow Past a Permeable Shrinking/Stretching Sheet Using a Non-Fourier Energy Model

et al. 2019

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“…This pioneering work offered a proper way to determine the stability of every solution that may exist. Many authors have applied stability analyses in their papers when more than one solution was obtained; some examples can be found in these papers, [31][32][33][34][35][36][37][38][39][40][41], which invariably arrived at the same conclusions on the first and second solutions as Merkin [27].…”

Section: Introductionmentioning

confidence: 99%

Unsteady Stagnation-Point Flow and Heat Transfer Over a Permeable Exponential Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect: A Stability Analysis

et al. 2018

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A model of unsteady stagnation-point flow and heat transfer over a permeable exponential stretching/shrinking sheet with the presence of velocity slip is considered in this paper. The nanofluid model proposed by Tiwari and Das is applied where water with Prandtl number 6.2 has been chosen as the base fluid, while three different nanoparticles are taken into consideration, namely Copper, Alumina, and Titania. The ordinary differential equations are solved using boundary value problem with fourth order accuracy (bvp4c) program in Matlab to find the numerical solutions of the skin friction and heat transfer coefficients for different parameters such as stretching/shrinking, velocity slip, nanoparticle volume fraction, suction/injection, and also different nanoparticles, for which the obtained results (dual solutions) are presented graphically. The velocity and temperature profiles are presented to show that the far field boundary conditions are asymptotically fulfilled, and validate the findings of dual solutions as displayed in the variations of the skin friction and heat transfer coefficients. The last part is to perform the stability analysis to determine a stable and physically-realizable solution.

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“…Rosca and Pop [4], and Weidman et al [10] have shown that the lower branch solutions are unstable (not physically realizable), while the upper branch solutions are stable (physically realizable). Because of the interesting findings mentioned previously, many works on stability analysis have been performed in order to prove the findings which can be found in [28][29][30][31]. Firstly, we consider the eqs.…”

Section: Stability Solutionsmentioning

confidence: 98%

Dual solutions on boundary-layer flow over a moving surface in a flowing nanofluid with second-order slip

et al. 2020

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The steady boundary-layer flow of a nanofluid past a moving semi-infinite flat plate in a uniform free stream in the presence of second order slip is studied using a second order slip flow model. The governing PDE are transformed into non-linear ODE by using appropriate similarity transformations, which are then solved numerically using bvp4c solver for different values of selected parameters. We found that the solutions existed for dual in a certain range of velocity ratio parameter. Therefore, a stability analysis has been analyzed to show which solutions are stable. The effects of velocity ratio parameter, Lewis number, Prandtl number, Brownian motion parameter, thermopherosis parameter, mass suction, first order slip parameter, and second order slip parameter on the skin friction coefficient, heat transfer coefficient, dimensionless velocity, temperature as well as nanoparticle volume fraction profiles are figured out graphically and discussed. These results reveals that the slip parameters expand the range of the solutions obtained. The increment of slip parameters lead to decrease the skin friction coefficient while increase the heat transfer coefficient. In addition, the value of Lewis nmber, Prandtl number, Brownian motion parameter, and thermopherosis parameter are significantly affected the heat transfer coefficient. Lastly, the first solution is stable and physically relevant, while the second solution is not.

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Stability Analysis of Stagnation-Point Flow in a Nanofluid over a Stretching/Shrinking Sheet with Second-Order Slip, Soret and Dufour Effects: A Revised Model

Cited by 35 publications

References 50 publications

Dual Stratified Nanofluid Flow Past a Permeable Shrinking/Stretching Sheet Using a Non-Fourier Energy Model

Dual Stratified Nanofluid Flow Past a Permeable Shrinking/Stretching Sheet Using a Non-Fourier Energy Model

Unsteady Stagnation-Point Flow and Heat Transfer Over a Permeable Exponential Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect: A Stability Analysis

Dual solutions on boundary-layer flow over a moving surface in a flowing nanofluid with second-order slip

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