The competing effects of wall transpiration and stretching on Homann stagnation-point flow

Weidman, P. D.; Ma, Yi-Ping

doi:10.1016/j.euromechflu.2016.07.003

Cited by 13 publications

(11 citation statements)

References 12 publications

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“…This problem, studied by Turner and Weidman (2017), has a complicated spiral behavior in the shear stress plane at negative values of the strain rate ratio, where the thickness of the boundary layer increases as one moves along the solution branches into the spiral. Also, when α = β the surface stretches radially and the flow is everywhere axisymmetric; this is the problem studied by Weidman and Ma (2016) in which the effect of suction/blowing through the surface is included. Finally, when α = β = 0 the solution of Homann (1936) is recovered.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Mahaptra and Gupta (2003) first examined a Homann stagnation-point flow directed toward a radially stretching plate, and they also included the effect of heat transfer, while Wang (2008) considered the case of a radially shrinking plate. The effect of suction/blowing with a radially stretching plate was investigated by Weidman and Ma (2016) who found that dual solutions are possible for a shrinking plate, in the case of suction. Weidman and Turner (2017) broke the radial symmetry of the flow by considering the Homann flow with a plate stretching only along one axis.…”

Section: Introductionmentioning

confidence: 99%

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Homann stagnation-point flow impinging on a biaxially stretching surface

Turner

Weidman

2021

European Journal of Mechanics - B/Fluids

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Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Homann stagnation-point flow impinging on a biaxially stretching surface

Turner

Weidman

2021

European Journal of Mechanics - B/Fluids

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“…Another physical interest is the asymptotic solution behavior for large stretching (l >> 1) for fixed L. To do this, we first rescale the variables as (Ref. Weidman and Ma, 2016):…”

Section: Asymptotic Behaviormentioning

confidence: 99%

“…The pioneering work was first proposed by Merkin (1986). Later, Merkin’s technique was implemented by (Weidman et al , 2006; Weidman and Ma, 2016; Kamal et al , 2018; Sarkar and Sahoo, 2020a) and many others in their works.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Hiemenz flow of Reiner-Rivlin fluid over a stretching/shrinking sheet

Sarkar

Sahoo

2021

WJE

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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.

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“…studied the stagnation-point flow with various aspects, such as Azam et al (2017), Ibrahim (2017), Merkin et al (2017), Naganthran et al (2017), Othman et al (2017), Qayyum et al (2017), Rehman et al 2017), Seth et al (2017), Sharma et al (2018), Wang (2008) and Weidman and Ma (2016).…”

Section: Stability Analysis On Stagnationpoint Flowmentioning

confidence: 99%

Stability analysis on the stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet with heat source effect

Kamal

Zaimi

Ishak

et al. 2018

HFF

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Purpose This paper aims to analyze the behavior of the stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet in the presence of the viscous dissipation and heat source effects. Design/methodology/approach The governing partial differential equations are converted into ordinary differential equations by similarity transformations before being solved numerically using the bvp4c function built in Matlab software. Effects of suction/injection parameter and heat source parameter on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented in the forms of tables and graphs. A temporal stability analysis will be conducted to verify which solution is stable for the dual solutions exist for the shrinking case. Findings The analysis indicates that the skin friction coefficient and the local Nusselt number as well as the velocity and temperature were influenced by suction/injection parameter. In contrast, only the local Nusselt number, which represents heat transfer rate at the surface, was affected by heat source effect. Further, numerical results showed that dual solutions were found to exist for the certain range of shrinking case. Then, the stability analysis is performed, and it is confirmed that the first solution is linearly stable and has real physical implication, while the second solution is not. Practical implications In practice, the study of the steady two-dimensional stagnation-point flow and heat transfer past a permeable stretching/shrinking sheet in the presence of heat source effect is very crucial and useful. The problems involving fluid flow over stretching or shrinking surfaces can be found in many industrial manufacturing processes such as hot rolling, paper production and spinning of fibers. Owing to the numerous applications, the study of stretching/shrinking sheet was subsequently extended by many authors to explore various aspects of skin friction coefficient and heat transfer in a fluid. Besides that, the study of suction/injection on the boundary layer flow also has important applications in the field of aerodynamics and space science. Originality/value Although many studies on viscous fluid has been investigated, there is still limited discoveries found on the heat source and suction/injection effects. Indeed, this paper managed to obtain the second (dual) solutions and stability analysis is performed. The authors believe that all the results are original and have not been published elsewhere.

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The competing effects of wall transpiration and stretching on Homann stagnation-point flow

Cited by 13 publications

References 12 publications

Homann stagnation-point flow impinging on a biaxially stretching surface

Homann stagnation-point flow impinging on a biaxially stretching surface

Analysis of Hiemenz flow of Reiner-Rivlin fluid over a stretching/shrinking sheet

Stability analysis on the stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet with heat source effect

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