Stefan Blowing and Slip Effects on Unsteady Nanofluid Transport Past a Shrinking Sheet: Multiple Solutions

Dero, Sumera; Uddin, Md. Jashim; Rohni, Azizah Mohd

doi:10.1002/htj.21470

Cited by 31 publications

(26 citation statements)

References 30 publications

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“…In order to perform a temporal analysis of the solutions' stability, introducing a new dimensionless time-dependent similarity transformation variable is required, as recommended by Merkin [32], Dero et al [33,34], and Lund et al [35][36][37]. Letting τ = ct (1−εt) yields the following new similarity transformation variables:…”

Section: Stability Analysismentioning

confidence: 99%

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

et al. 2020

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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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Section: Stability Analysismentioning

confidence: 99%

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

et al. 2020

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“…Nanofluid with the effect of Soret and Dufour was investigated and noticed a dual solution without performing the analysis of the stability of the solutions [34]. Dero et al [35] studied the unsteady flow of nanofluid on stretching/shrinking surface by considering various slip effects. Zaib et al [36] used a single-phase nanofluids model for micropolar fluid and found dual solutions.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis and Dual Solutions of Micropolar Nanofluid over the Inclined Stretching/Shrinking Surface with Convective Boundary Condition

et al. 2020

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The present study accentuates the heat transfer characteristics of a convective condition of micropolar nanofluid on a permeable shrinking/stretching inclined surface. Brownian and thermophoresis effects are also involved to incorporate energy and concentration equations. Moreover, linear similarity transformation has been used to transform the system of governing partial differential equations (PDEs) into a set of nonlinear ordinary differential equations (ODEs). The numerical comparison has been done with the previously published results and found in good agreement graphically and tabular form by using the shooting method in MAPLE software. Dual solutions have been found in the specific range of shrinking/stretching surface parameters and the mass suction parameter for the opposing flow case. Moreover, the skin friction coefficient, the heat transfer coefficient, the couple stress coefficient, and the concentration transfer rate decelerate in both solutions against the mass suction parameter for the augmentation of the micropolar parameter respectively. The first (second) solution is the stable (unstable) solution and can (not) be considered as a real solution as the values of the smallest eigenvalues are positive (negative).

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“…Crane 1 studied the stretching sheet flow problem for the first time and found analytical solutions to the Navier–Stokes equations. Then, many other researchers 2–5 worked on the stretching sheet with different physical features. However, Miklavcic and Wang 6 for the first time discussed flow on shrinking sheet while studying the liquid films flow on the unsteady stretching surface.…”

Section: Introductionmentioning

confidence: 99%

Effects of the viscous dissipation and chemical reaction on Casson nanofluid flow over the permeable stretching/shrinking sheet

2020

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A steady two-dimensional Casson nanofluid flow over the permeable stretching/shrinking sheet along the viscous dissipation and the chemical reaction is studied in this article. The convective boundary condition is incorporated in energy equation. Similarity variables are applied to convert the governing partial differential equations into ordinary differential equations. The numerical solutions of the equations are obtained by using the shooting method with Maple implementation. The numerical findings indicate occurrence of the dual solutions for a certain range of stretching/ shrinking and suction parameters. Therefore, a stability analysis is done to find the solution that is stable and physically realizable. The effects of the pertinent physical parameters on velocity, temperature, and concentration profiles are investigated graphically. Numerical results of various parameters involved for skin friction coefficient, the local Nusselt as well as Sherwood numbers are determined and also discussed in detail. The Casson and suction parameters decrease the velocity in the first solution, whereas they increase it in the second solution. The rate of heat transfer increases in both solutions with an increment in Eckert number, Biot number, thermophoresis, and Brownian motion parameters. Thermophoresis and Brownian motion parameters show opposite behavior in the nanoparticle's concentration. The nanoparticle concentration decreases in both solutions with increment in Schmidt number, Brownian motion, and chemical reaction parameters. K E Y W O R D S Casson nanofluid, chemical reaction, convective boundary conditions, viscous dissipation 1 | INTRODUCTIONThe boundary layer flow of the incompressible fluids on the stretching and shrinking sheets has attracted much attention from the researchers, as it has many applications in industrial and the engineering processes, such as polymer extrusions, cooling of electronic devices through fans, nuclear reactors, wire drawing, shrinking swell behaviors, capillary effects in the small pores, and shrinking film. The main aim of selecting different sheets is to produce a better quality sheet that generally depends on the rate of cooling. As opposed to the stretching sheet, in shrinking case, the flow on the boundary is observed toward a fixed point. The importance of the fluid flows in the fluid mechanics have inspired many researchers to study all types of fluids from different physical point of views over various types of surfaces. Crane 1 studied the stretching sheet flow problem for the first time and found analytical solutions to the Navier-Stokes equations. Then, many other researchers 2-5 worked on the stretching sheet with different physical features. However, Miklavcic and Wang 6 for the first time discussed flow on shrinking sheet while studying the liquid films flow on the unsteady stretching surface. Fang 7 analyzed the boundary layer flow on the shrinking sheet through the power law velocity. Later, Wang 8 mentioned that at large shrinking rates, there exists nonexistenc...

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Stefan Blowing and Slip Effects on Unsteady Nanofluid Transport Past a Shrinking Sheet: Multiple Solutions

Cited by 31 publications

References 30 publications

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

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

Stability Analysis and Dual Solutions of Micropolar Nanofluid over the Inclined Stretching/Shrinking Surface with Convective Boundary Condition

Effects of the viscous dissipation and chemical reaction on Casson nanofluid flow over the permeable stretching/shrinking sheet

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