Boundary Layer Theory and Symmetry Analysis of a Williamson Fluid

Aksoy, Yiğit; Hayat, Tasawar; Pakdemi̇rli̇, Mehmet

doi:10.5560/zna.2012-0028

Cited by 5 publications

(5 citation statements)

References 10 publications

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“…Williamson [11] exposed this model to express pseudo-plastic physiognomies with both characteristics of minimum and maximum viscosity effects. Then rest of motivated researchers explore more heads for this non-Newtonian fluid category like Aksoy et al [12] derived first boundary layer equations subject to Williamson fluid model and offered symmetry analysis. Akbar et al [13] found numerical solution of Williamson nanofluid flow by using both fourth and fifth order RK–Fehlberg method in an irregular channel.…”

Section: Methods Detailsmentioning

confidence: 99%

Mutual effects of stratification and mixed convection on Williamson fluid flow under stagnation region towards an inclined cylindrical surface

et al. 2017

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Section: Methods Detailsmentioning

confidence: 99%

Mutual effects of stratification and mixed convection on Williamson fluid flow under stagnation region towards an inclined cylindrical surface

et al. 2017

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“…Since the initial viscosity is greater than limit viscosity for shear thinning fluids, i.e., 0 ≫ ∞ , we can disregard ∞ from above by comparison with 0 . Substituting Equation (15) into Equation ( 14…”

Section: Energy Equationsmentioning

confidence: 99%

“…Although conventional forms of similarity are used in most studies, Lie group techniques detailed in [14] may unveil further by finding out invariants, i.e., symmetries, of the equations. Applications of Lie groups on non-Newtonian fluids, especially GNF, are given in [15][16][17] for consideration of readers. We intend to conduct an analytical study on a non-Newtonian fluid flow over a flat plate in light of previous studies.…”

Section: Introductionmentioning

confidence: 99%

Carreau-Yasuda Akışkanının Sınır Tabakası Denklemleri için Benzerlik Yaklaşımı

Aksoy¹,

Sümer²,

Samra³

2021

Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi

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ÖzetThe present study considers a non-Newtonian flow over a horizontally immersed flat plate kept at a different temperature relative to the fluid. An inviscid free stream with uniform velocity induces the flow over the plate where an incompressible boundary layer viscously occurs. It is stipulated that the fluid obeys the Carreau-Yasuda constitutive equation. Analytical investigations begin with the derivation of momentum and energy equations followed by boundary layer simplifications. Scaling symmetries are subsequently calculated to define similarity variables to transform boundary layer equations into ordinary differential forms. Later, solutions of the governing equations are pursued by a numerical scheme based on finite differences. Thanks to those solutions, the effects of significant non-dimensional parameters, such as Deborah and Prandtl numbers, on both momentum and thermal boundary layers are examined throughout the figures. The Nusselt number's variation with non-dimensional numbers is also questioned for the study's heat transfer part.Bu çalışmada, akışkana göre farklı bir sıcaklıkta ve yatay olarak yerleştirilmiş düz bir plaka üzerinde Newtonyan olmayan bir akış göz önüne alınmıştır. Sıkıştırılamaz, kararlı ve düzgün hıza sahip viskoz olmayan bir serbest akım plaka üzerinde viskoz bir sınır tabakası akışına neden olmaktadır. Newtonyen olmayan akışın Carreau-Yasuda akışkan modeline uyması öngörülmüştür. Analitik yaklaşım, momentum ve enerji denklemlerinin türetilmesi ve ardından sınır tabakası basitleştirmeleri ile başlar. Denklemlerin ölçekleme simetrileri kullanılarak hesaplanan benzerlik değişkenleri vasıtası ile kısmi diferansiyel denklem formunda olan sınır tabakası denklemleri adi forma indirgenmiştir. Daha sonra, Söz konusu denklemlerin sayısal çözümleri sonlu farklar algoritmasına dayanan sayısal bir çözümleyici ile bulunmuştur. Bu çözümler sayesinde, Deborah ve Prandtl sayıları gibi önemli boyutsuz parametrelerin hem momentum hem de termal sınır tabakası kalınlıkları üzerindeki etkileri grafikler üzerinden incelenmiştir. Ayrıca Nusselt sayısının boyutsuz sayılara göre değişimi de çalışmanın ısı transferi kısmı için araştırılmıştır.

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“…[17]. The first study available in the literature dealing with the flow of a Williamson fluid and solved by employing the Lie group approach was performed by Aksoy et al [17].…”

Section: Williamson Fluid Flow Problemsmentioning

confidence: 99%

“…[17]. The first study available in the literature dealing with the flow of a Williamson fluid and solved by employing the Lie group approach was performed by Aksoy et al [17]. In [17], the boundary layer equations for a Williamson fluid are derived for the first time.…”

Section: Williamson Fluid Flow Problemsmentioning

confidence: 99%

Applications of Group Theoretical Methods to Non‐Newtonian Fluid Flow Models: Survey of Results

Aziz

Mahomed

2017

Mathematical Problems in Engineering

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The present review is intended to encompass the applications of symmetry based approaches for solving non-Newtonian fluid flow problems in various physical situations. Works which deal with the fundamental science of non-Newtonian fluids that are analyzed using the Lie group method and conditional symmetries are reviewed. We provide the mathematical modelling, the symmetries deduced, and the solutions obtained for all the models considered. This survey includes, as far as possible, all the articles published until 2015. Only papers published by a process of peer review in archival journals are reviewed and are grouped together according to the specific non-Newtonian models under investigation.

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Boundary Layer Theory and Symmetry Analysis of a Williamson Fluid

Cited by 5 publications

References 10 publications

Mutual effects of stratification and mixed convection on Williamson fluid flow under stagnation region towards an inclined cylindrical surface

Mutual effects of stratification and mixed convection on Williamson fluid flow under stagnation region towards an inclined cylindrical surface

Carreau-Yasuda Akışkanının Sınır Tabakası Denklemleri için Benzerlik Yaklaşımı

Applications of Group Theoretical Methods to Non‐Newtonian Fluid Flow Models: Survey of Results

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