Triple Solutions and Stability Analysis of Micropolar Fluid Flow on an Exponentially Shrinking Surface

Lund, Liaquat Ali; Omar, Zurni; Khan, Ilyas; Băleanu, Dumitru; Nisar, Kottakkaran Sooppy

doi:10.3390/cryst10040283

Cited by 10 publications

(9 citation statements)

References 34 publications

(51 reference statements)

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“…Meanwhile the decreasing trend of Nusselt number corresponds to the increase in values of b and β is observed, as shown in Figure 17. These observations are expected, since the fluid temperature at the surface is inversely proportional to Nusselt number, as denoted in Equation (24). As a result, the decrease in value of surface temperature leads to the increase in Nusselt number.…”

Section: Resultsmentioning

confidence: 66%

“…The unsteady state of mixed convection flow of micropolar fluid moving along an inclined stretching plate has been scrutinized by Kasim et al [12]. Furthermore, some interesting studies regarding fluid flow and heat transfer for various aspects have been investigated, as reported in [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

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Convective Transport of Fluid–Solid Interaction: A Study between Non-Newtonian Casson Model with Dust Particles

et al. 2020

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The Casson model is a fascinating model, which is genuinely recommended for use with fluids of a non-Newtonian type. The conventional model is not capable to represent the Casson model with the suspension of foreign bodies (dust particles). Due to this, the two-phase model for the mixture of Casson model fluid and dust particles is formulated. This study examines the emerging role of dust particles in changing the behavior of Casson model. In particular, two-phase flow of dusty Casson model with modified magnetic field and buoyancy effect under Newtonian heating boundary condition along a vertically stretching sheet is considered. The equations that govern under Casson model, together with dust particles, are reduced to a system of nonlinear ordinary differential equations by employing the suitable similarity variables. These transformed equations are then solved numerically by implementing the Runge–Kutta–Fehlberg (RKF45) method. The numerical results of skin friction coefficient plus Nusselt number are displayed graphically. The results revealed the fluid’s velocity tends to deteriorate due to the existence of dust particles, whilst its temperature is increased. The two-phase flow is one of the mathematical modeling techniques for multiphase flow, where the relationship between the fluid and solid is examined more closely. It is expected that the present findings can contribute to the understanding of the theory of two-phase flow mathematically, which will continue to produce significant research in this field.

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Section: Resultsmentioning

confidence: 66%

Section: Introductionmentioning

confidence: 99%

Convective Transport of Fluid–Solid Interaction: A Study between Non-Newtonian Casson Model with Dust Particles

et al. 2020

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“…According to Lund et al [29,30], Hamid et al [31], and Mustafa et al [32], the stability analysis of the dual solutions is verified by perturbing the steady solution by using following functions…”

Section: Stability Analysismentioning

confidence: 99%

Convective Effect on Magnetohydrodynamic (MHD) Stagnation Point Flow of Casson Fluid over a Vertical Exponentially Stretching/Shrinking Surface: Triple Solutions

et al. 2020

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In the current study, the characteristics of heat transfer of a steady, two-dimensional, stagnation point, and magnetohydrodynamic (MHD) flow of shear thickening Casson fluid on an exponentially vertical shrinking/stretching surface are examined in attendance of convective boundary conditions. The impact of the suction parameter is also considered. The system of governing partial differential equations (PDEs) and boundary conditions is converted into ordinary differential equations (ODEs) with the suitable exponential similarity variables of transformations and then solved using the shooting method with the fourth order Runge–Kutta method. Similarity transformation is an important class of phenomena in which scale symmetry allows one to reduce the number of independent variables of the problem. It should be noted that solutions of the ODEs show the symmetrical behavior of the PDES for the profiles of velocity and temperature. Similarity solutions are obtained for the case of stretching/shrinking and suction parameters. It is revealed that there exist two ranges of the solutions in the specific ranges of the physical parameters, three solutions depend on the opposing flow case where stagnation point (A) should be equal to 0.1, two solutions exist when λ1 = 0 where λ1 is a mixed convection parameter and A > 0.1, and a single solution exists when λ1 > 0. Moreover, the effects of numerous applied parameters on velocity, temperature distributions, skin friction, and local Nusselt number are examined and given through tables and graphs for both shrinking and stretching surfaces.

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“…The boundary layer flow of micropolar fluid over a sheet, shrinking exponentially, was then discussed by Aurangzaib et al 27 It was concluded in this study that strong suction is required for the solution to exist, and dual solutions were found at certain suction rates. However, Lund et al 28 prove that triple solutions exist in this problem. Recently, Lund et al 3 extended the study by analysing the effects of the magnetic field, viscous dissipation and Joule heating to the fluid flow.…”

Section: Introductionmentioning

confidence: 99%

Magnetohydrodynamics boundary layer flow of micropolar fluid over an exponentially shrinking sheet with thermal radiation: Triple solutions and stability analysis

Yahaya

Arifin

Isa

et al. 2021

Math Methods in App Sciences

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The flow of electrically conducting micropolar fluid past an exponentially permeable shrinking sheet in the presence of a magnetic field and thermal radiation is studied. Similarity transformations are applied to the governing partial differential equations to form ordinary differential equations. The solution for the resultant equations, subject to boundary conditions, is then computed numerically using the bvp4c solver in MATLAB. The effects of several parameters on the local skin friction coefficient, couple stress, Nusselt number, velocity, microrotation and temperature of the fluid are analysed. Because the numerical computations for this problem result in triple solutions, stability analysis is carried out to ascertain the stability and significance of these solutions. The first solution is revealed to be stable, hence more physically meaningful than the other solutions. Meanwhile, it is found that the increase in magnetic and thermal radiation parameters reduces the fluid temperature.

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Triple Solutions and Stability Analysis of Micropolar Fluid Flow on an Exponentially Shrinking Surface

Cited by 10 publications

References 34 publications

Convective Transport of Fluid–Solid Interaction: A Study between Non-Newtonian Casson Model with Dust Particles

Convective Transport of Fluid–Solid Interaction: A Study between Non-Newtonian Casson Model with Dust Particles

Convective Effect on Magnetohydrodynamic (MHD) Stagnation Point Flow of Casson Fluid over a Vertical Exponentially Stretching/Shrinking Surface: Triple Solutions

Magnetohydrodynamics boundary layer flow of micropolar fluid over an exponentially shrinking sheet with thermal radiation: Triple solutions and stability analysis

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