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Barker, Jon; Wilks, Graham

doi:10.1007/s00033-002-8140-0

Cited by 11 publications

(2 citation statements)

References 6 publications

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“…Expanding on this foundational research, contemporary investigations have unveiled diverse aspects of laminar wall jet flows. Notable contributions include studies on free laminar jets by Magyari and Keller (2001), the interpretation of the Falkner–Skan equation as a jet by Barker and Wilks (2002), investigations into axisymmetric jets by Kalteh and Abbassi (2006) and examinations of circular jets by Turkyilmazoglu (2014). Additionally, the transition to turbulent jet flows was addressed by Jafarimoghaddam (2017), further broadening our understanding of these dynamic systems.…”

Section: Introductionmentioning

confidence: 99%

Viscous fluid flow and heat transfer past a permeable wall jet with convective boundary conditions

Aly,

Khan Usafzai,

Merkin

et al. 2024

MMMS

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PurposeThe steady laminar wall jet flow over a stretching/shrinking surface in the presence of lateral suction or injection with a convective boundary condition is considered.Design/methodology/approachThe partial differential equations for mass, momentum and energy conservation are changed to the system of ordinary differential equations through similarity solution transformations. Solutions, both numerical and asymptotic, to these similarity equations are found in some new ranges of parameters in the governing equations.FindingsThe equations are solved both asymptotically and numerically for a range of the transpiration parameter S and the flow parameter λ given in Mahros et al. (2023), thus greatly extending the range of these previous solutions. Asymptotic solutions for both large and small values of the Prandtl number σ are derived, showing good agreement with additional numerical integrations. It should be noted that in Mahros et al. (2023), only the case when σ=1 was treated. A solution for large λ when S=1 is obtained, showing a different asymptotic form to the case when S>0 in Mahros et al. (2023). Multiple solutions were seen by them for S<0 and the nature of the lower solution branch as S→0 from below is discussed. The question as to whether the lower branch solutions join as λ>0 when S<0 is resolved through obtaining an asymptotic solution λ small.Originality/valueThe accuracy of the solutions has been checked through a detailed comparison between the solutions obtained numerically and analytically, where excellent agreement has been found. This study is important for scientists working in the area of jet flows to become familiar with the flow properties and behaviour of jets.

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Section: Introductionmentioning

confidence: 99%

Viscous fluid flow and heat transfer past a permeable wall jet with convective boundary conditions

Aly,

Khan Usafzai,

Merkin

et al. 2024

MMMS

View full text Add to dashboard Cite

show abstract

“…The perturbation solution and numerical solutions for moving surface was given by Mahmood (1988). The Falkner–Skan equation, which assimilate jet-like behavior was studied by Astin and Wilks (1996, 1997) and Barker and Wilks (2002).…”

Section: Introductionmentioning

confidence: 99%

Wall laminar nanofluid jet flow and heat transfer

Usafzai

Haq²,

Aly³

2022

HFF

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Purpose This work aims to investigates exact solutions of the classical Glauert’s laminar wall jet mass and heat transfer under wall suction, wall contraction or dilation, and two thermal transport boundary conditions; prescribed constant surface temperature and prescribed constant surface flux in nanofluidic environment. Design/methodology/approach The flow system arranged in terms of partial dif- ferential equations is non-dimensionalized with suitable dimensionless transformation variables, and this new set of equations is reduced into ordinary differential equations via a set of similarity transformations, where they are treated analytically for closed form solutions. Findings Exact solutions of nanofluid flow for velocity distributions, momentum flux, wall shear stress and heat transfer boundary layers for commonly studied nanoparticles; namely copper, alumina, silver, and titanium oxide are presented. The flow behavior of alumina and titanium oxide is identical, and a similar behavior is seen for copper and silver, making two pairs of identical traits. The mathematical expressions as well as visual analysis of wall shear drag and temperature gradient which are of practical interest are analyzed. It is shown that wall stretching or shrinking, wall transpiration and velocity slip together influences the jet flow mechanism and extends the original Glauert’s jet solutions. The exact solutions for the two temperature boundary layer conditions and temperature gradients are analyzed analytically. It is found that the effect of nanopar- ticles concentration on thermal boundary layer is intense, causing temperature uplift, whereas the wall transpiration causes a decrease in thermal layers. Originality/value The analysis carried out in nanofluid environment is genuinely new and unique, as our work generalizes the Glauert’s classical regular wall jet fluid problem.

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Exact solutions for MHD and radiative wall jet hybrid nanofluid flow over a permeable surface with velocity slip and convective boundary conditions

et al. 2022

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In this research, we investigated the wall jet problem for a hybrid nanofluid with MHD, thermal radiation, velocity slip, and convective boundary conditions. After converting the governing partial differential equations into nonlinear ordinary ones, by using the proper similarity transformations, they were theoretically solved in view of the hypergeometric function. Comparing the present results with those in the literature, a very good agreement was obtained for fixed values of the included parameters. For some included parameters, regions of physical solutions were presented. By deducing the critical and terminated values of the suction/injection parameter, dual solutions for the reduced skin friction coefficient have been determined. It was found that the hybrid nanofluid temperature is efficiently heated by increasing values of the moving wall, absolute value of the Biot number, and thermal radiation parameters. However, it is cooled by enlarging values of the velocity slip and suction parameters.

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Cited by 11 publications

References 6 publications

Viscous fluid flow and heat transfer past a permeable wall jet with convective boundary conditions

Viscous fluid flow and heat transfer past a permeable wall jet with convective boundary conditions

Wall laminar nanofluid jet flow and heat transfer

Exact solutions for MHD and radiative wall jet hybrid nanofluid flow over a permeable surface with velocity slip and convective boundary conditions

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