The stagnation-point flow towards a shrinking sheet with homogeneous – heterogeneous reactions effects: A stability analysis

Ismail, Nurul Syuhada; Arifin, Norihan Md; Bachok, Norfifah; Mahiddin, Norhasimah

doi:10.1063/1.4972153

Cited by 2 publications

(4 citation statements)

References 19 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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“…The suggestion of Harris et al, [8] has been used by the next researchers. Some of these papers can be seen in this regard, such as Roşca and Pop [9], Weidman et al, [10], Postelnicu and Pop [11], Ishak [12,13], and Ismail et al, [14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

“… → as  → (23)To ascertain the steady flow solution's stability, the boundary -value problem (1)-(5)[6][7][8][9][10][11][12][13][14][15][16][17] …”

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confidence: 99%

Stability Analysis of The Stagnation-Point Flow and Heat Transfer Over a Shrinking Sheet in Nanofluid in The Presence of MHD and Thermal Radiation

Ismail

Rahim

Arifin

et al. 2022

ARFMTS

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Recent developments in the field of fluid dynamics have led to a new interest in stability analysis. The numerical solution obtained from the problems of the flow at the stagnation point, as well as the heat transfer with MHD and thermal radiation effects over a shrinking sheet, is used to carry out a stability analysis. The flow of this problem is considered in nanofluids and Buongiorno's model is employed. The boundary layer equation is obtained by reducing the governing equations to an ordinary differential equation. Partial differential equations are converted to ordinary differential equations using a suitable similarity transformation. The bvp4c simulation on Matlab is then used to solve ordinary differential equations. According to the numerical data, the dual solutions occur in a specific range of α. The parameter α refers to the stretching/shrinking where shrinking (less than 0) is the main reason the dual solution exists. The stability analysis is presented graphically and in tabular form to prove that there are two solutions to the problem and only one of them is stable. As a result, our research shows that the solution is only stable in the first solution, but not in the second.

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The stagnation-point flow towards a shrinking sheet with homogeneous – heterogeneous reactions effects: A stability analysis

Cited by 2 publications

References 19 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

Stability Analysis of The Stagnation-Point Flow and Heat Transfer Over a Shrinking Sheet in Nanofluid in The Presence of MHD and Thermal Radiation

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