Boundary layers for the upper convected Maxwell fluid

Renardy, Michael; Wang, Xiaojun

doi:10.1016/j.jnnfm.2012.09.010

Cited by 24 publications

(15 citation statements)

References 19 publications

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“…The study indicated that velocity field is a decreasing function of Deborah number. The boundary layer flow of the upper convected Maxwell fluid was investigated by Renardy and Wang (2012). Moreover, Hayat et al (2011) studied the effects of mass transfer on the two-dimensional stagnation point flow of an upper-convected Maxwell (UCM) fluid over a stretching surface.…”

Section: Introductionmentioning

confidence: 99%

Magnetohydrodynamic(mhd) Stagnation Point Flow and Heat Transfer of Upper-Convected Maxwell Fluid Past a Stretching Sheet in the Presence of Nanoparticles With Convective Heating

Ibrahim¹

2016

Frontiers in Heat and Mass Transfer

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The study scrutinizes the effect of convective heating on magnetohydrodynamic (MHD) stagnation point flow and heat transfer of upper-convected Maxell fluid p ast a s tretching s heet i n t he p resence o f n anoparticles. T he m odel u sed i n t he s tudy i ncludes t he e ffect o f B rownian m otion and thermophoresis parameters. The non-linear governing equations and their boundary conditions are initially cast into dimensionless forms by similarity transformation. The resulting system of equations is then solved numerically using fourth order Runge-Kutta method along with shooting technique. Numerical results are obtained for velocity, temperature, concentration profiles, skin friction coefficient, local Nusselt number and Sherwood number. It is found that the skin friction coefficient, the local Nusselt number and Sherwood number increase with an increase in A and β and decreases as the values of M increase. Moreover, the local Nusselt number -θ (0) and local Sherwood number -φ (0) increases with an increase in Bi.

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Section: Introductionmentioning

confidence: 99%

Magnetohydrodynamic(mhd) Stagnation Point Flow and Heat Transfer of Upper-Convected Maxwell Fluid Past a Stretching Sheet in the Presence of Nanoparticles With Convective Heating

Ibrahim¹

2016

Frontiers in Heat and Mass Transfer

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“…High Weissenberg flows mean long relaxation time in which the velocity of fluid vanishes at the wall and particles away from the wall travel long distances within one relaxation time so that particles close to the wall travel only a short distance. This leads to boundary layer in the shear stress [19]. The viscoelastic boundary layer is formed in a thin region closer to the wall in which the relaxation terms are recovered.…”

Section: Introductionmentioning

confidence: 99%

“…Up to now the boundary layer equations for the UCM fluids in two-dimensional creeping flow along a flat boundary for high Weissenberg numbers are derived [19,20]. It was shown that scaling parameters in view of the high Weissenberg condition and taking the leading terms of the upperconvected Maxwell fluid governing equations result in the viscoelastic boundary layer development of order Wi −1 .…”

Section: Introductionmentioning

confidence: 99%

“…In some aspects, the problem of high Weissenberg number asymptotic for viscoelastic flows is similar to high Reynolds number asymptotic for Newtonian flows. The boundary layer also arises in high Weissenberg number flows since the convected derivative terms become essential at a short distance from the wall, leading to the formation of the aforementioned sharp boundary layer in the stresses [19].…”

Section: Introductionmentioning

confidence: 99%

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Similarity Solution for High Weissenberg Number Flow of Upper-Convected Maxwell Fluid on a Linearly Stretching Sheet

Mohamadali

Ashrafi

2016

Journal of Engineering

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High Weissenberg boundary layer flow of viscoelastic fluids on a stretching surface has been studied. The flow is considered to be steady, low inertial, and two-dimensional. Upon proper scaling and by means of an exact similarity transformation, the nonlinear momentum and constitutive equations of each layer transform into the respective system of highly nonlinear and coupled ordinary differential equations. Numerical solutions to the resulting boundary value problem are obtained using an efficient shooting technique in conjunction with a variable stepping method for different values of pressure gradients. It is observed that, unlike the Newtonian flows, in order to maintain a potential flow, normal stresses must inevitably develop. The velocity field and stresses distributions over plate are presented for difference values of pressure gradient and Weissenberg numbers.

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“…Abel et al [12] used similarity transformation to investigate magnetohydrodynamic flow and heat transfer in a boundary layer of UCM flow over a stretching sheet applying numerical solution. Renardy and Wang [13] studied boundary layers arising in the high Weissenberg number limit of viscoelastic UCM flows using two mechanisms for the formation of viscoelastic boundary layer.…”

Section: Introductionmentioning

confidence: 99%

Investigation of the viscoelastic flow and species diffusion in a porous channel with high permeability

Mosayebidorcheh

Vatani

Ganji

et al. 2014

Alexandria Engineering Journal

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In this study, effect of mass transfer on laminar flow of viscoelastic fluid in a porous channel with high permeability medium is investigated. The viscoelastic model used in this work is the upper convected Maxwell (UCM) model. Applying the similarity transformation, the governing partial equations are converted to ordinary differential equations. The problem is studied by a hybrid technique based on Differential Transformation Method (DTM) and iterative Newton's method (INM). Also a numerical solution is done to validate the present analytical method. The effects of active parameters such as Darcy number (Da), transpiration Reynolds number (Re T ) Deborah number (De) and Schmidt number (Sc) on the both velocity components and concentration function are discussed in this work. The results indicate that the stream function increases for large Deborah and Darcy numbers. The axial velocity is initially decreased by increasing the Deborah number but then increased while approaching the upper channel wall.ª 2014 Production and hosting by Elsevier B.V. on behalf

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Boundary layers for the upper convected Maxwell fluid

Cited by 24 publications

References 19 publications

Magnetohydrodynamic(mhd) Stagnation Point Flow and Heat Transfer of Upper-Convected Maxwell Fluid Past a Stretching Sheet in the Presence of Nanoparticles With Convective Heating

Magnetohydrodynamic(mhd) Stagnation Point Flow and Heat Transfer of Upper-Convected Maxwell Fluid Past a Stretching Sheet in the Presence of Nanoparticles With Convective Heating

Similarity Solution for High Weissenberg Number Flow of Upper-Convected Maxwell Fluid on a Linearly Stretching Sheet

Investigation of the viscoelastic flow and species diffusion in a porous channel with high permeability

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